MCAT: Chemistry and Physics practice exam

Vehicle accidents on icy roads result in significant property damage and injuries annually. National transportation statistics indicate that winter-related collisions cost millions in repairs and lost productivity. A local municipality is investigating methods to improve vehicle traction on a particularly hazardous, inclined bridge during freezing conditions. A diagram of the bridge is shown below.

One approach to reducing these accidents is to implement advanced road surface treatments that enhance tire grip.

Test vehicles, equipped with specialized winter tires, were used to assess the frictional properties of the bridge surface. The coefficients of friction between the winter tires and the icy bridge surface are as follows:

Coefficient of static friction = 0.2 Coefficient of kinetic friction = 0.1

Vehicle accidents on icy roads result in significant property damage and injuries annually. National transportation statistics indicate that winter-related collisions cost millions in repairs and lost productivity. A local municipality is investigating methods to improve vehicle traction on a particularly hazardous, inclined bridge during freezing conditions. A diagram of the bridge is shown below.

One approach to reducing these accidents is to implement advanced road surface treatments that enhance tire grip.

Test vehicles, equipped with specialized winter tires, were used to assess the frictional properties of the bridge surface. The coefficients of friction between the winter tires and the icy bridge surface are as follows:

Coefficient of static friction = 0.2 Coefficient of kinetic friction = 0.1

Vehicle accidents on icy roads result in significant property damage and injuries annually. National transportation statistics indicate that winter-related collisions cost millions in repairs and lost productivity. A local municipality is investigating methods to improve vehicle traction on a particularly hazardous, inclined bridge during freezing conditions. A diagram of the bridge is shown below.

One approach to reducing these accidents is to implement advanced road surface treatments that enhance tire grip.

Test vehicles, equipped with specialized winter tires, were used to assess the frictional properties of the bridge surface. The coefficients of friction between the winter tires and the icy bridge surface are as follows:

Coefficient of static friction = 0.2 Coefficient of kinetic friction = 0.1

Vehicle accidents on icy roads result in significant property damage and injuries annually. National transportation statistics indicate that winter-related collisions cost millions in repairs and lost productivity. A local municipality is investigating methods to improve vehicle traction on a particularly hazardous, inclined bridge during freezing conditions. A diagram of the bridge is shown below.

One approach to reducing these accidents is to implement advanced road surface treatments that enhance tire grip.

Test vehicles, equipped with specialized winter tires, were used to assess the frictional properties of the bridge surface. The coefficients of friction between the winter tires and the icy bridge surface are as follows:

Coefficient of static friction = 0.2 Coefficient of kinetic friction = 0.1

Vehicle accidents on icy roads result in significant property damage and injuries annually. National transportation statistics indicate that winter-related collisions cost millions in repairs and lost productivity. A local municipality is investigating methods to improve vehicle traction on a particularly hazardous, inclined bridge during freezing conditions. A diagram of the bridge is shown below.

One approach to reducing these accidents is to implement advanced road surface treatments that enhance tire grip.

Test vehicles, equipped with specialized winter tires, were used to assess the frictional properties of the bridge surface. The coefficients of friction between the winter tires and the icy bridge surface are as follows:

Coefficient of static friction = 0.2 Coefficient of kinetic friction = 0.1

Energy Losses on a Swinging-Ship Ride

A swinging-ship ride is a giant pendulum: a boat-shaped gondola hangs from a pivot and swings back and forth along a circular arc. Each time the gondola passes through the bottom of the arc, a motor-driven tire presses against the hull and pushes it, adding energy until the gondola reaches its operating height. Between pushes, the gondola's mechanical energy shifts back and forth between gravitational potential energy at the ends of the arc and kinetic energy at the bottom, while air resistance and friction at the pivot convert some of it into thermal energy.

Engineers tested a ride whose loaded gondola has a mass of 5,000 kg and whose center of mass hangs 16 m below the pivot. They drove the gondola until its center of mass rose 7.20 m above its lowest point at the end of each swing, then pulled the tire away and let the gondola coast. Table 1 gives the greatest height the center of mass reached at the end of each full swing that followed, where a full swing is one complete back-and-forth cycle, lasting one period. For calculations, treat the ride as a simple pendulum whose period, about 8.0 s, does not depend on the size of the swing, and use g = 10 m/s².

Table 1. Maximum height of the gondola's center of mass while coasting

Energy Losses on a Swinging-Ship Ride

A swinging-ship ride is a giant pendulum: a boat-shaped gondola hangs from a pivot and swings back and forth along a circular arc. Each time the gondola passes through the bottom of the arc, a motor-driven tire presses against the hull and pushes it, adding energy until the gondola reaches its operating height. Between pushes, the gondola's mechanical energy shifts back and forth between gravitational potential energy at the ends of the arc and kinetic energy at the bottom, while air resistance and friction at the pivot convert some of it into thermal energy.

Engineers tested a ride whose loaded gondola has a mass of 5,000 kg and whose center of mass hangs 16 m below the pivot. They drove the gondola until its center of mass rose 7.20 m above its lowest point at the end of each swing, then pulled the tire away and let the gondola coast. Table 1 gives the greatest height the center of mass reached at the end of each full swing that followed, where a full swing is one complete back-and-forth cycle, lasting one period. For calculations, treat the ride as a simple pendulum whose period, about 8.0 s, does not depend on the size of the swing, and use g = 10 m/s².

Table 1. Maximum height of the gondola's center of mass while coasting

Energy Losses on a Swinging-Ship Ride

A swinging-ship ride is a giant pendulum: a boat-shaped gondola hangs from a pivot and swings back and forth along a circular arc. Each time the gondola passes through the bottom of the arc, a motor-driven tire presses against the hull and pushes it, adding energy until the gondola reaches its operating height. Between pushes, the gondola's mechanical energy shifts back and forth between gravitational potential energy at the ends of the arc and kinetic energy at the bottom, while air resistance and friction at the pivot convert some of it into thermal energy.

Engineers tested a ride whose loaded gondola has a mass of 5,000 kg and whose center of mass hangs 16 m below the pivot. They drove the gondola until its center of mass rose 7.20 m above its lowest point at the end of each swing, then pulled the tire away and let the gondola coast. Table 1 gives the greatest height the center of mass reached at the end of each full swing that followed, where a full swing is one complete back-and-forth cycle, lasting one period. For calculations, treat the ride as a simple pendulum whose period, about 8.0 s, does not depend on the size of the swing, and use g = 10 m/s².

Table 1. Maximum height of the gondola's center of mass while coasting

Energy Losses on a Swinging-Ship Ride

A swinging-ship ride is a giant pendulum: a boat-shaped gondola hangs from a pivot and swings back and forth along a circular arc. Each time the gondola passes through the bottom of the arc, a motor-driven tire presses against the hull and pushes it, adding energy until the gondola reaches its operating height. Between pushes, the gondola's mechanical energy shifts back and forth between gravitational potential energy at the ends of the arc and kinetic energy at the bottom, while air resistance and friction at the pivot convert some of it into thermal energy.

Engineers tested a ride whose loaded gondola has a mass of 5,000 kg and whose center of mass hangs 16 m below the pivot. They drove the gondola until its center of mass rose 7.20 m above its lowest point at the end of each swing, then pulled the tire away and let the gondola coast. Table 1 gives the greatest height the center of mass reached at the end of each full swing that followed, where a full swing is one complete back-and-forth cycle, lasting one period. For calculations, treat the ride as a simple pendulum whose period, about 8.0 s, does not depend on the size of the swing, and use g = 10 m/s².

Table 1. Maximum height of the gondola's center of mass while coasting

Energy Losses on a Swinging-Ship Ride

A swinging-ship ride is a giant pendulum: a boat-shaped gondola hangs from a pivot and swings back and forth along a circular arc. Each time the gondola passes through the bottom of the arc, a motor-driven tire presses against the hull and pushes it, adding energy until the gondola reaches its operating height. Between pushes, the gondola's mechanical energy shifts back and forth between gravitational potential energy at the ends of the arc and kinetic energy at the bottom, while air resistance and friction at the pivot convert some of it into thermal energy.

Engineers tested a ride whose loaded gondola has a mass of 5,000 kg and whose center of mass hangs 16 m below the pivot. They drove the gondola until its center of mass rose 7.20 m above its lowest point at the end of each swing, then pulled the tire away and let the gondola coast. Table 1 gives the greatest height the center of mass reached at the end of each full swing that followed, where a full swing is one complete back-and-forth cycle, lasting one period. For calculations, treat the ride as a simple pendulum whose period, about 8.0 s, does not depend on the size of the swing, and use g = 10 m/s².

Table 1. Maximum height of the gondola's center of mass while coasting

Water Pressure, Lung Gas and Buoyancy in Breath-Hold Diving

Because the chest wall is flexible, the gas in a submerged person's lungs is squeezed to nearly the pressure of the surrounding water. In seawater (density 1020 kg/m³), that pressure rises by about 10 kPa for every meter of depth. Take atmospheric pressure at the surface as 100 kPa and g as 9.8 m/s².

Water pressure limits snorkeling. A snorkeler draws in air at atmospheric pressure while the water presses on her chest. In one test in seawater, a volunteer could expand her chest to inhale only when the water pressure on her chest exceeded the pressure of the inhaled air by no more than 8.0 kPa.

Water pressure also compresses a breath-hold diver's lungs. Researchers modeled a diver who inhales 6.0 L of air at the surface and then descends. The model assumes the lung gas stays at body temperature and exchanges no gas with the blood (Table 1). Together, the diver and her equipment have a mass of 78.5 kg and, not counting the lung gas, a volume of 74.0 L.

Table 1. Modeled lung gas volume during a descent in seawater

In a real dive, the blood also takes up oxygen from the lung gas. When the diver reached the bottom of a 30-m dive, oxygen made up 5.0% of her lung gas, and this fraction changed little during her rapid ascent. Divers can lose consciousness from lack of oxygen in the last few meters of an ascent, even when they felt well at the bottom.

Water Pressure, Lung Gas and Buoyancy in Breath-Hold Diving

Because the chest wall is flexible, the gas in a submerged person's lungs is squeezed to nearly the pressure of the surrounding water. In seawater (density 1020 kg/m³), that pressure rises by about 10 kPa for every meter of depth. Take atmospheric pressure at the surface as 100 kPa and g as 9.8 m/s².

Water pressure limits snorkeling. A snorkeler draws in air at atmospheric pressure while the water presses on her chest. In one test in seawater, a volunteer could expand her chest to inhale only when the water pressure on her chest exceeded the pressure of the inhaled air by no more than 8.0 kPa.

Water pressure also compresses a breath-hold diver's lungs. Researchers modeled a diver who inhales 6.0 L of air at the surface and then descends. The model assumes the lung gas stays at body temperature and exchanges no gas with the blood (Table 1). Together, the diver and her equipment have a mass of 78.5 kg and, not counting the lung gas, a volume of 74.0 L.

Table 1. Modeled lung gas volume during a descent in seawater

In a real dive, the blood also takes up oxygen from the lung gas. When the diver reached the bottom of a 30-m dive, oxygen made up 5.0% of her lung gas, and this fraction changed little during her rapid ascent. Divers can lose consciousness from lack of oxygen in the last few meters of an ascent, even when they felt well at the bottom.

Water Pressure, Lung Gas and Buoyancy in Breath-Hold Diving

Because the chest wall is flexible, the gas in a submerged person's lungs is squeezed to nearly the pressure of the surrounding water. In seawater (density 1020 kg/m³), that pressure rises by about 10 kPa for every meter of depth. Take atmospheric pressure at the surface as 100 kPa and g as 9.8 m/s².

Water pressure limits snorkeling. A snorkeler draws in air at atmospheric pressure while the water presses on her chest. In one test in seawater, a volunteer could expand her chest to inhale only when the water pressure on her chest exceeded the pressure of the inhaled air by no more than 8.0 kPa.

Water pressure also compresses a breath-hold diver's lungs. Researchers modeled a diver who inhales 6.0 L of air at the surface and then descends. The model assumes the lung gas stays at body temperature and exchanges no gas with the blood (Table 1). Together, the diver and her equipment have a mass of 78.5 kg and, not counting the lung gas, a volume of 74.0 L.

Table 1. Modeled lung gas volume during a descent in seawater

In a real dive, the blood also takes up oxygen from the lung gas. When the diver reached the bottom of a 30-m dive, oxygen made up 5.0% of her lung gas, and this fraction changed little during her rapid ascent. Divers can lose consciousness from lack of oxygen in the last few meters of an ascent, even when they felt well at the bottom.

Water Pressure, Lung Gas and Buoyancy in Breath-Hold Diving

Because the chest wall is flexible, the gas in a submerged person's lungs is squeezed to nearly the pressure of the surrounding water. In seawater (density 1020 kg/m³), that pressure rises by about 10 kPa for every meter of depth. Take atmospheric pressure at the surface as 100 kPa and g as 9.8 m/s².

Water pressure limits snorkeling. A snorkeler draws in air at atmospheric pressure while the water presses on her chest. In one test in seawater, a volunteer could expand her chest to inhale only when the water pressure on her chest exceeded the pressure of the inhaled air by no more than 8.0 kPa.

Water pressure also compresses a breath-hold diver's lungs. Researchers modeled a diver who inhales 6.0 L of air at the surface and then descends. The model assumes the lung gas stays at body temperature and exchanges no gas with the blood (Table 1). Together, the diver and her equipment have a mass of 78.5 kg and, not counting the lung gas, a volume of 74.0 L.

Table 1. Modeled lung gas volume during a descent in seawater

In a real dive, the blood also takes up oxygen from the lung gas. When the diver reached the bottom of a 30-m dive, oxygen made up 5.0% of her lung gas, and this fraction changed little during her rapid ascent. Divers can lose consciousness from lack of oxygen in the last few meters of an ascent, even when they felt well at the bottom.

Water Pressure, Lung Gas and Buoyancy in Breath-Hold Diving

Because the chest wall is flexible, the gas in a submerged person's lungs is squeezed to nearly the pressure of the surrounding water. In seawater (density 1020 kg/m³), that pressure rises by about 10 kPa for every meter of depth. Take atmospheric pressure at the surface as 100 kPa and g as 9.8 m/s².

Water pressure limits snorkeling. A snorkeler draws in air at atmospheric pressure while the water presses on her chest. In one test in seawater, a volunteer could expand her chest to inhale only when the water pressure on her chest exceeded the pressure of the inhaled air by no more than 8.0 kPa.

Water pressure also compresses a breath-hold diver's lungs. Researchers modeled a diver who inhales 6.0 L of air at the surface and then descends. The model assumes the lung gas stays at body temperature and exchanges no gas with the blood (Table 1). Together, the diver and her equipment have a mass of 78.5 kg and, not counting the lung gas, a volume of 74.0 L.

Table 1. Modeled lung gas volume during a descent in seawater

In a real dive, the blood also takes up oxygen from the lung gas. When the diver reached the bottom of a 30-m dive, oxygen made up 5.0% of her lung gas, and this fraction changed little during her rapid ascent. Divers can lose consciousness from lack of oxygen in the last few meters of an ascent, even when they felt well at the bottom.

Arteriole Radius and Flow in an Isolated Vessel

Arterioles account for most of the resistance to blood flow in the systemic circulation, and their smooth muscle adjusts that resistance by narrowing or widening the lumen. For steady, laminar flow of a fluid of constant viscosity through a rigid tube, Poiseuille's law gives the volume flow rate:

$Q = \dfrac{\pi\,\Delta P\,r^4}{8\,\eta\,L}$

where $\Delta P$ is the pressure difference between the ends of the tube, $r$ is its inner radius, $\eta$ is the fluid's viscosity and $L$ is its length.

In one study, researchers removed a 2.0-mm segment of arteriole from a rat's skeletal muscle and mounted it between two glass cannulas. They held the pressure difference along the segment at 1.0 mmHg and perfused it with a salt solution. They measured the flow rate at baseline, after adding either a vasodilator (adenosine) or a vasoconstrictor (phenylephrine) to the bath, and, in a final trial with no drug, after adding dextran, a large sugar polymer, to raise the perfusate's viscosity. In each trial they measured the vessel's inner radius through a microscope (Table 1).

Table 1. Flow through the arteriole at a constant pressure difference of 1.0 mmHg

In every trial, the measured flow rate matched the value Poiseuille's law predicts from the measured radius and viscosity.

Arteriole Radius and Flow in an Isolated Vessel

Arterioles account for most of the resistance to blood flow in the systemic circulation, and their smooth muscle adjusts that resistance by narrowing or widening the lumen. For steady, laminar flow of a fluid of constant viscosity through a rigid tube, Poiseuille's law gives the volume flow rate:

$Q = \dfrac{\pi\,\Delta P\,r^4}{8\,\eta\,L}$

where $\Delta P$ is the pressure difference between the ends of the tube, $r$ is its inner radius, $\eta$ is the fluid's viscosity and $L$ is its length.

In one study, researchers removed a 2.0-mm segment of arteriole from a rat's skeletal muscle and mounted it between two glass cannulas. They held the pressure difference along the segment at 1.0 mmHg and perfused it with a salt solution. They measured the flow rate at baseline, after adding either a vasodilator (adenosine) or a vasoconstrictor (phenylephrine) to the bath, and, in a final trial with no drug, after adding dextran, a large sugar polymer, to raise the perfusate's viscosity. In each trial they measured the vessel's inner radius through a microscope (Table 1).

Table 1. Flow through the arteriole at a constant pressure difference of 1.0 mmHg

In every trial, the measured flow rate matched the value Poiseuille's law predicts from the measured radius and viscosity.

Arteriole Radius and Flow in an Isolated Vessel

Arterioles account for most of the resistance to blood flow in the systemic circulation, and their smooth muscle adjusts that resistance by narrowing or widening the lumen. For steady, laminar flow of a fluid of constant viscosity through a rigid tube, Poiseuille's law gives the volume flow rate:

$Q = \dfrac{\pi\,\Delta P\,r^4}{8\,\eta\,L}$

where $\Delta P$ is the pressure difference between the ends of the tube, $r$ is its inner radius, $\eta$ is the fluid's viscosity and $L$ is its length.

In one study, researchers removed a 2.0-mm segment of arteriole from a rat's skeletal muscle and mounted it between two glass cannulas. They held the pressure difference along the segment at 1.0 mmHg and perfused it with a salt solution. They measured the flow rate at baseline, after adding either a vasodilator (adenosine) or a vasoconstrictor (phenylephrine) to the bath, and, in a final trial with no drug, after adding dextran, a large sugar polymer, to raise the perfusate's viscosity. In each trial they measured the vessel's inner radius through a microscope (Table 1).

Table 1. Flow through the arteriole at a constant pressure difference of 1.0 mmHg

In every trial, the measured flow rate matched the value Poiseuille's law predicts from the measured radius and viscosity.

Arteriole Radius and Flow in an Isolated Vessel

Arterioles account for most of the resistance to blood flow in the systemic circulation, and their smooth muscle adjusts that resistance by narrowing or widening the lumen. For steady, laminar flow of a fluid of constant viscosity through a rigid tube, Poiseuille's law gives the volume flow rate:

$Q = \dfrac{\pi\,\Delta P\,r^4}{8\,\eta\,L}$

where $\Delta P$ is the pressure difference between the ends of the tube, $r$ is its inner radius, $\eta$ is the fluid's viscosity and $L$ is its length.

In one study, researchers removed a 2.0-mm segment of arteriole from a rat's skeletal muscle and mounted it between two glass cannulas. They held the pressure difference along the segment at 1.0 mmHg and perfused it with a salt solution. They measured the flow rate at baseline, after adding either a vasodilator (adenosine) or a vasoconstrictor (phenylephrine) to the bath, and, in a final trial with no drug, after adding dextran, a large sugar polymer, to raise the perfusate's viscosity. In each trial they measured the vessel's inner radius through a microscope (Table 1).

Table 1. Flow through the arteriole at a constant pressure difference of 1.0 mmHg

In every trial, the measured flow rate matched the value Poiseuille's law predicts from the measured radius and viscosity.

Arteriole Radius and Flow in an Isolated Vessel

Arterioles account for most of the resistance to blood flow in the systemic circulation, and their smooth muscle adjusts that resistance by narrowing or widening the lumen. For steady, laminar flow of a fluid of constant viscosity through a rigid tube, Poiseuille's law gives the volume flow rate:

$Q = \dfrac{\pi\,\Delta P\,r^4}{8\,\eta\,L}$

where $\Delta P$ is the pressure difference between the ends of the tube, $r$ is its inner radius, $\eta$ is the fluid's viscosity and $L$ is its length.

In one study, researchers removed a 2.0-mm segment of arteriole from a rat's skeletal muscle and mounted it between two glass cannulas. They held the pressure difference along the segment at 1.0 mmHg and perfused it with a salt solution. They measured the flow rate at baseline, after adding either a vasodilator (adenosine) or a vasoconstrictor (phenylephrine) to the bath, and, in a final trial with no drug, after adding dextran, a large sugar polymer, to raise the perfusate's viscosity. In each trial they measured the vessel's inner radius through a microscope (Table 1).

Table 1. Flow through the arteriole at a constant pressure difference of 1.0 mmHg

In every trial, the measured flow rate matched the value Poiseuille's law predicts from the measured radius and viscosity.

Maintaining a stable blood pH is crucial for survival and involves various regulatory systems working together. Under normal conditions, the pH of blood plasma is tightly regulated around 7.4. Deviations below 6.9 or above 7.7 can be fatal.

One major contributor to this balance is the enzyme carbonic anhydrase, which speeds up the reaction converting carbon dioxide ($CO_2$) and water into carbonic acid. This carbonic acid can dissociate into hydrogen ions and bicarbonate, forming the carbonic acid–bicarbonate buffer system shown below:

In the absence of a catalyst, $CO_2$ and $H^+$ in the blood can bind to hemoglobin after it releases oxygen in peripheral tissues. Once hemoglobin reaches the lungs, it rebinds oxygen and releases $CO_2$ and $H^+$, reversing the prior binding. This continuous exchange of gases is part of the process of respiration.

Maintaining a stable blood pH is crucial for survival and involves various regulatory systems working together. Under normal conditions, the pH of blood plasma is tightly regulated around 7.4. Deviations below 6.9 or above 7.7 can be fatal.

One major contributor to this balance is the enzyme carbonic anhydrase, which speeds up the reaction converting carbon dioxide ($CO_2$) and water into carbonic acid. This carbonic acid can dissociate into hydrogen ions and bicarbonate, forming the carbonic acid–bicarbonate buffer system shown below:

In the absence of a catalyst, $CO_2$ and $H^+$ in the blood can bind to hemoglobin after it releases oxygen in peripheral tissues. Once hemoglobin reaches the lungs, it rebinds oxygen and releases $CO_2$ and $H^+$, reversing the prior binding. This continuous exchange of gases is part of the process of respiration.

Maintaining a stable blood pH is crucial for survival and involves various regulatory systems working together. Under normal conditions, the pH of blood plasma is tightly regulated around 7.4. Deviations below 6.9 or above 7.7 can be fatal.

One major contributor to this balance is the enzyme carbonic anhydrase, which speeds up the reaction converting carbon dioxide ($CO_2$) and water into carbonic acid. This carbonic acid can dissociate into hydrogen ions and bicarbonate, forming the carbonic acid–bicarbonate buffer system shown below:

In the absence of a catalyst, $CO_2$ and $H^+$ in the blood can bind to hemoglobin after it releases oxygen in peripheral tissues. Once hemoglobin reaches the lungs, it rebinds oxygen and releases $CO_2$ and $H^+$, reversing the prior binding. This continuous exchange of gases is part of the process of respiration.

Maintaining a stable blood pH is crucial for survival and involves various regulatory systems working together. Under normal conditions, the pH of blood plasma is tightly regulated around 7.4. Deviations below 6.9 or above 7.7 can be fatal.

One major contributor to this balance is the enzyme carbonic anhydrase, which speeds up the reaction converting carbon dioxide ($CO_2$) and water into carbonic acid. This carbonic acid can dissociate into hydrogen ions and bicarbonate, forming the carbonic acid–bicarbonate buffer system shown below:

In the absence of a catalyst, $CO_2$ and $H^+$ in the blood can bind to hemoglobin after it releases oxygen in peripheral tissues. Once hemoglobin reaches the lungs, it rebinds oxygen and releases $CO_2$ and $H^+$, reversing the prior binding. This continuous exchange of gases is part of the process of respiration.

Maintaining a stable blood pH is crucial for survival and involves various regulatory systems working together. Under normal conditions, the pH of blood plasma is tightly regulated around 7.4. Deviations below 6.9 or above 7.7 can be fatal.

One major contributor to this balance is the enzyme carbonic anhydrase, which speeds up the reaction converting carbon dioxide ($CO_2$) and water into carbonic acid. This carbonic acid can dissociate into hydrogen ions and bicarbonate, forming the carbonic acid–bicarbonate buffer system shown below:

In the absence of a catalyst, $CO_2$ and $H^+$ in the blood can bind to hemoglobin after it releases oxygen in peripheral tissues. Once hemoglobin reaches the lungs, it rebinds oxygen and releases $CO_2$ and $H^+$, reversing the prior binding. This continuous exchange of gases is part of the process of respiration.

Carnosine: A Built-In Buffer for Sprinting Muscle

During a sprint, fast-twitch muscle makes lactic acid faster than it can export it, and the hydrogen ions released can push intracellular pH from about 7.1 toward 6.5, low enough to inhibit enzymes such as phosphofructokinase-1. Besides bicarbonate, phosphate and proteins, these fibers buffer acid with carnosine (β-alanyl-L-histidine), a dipeptide stored at high concentrations in the muscles of sprinting animals. Between pH 5.5 and 7.5, the only group of carnosine that gains or loses a proton is the imidazole ring of its histidine, written below as Im:

$\text{ImH}^+ \rightleftharpoons \text{Im} + \text{H}^+ \qquad \text{p}K_a = 6.83 \text{ at } 37\ ^\circ\text{C}$

To measure this group's buffering, researchers prepared a 30 mM carnosine solution in 150 mM KCl at 37 °C, adjusted it to pH 7.13, and added HCl in steps, recording the pH after each addition. A KCl solution with no carnosine, also adjusted to pH 7.13, served as the control (Table 1).

Table 1. pH after adding HCl (mmol per liter of solution)

Carnosine: A Built-In Buffer for Sprinting Muscle

During a sprint, fast-twitch muscle makes lactic acid faster than it can export it, and the hydrogen ions released can push intracellular pH from about 7.1 toward 6.5, low enough to inhibit enzymes such as phosphofructokinase-1. Besides bicarbonate, phosphate and proteins, these fibers buffer acid with carnosine (β-alanyl-L-histidine), a dipeptide stored at high concentrations in the muscles of sprinting animals. Between pH 5.5 and 7.5, the only group of carnosine that gains or loses a proton is the imidazole ring of its histidine, written below as Im:

$\text{ImH}^+ \rightleftharpoons \text{Im} + \text{H}^+ \qquad \text{p}K_a = 6.83 \text{ at } 37\ ^\circ\text{C}$

To measure this group's buffering, researchers prepared a 30 mM carnosine solution in 150 mM KCl at 37 °C, adjusted it to pH 7.13, and added HCl in steps, recording the pH after each addition. A KCl solution with no carnosine, also adjusted to pH 7.13, served as the control (Table 1).

Table 1. pH after adding HCl (mmol per liter of solution)

Carnosine: A Built-In Buffer for Sprinting Muscle

During a sprint, fast-twitch muscle makes lactic acid faster than it can export it, and the hydrogen ions released can push intracellular pH from about 7.1 toward 6.5, low enough to inhibit enzymes such as phosphofructokinase-1. Besides bicarbonate, phosphate and proteins, these fibers buffer acid with carnosine (β-alanyl-L-histidine), a dipeptide stored at high concentrations in the muscles of sprinting animals. Between pH 5.5 and 7.5, the only group of carnosine that gains or loses a proton is the imidazole ring of its histidine, written below as Im:

$\text{ImH}^+ \rightleftharpoons \text{Im} + \text{H}^+ \qquad \text{p}K_a = 6.83 \text{ at } 37\ ^\circ\text{C}$

To measure this group's buffering, researchers prepared a 30 mM carnosine solution in 150 mM KCl at 37 °C, adjusted it to pH 7.13, and added HCl in steps, recording the pH after each addition. A KCl solution with no carnosine, also adjusted to pH 7.13, served as the control (Table 1).

Table 1. pH after adding HCl (mmol per liter of solution)

Carnosine: A Built-In Buffer for Sprinting Muscle

During a sprint, fast-twitch muscle makes lactic acid faster than it can export it, and the hydrogen ions released can push intracellular pH from about 7.1 toward 6.5, low enough to inhibit enzymes such as phosphofructokinase-1. Besides bicarbonate, phosphate and proteins, these fibers buffer acid with carnosine (β-alanyl-L-histidine), a dipeptide stored at high concentrations in the muscles of sprinting animals. Between pH 5.5 and 7.5, the only group of carnosine that gains or loses a proton is the imidazole ring of its histidine, written below as Im:

$\text{ImH}^+ \rightleftharpoons \text{Im} + \text{H}^+ \qquad \text{p}K_a = 6.83 \text{ at } 37\ ^\circ\text{C}$

To measure this group's buffering, researchers prepared a 30 mM carnosine solution in 150 mM KCl at 37 °C, adjusted it to pH 7.13, and added HCl in steps, recording the pH after each addition. A KCl solution with no carnosine, also adjusted to pH 7.13, served as the control (Table 1).

Table 1. pH after adding HCl (mmol per liter of solution)

Carnosine: A Built-In Buffer for Sprinting Muscle

During a sprint, fast-twitch muscle makes lactic acid faster than it can export it, and the hydrogen ions released can push intracellular pH from about 7.1 toward 6.5, low enough to inhibit enzymes such as phosphofructokinase-1. Besides bicarbonate, phosphate and proteins, these fibers buffer acid with carnosine (β-alanyl-L-histidine), a dipeptide stored at high concentrations in the muscles of sprinting animals. Between pH 5.5 and 7.5, the only group of carnosine that gains or loses a proton is the imidazole ring of its histidine, written below as Im:

$\text{ImH}^+ \rightleftharpoons \text{Im} + \text{H}^+ \qquad \text{p}K_a = 6.83 \text{ at } 37\ ^\circ\text{C}$

To measure this group's buffering, researchers prepared a 30 mM carnosine solution in 150 mM KCl at 37 °C, adjusted it to pH 7.13, and added HCl in steps, recording the pH after each addition. A KCl solution with no carnosine, also adjusted to pH 7.13, served as the control (Table 1).

Table 1. pH after adding HCl (mmol per liter of solution)

Three Alcohols, One Enzyme: Why Methanol Is Dangerous

Methanol, ethanol and 2-propanol are all oxidized in the liver by alcohol dehydrogenase (ADH), which removes a hydride ion from the carbon bearing the –OH group and passes it to $\text{NAD}^+$. Aldehyde products are then oxidized further, by aldehyde dehydrogenases, to carboxylic acids. For methanol, this path ends at formic acid ($\text{p}K_a = 3.75$). Humans convert formate to $\text{CO}_2$ only slowly, so after a large methanol dose, formic acid accumulates and blood pH falls.

In one study, researchers purified a human liver ADH and measured its kinetics with each alcohol at saturating $\text{NAD}^+$ (Table 1).

Table 1. Kinetic constants of purified liver ADH at 37 °C

The researchers then measured how much of each carbonyl product exists as its hydrate, a geminal diol, at equilibrium in water at 25 °C (Table 2):

$\text{R}_2\text{C=O} + \text{H}_2\text{O} \rightleftharpoons \text{R}_2\text{C(OH)}_2$

Table 2. Hydration equilibria of the carbonyl products

A patient who drank windshield-washer fluid arrives with a blood methanol concentration of 15 mM. Until dialysis can remove the methanol, clinicians infuse ethanol to hold blood ethanol near 22 mM.

Three Alcohols, One Enzyme: Why Methanol Is Dangerous

Methanol, ethanol and 2-propanol are all oxidized in the liver by alcohol dehydrogenase (ADH), which removes a hydride ion from the carbon bearing the –OH group and passes it to $\text{NAD}^+$. Aldehyde products are then oxidized further, by aldehyde dehydrogenases, to carboxylic acids. For methanol, this path ends at formic acid ($\text{p}K_a = 3.75$). Humans convert formate to $\text{CO}_2$ only slowly, so after a large methanol dose, formic acid accumulates and blood pH falls.

In one study, researchers purified a human liver ADH and measured its kinetics with each alcohol at saturating $\text{NAD}^+$ (Table 1).

Table 1. Kinetic constants of purified liver ADH at 37 °C

The researchers then measured how much of each carbonyl product exists as its hydrate, a geminal diol, at equilibrium in water at 25 °C (Table 2):

$\text{R}_2\text{C=O} + \text{H}_2\text{O} \rightleftharpoons \text{R}_2\text{C(OH)}_2$

Table 2. Hydration equilibria of the carbonyl products

A patient who drank windshield-washer fluid arrives with a blood methanol concentration of 15 mM. Until dialysis can remove the methanol, clinicians infuse ethanol to hold blood ethanol near 22 mM.

Three Alcohols, One Enzyme: Why Methanol Is Dangerous

Methanol, ethanol and 2-propanol are all oxidized in the liver by alcohol dehydrogenase (ADH), which removes a hydride ion from the carbon bearing the –OH group and passes it to $\text{NAD}^+$. Aldehyde products are then oxidized further, by aldehyde dehydrogenases, to carboxylic acids. For methanol, this path ends at formic acid ($\text{p}K_a = 3.75$). Humans convert formate to $\text{CO}_2$ only slowly, so after a large methanol dose, formic acid accumulates and blood pH falls.

In one study, researchers purified a human liver ADH and measured its kinetics with each alcohol at saturating $\text{NAD}^+$ (Table 1).

Table 1. Kinetic constants of purified liver ADH at 37 °C

The researchers then measured how much of each carbonyl product exists as its hydrate, a geminal diol, at equilibrium in water at 25 °C (Table 2):

$\text{R}_2\text{C=O} + \text{H}_2\text{O} \rightleftharpoons \text{R}_2\text{C(OH)}_2$

Table 2. Hydration equilibria of the carbonyl products

A patient who drank windshield-washer fluid arrives with a blood methanol concentration of 15 mM. Until dialysis can remove the methanol, clinicians infuse ethanol to hold blood ethanol near 22 mM.

Three Alcohols, One Enzyme: Why Methanol Is Dangerous

Methanol, ethanol and 2-propanol are all oxidized in the liver by alcohol dehydrogenase (ADH), which removes a hydride ion from the carbon bearing the –OH group and passes it to $\text{NAD}^+$. Aldehyde products are then oxidized further, by aldehyde dehydrogenases, to carboxylic acids. For methanol, this path ends at formic acid ($\text{p}K_a = 3.75$). Humans convert formate to $\text{CO}_2$ only slowly, so after a large methanol dose, formic acid accumulates and blood pH falls.

In one study, researchers purified a human liver ADH and measured its kinetics with each alcohol at saturating $\text{NAD}^+$ (Table 1).

Table 1. Kinetic constants of purified liver ADH at 37 °C

The researchers then measured how much of each carbonyl product exists as its hydrate, a geminal diol, at equilibrium in water at 25 °C (Table 2):

$\text{R}_2\text{C=O} + \text{H}_2\text{O} \rightleftharpoons \text{R}_2\text{C(OH)}_2$

Table 2. Hydration equilibria of the carbonyl products

A patient who drank windshield-washer fluid arrives with a blood methanol concentration of 15 mM. Until dialysis can remove the methanol, clinicians infuse ethanol to hold blood ethanol near 22 mM.

Three Alcohols, One Enzyme: Why Methanol Is Dangerous

Methanol, ethanol and 2-propanol are all oxidized in the liver by alcohol dehydrogenase (ADH), which removes a hydride ion from the carbon bearing the –OH group and passes it to $\text{NAD}^+$. Aldehyde products are then oxidized further, by aldehyde dehydrogenases, to carboxylic acids. For methanol, this path ends at formic acid ($\text{p}K_a = 3.75$). Humans convert formate to $\text{CO}_2$ only slowly, so after a large methanol dose, formic acid accumulates and blood pH falls.

In one study, researchers purified a human liver ADH and measured its kinetics with each alcohol at saturating $\text{NAD}^+$ (Table 1).

Table 1. Kinetic constants of purified liver ADH at 37 °C

The researchers then measured how much of each carbonyl product exists as its hydrate, a geminal diol, at equilibrium in water at 25 °C (Table 2):

$\text{R}_2\text{C=O} + \text{H}_2\text{O} \rightleftharpoons \text{R}_2\text{C(OH)}_2$

Table 2. Hydration equilibria of the carbonyl products

A patient who drank windshield-washer fluid arrives with a blood methanol concentration of 15 mM. Until dialysis can remove the methanol, clinicians infuse ethanol to hold blood ethanol near 22 mM.

Penicillin is widely regarded as one of the most iconic and influential antibiotics in medical history. Its chemical structure is defined by a key component called a beta-lactam—a four-membered ring containing an amide group. Figure 1 demonstrates the beta-lactam structure in several different antibiotics. This beta-lactam structure allows the drug to form a covalent bond with Penicillin Binding Proteins (PBPs), which play a crucial role in bacterial cell wall integrity by facilitating the cross-linking of peptidoglycan chains. When penicillin or related compounds attach to PBPs, this cross-linking process is disrupted, weakening the cell wall and leading to bacterial death through lysis.

The beta-lactam ring is especially reactive due to its geometric strain; the four-membered ring creates 90° bond angles, which deviate significantly from ideal angles for sp$^2$ or sp$^3$ hybridized atoms. This strain contributes to the ring's high reactivity and ability to acylate PBPs effectively. In contrast, larger lactam rings, which are less strained, show markedly lower reactivity. To counteract the effects of beta-lactam antibiotics, some bacteria produce an enzyme called beta-lactamase. This enzyme cleaves the beta-lactam ring, neutralizing the antibiotic's activity by preventing it from interacting with PBPs.

Penicillin is widely regarded as one of the most iconic and influential antibiotics in medical history. Its chemical structure is defined by a key component called a beta-lactam—a four-membered ring containing an amide group. Figure 1 demonstrates the beta-lactam structure in several different antibiotics. This beta-lactam structure allows the drug to form a covalent bond with Penicillin Binding Proteins (PBPs), which play a crucial role in bacterial cell wall integrity by facilitating the cross-linking of peptidoglycan chains. When penicillin or related compounds attach to PBPs, this cross-linking process is disrupted, weakening the cell wall and leading to bacterial death through lysis.

The beta-lactam ring is especially reactive due to its geometric strain; the four-membered ring creates 90° bond angles, which deviate significantly from ideal angles for sp$^2$ or sp$^3$ hybridized atoms. This strain contributes to the ring's high reactivity and ability to acylate PBPs effectively. In contrast, larger lactam rings, which are less strained, show markedly lower reactivity. To counteract the effects of beta-lactam antibiotics, some bacteria produce an enzyme called beta-lactamase. This enzyme cleaves the beta-lactam ring, neutralizing the antibiotic's activity by preventing it from interacting with PBPs.

Penicillin is widely regarded as one of the most iconic and influential antibiotics in medical history. Its chemical structure is defined by a key component called a beta-lactam—a four-membered ring containing an amide group. Figure 1 demonstrates the beta-lactam structure in several different antibiotics. This beta-lactam structure allows the drug to form a covalent bond with Penicillin Binding Proteins (PBPs), which play a crucial role in bacterial cell wall integrity by facilitating the cross-linking of peptidoglycan chains. When penicillin or related compounds attach to PBPs, this cross-linking process is disrupted, weakening the cell wall and leading to bacterial death through lysis.

The beta-lactam ring is especially reactive due to its geometric strain; the four-membered ring creates 90° bond angles, which deviate significantly from ideal angles for sp$^2$ or sp$^3$ hybridized atoms. This strain contributes to the ring's high reactivity and ability to acylate PBPs effectively. In contrast, larger lactam rings, which are less strained, show markedly lower reactivity. To counteract the effects of beta-lactam antibiotics, some bacteria produce an enzyme called beta-lactamase. This enzyme cleaves the beta-lactam ring, neutralizing the antibiotic's activity by preventing it from interacting with PBPs.

Penicillin is widely regarded as one of the most iconic and influential antibiotics in medical history. Its chemical structure is defined by a key component called a beta-lactam—a four-membered ring containing an amide group. Figure 1 demonstrates the beta-lactam structure in several different antibiotics. This beta-lactam structure allows the drug to form a covalent bond with Penicillin Binding Proteins (PBPs), which play a crucial role in bacterial cell wall integrity by facilitating the cross-linking of peptidoglycan chains. When penicillin or related compounds attach to PBPs, this cross-linking process is disrupted, weakening the cell wall and leading to bacterial death through lysis.

The beta-lactam ring is especially reactive due to its geometric strain; the four-membered ring creates 90° bond angles, which deviate significantly from ideal angles for sp$^2$ or sp$^3$ hybridized atoms. This strain contributes to the ring's high reactivity and ability to acylate PBPs effectively. In contrast, larger lactam rings, which are less strained, show markedly lower reactivity. To counteract the effects of beta-lactam antibiotics, some bacteria produce an enzyme called beta-lactamase. This enzyme cleaves the beta-lactam ring, neutralizing the antibiotic's activity by preventing it from interacting with PBPs.

A Cyclist Who Cannot Sprint: The Isozymes of Lactate Dehydrogenase

Lactate dehydrogenase (LDH) catalyzes the last step of anaerobic glycolysis:

$\text{pyruvate} + \text{NADH} + \text{H}^+ \rightleftharpoons \text{lactate} + \text{NAD}^+ \qquad \Delta G^{\circ\prime} = -25\ \text{kJ/mol}$

Active LDH is a tetramer built from two kinds of subunit: M, encoded by the LDHA gene and dominant in skeletal muscle, and H, encoded by LDHB and dominant in heart. Heart muscle takes up lactate from the blood, runs the reaction in reverse, and oxidizes the resulting pyruvate in its mitochondria. In one study, the two pure tetramers were compared at low pyruvate concentrations (Table 1).

Table 1. Pyruvate affinity of the two pure LDH tetramers

A 19-year-old cyclist reports cramps and dark urine after short sprints, yet can ride for hours at an easy pace. Clinicians performed an ischemic forearm test: with a cuff stopping blood flow to the forearm, the patient squeezed a hand grip hard for one minute; the cuff was then released. Blood was drawn from a forearm vein before exercise and two minutes after it. Ammonia, which muscle releases by deaminating AMP during intense effort, rises whether or not glycolysis works, so it confirms that the effort was adequate. A healthy volunteer served as the control (Table 2). A later muscle biopsy found no M subunits.

Table 2. Venous blood in the ischemic forearm test

A Cyclist Who Cannot Sprint: The Isozymes of Lactate Dehydrogenase

Lactate dehydrogenase (LDH) catalyzes the last step of anaerobic glycolysis:

$\text{pyruvate} + \text{NADH} + \text{H}^+ \rightleftharpoons \text{lactate} + \text{NAD}^+ \qquad \Delta G^{\circ\prime} = -25\ \text{kJ/mol}$

Active LDH is a tetramer built from two kinds of subunit: M, encoded by the LDHA gene and dominant in skeletal muscle, and H, encoded by LDHB and dominant in heart. Heart muscle takes up lactate from the blood, runs the reaction in reverse, and oxidizes the resulting pyruvate in its mitochondria. In one study, the two pure tetramers were compared at low pyruvate concentrations (Table 1).

Table 1. Pyruvate affinity of the two pure LDH tetramers

A 19-year-old cyclist reports cramps and dark urine after short sprints, yet can ride for hours at an easy pace. Clinicians performed an ischemic forearm test: with a cuff stopping blood flow to the forearm, the patient squeezed a hand grip hard for one minute; the cuff was then released. Blood was drawn from a forearm vein before exercise and two minutes after it. Ammonia, which muscle releases by deaminating AMP during intense effort, rises whether or not glycolysis works, so it confirms that the effort was adequate. A healthy volunteer served as the control (Table 2). A later muscle biopsy found no M subunits.

Table 2. Venous blood in the ischemic forearm test

A Cyclist Who Cannot Sprint: The Isozymes of Lactate Dehydrogenase

Lactate dehydrogenase (LDH) catalyzes the last step of anaerobic glycolysis:

$\text{pyruvate} + \text{NADH} + \text{H}^+ \rightleftharpoons \text{lactate} + \text{NAD}^+ \qquad \Delta G^{\circ\prime} = -25\ \text{kJ/mol}$

Active LDH is a tetramer built from two kinds of subunit: M, encoded by the LDHA gene and dominant in skeletal muscle, and H, encoded by LDHB and dominant in heart. Heart muscle takes up lactate from the blood, runs the reaction in reverse, and oxidizes the resulting pyruvate in its mitochondria. In one study, the two pure tetramers were compared at low pyruvate concentrations (Table 1).

Table 1. Pyruvate affinity of the two pure LDH tetramers

A 19-year-old cyclist reports cramps and dark urine after short sprints, yet can ride for hours at an easy pace. Clinicians performed an ischemic forearm test: with a cuff stopping blood flow to the forearm, the patient squeezed a hand grip hard for one minute; the cuff was then released. Blood was drawn from a forearm vein before exercise and two minutes after it. Ammonia, which muscle releases by deaminating AMP during intense effort, rises whether or not glycolysis works, so it confirms that the effort was adequate. A healthy volunteer served as the control (Table 2). A later muscle biopsy found no M subunits.

Table 2. Venous blood in the ischemic forearm test

A Cyclist Who Cannot Sprint: The Isozymes of Lactate Dehydrogenase

Lactate dehydrogenase (LDH) catalyzes the last step of anaerobic glycolysis:

$\text{pyruvate} + \text{NADH} + \text{H}^+ \rightleftharpoons \text{lactate} + \text{NAD}^+ \qquad \Delta G^{\circ\prime} = -25\ \text{kJ/mol}$

Active LDH is a tetramer built from two kinds of subunit: M, encoded by the LDHA gene and dominant in skeletal muscle, and H, encoded by LDHB and dominant in heart. Heart muscle takes up lactate from the blood, runs the reaction in reverse, and oxidizes the resulting pyruvate in its mitochondria. In one study, the two pure tetramers were compared at low pyruvate concentrations (Table 1).

Table 1. Pyruvate affinity of the two pure LDH tetramers

A 19-year-old cyclist reports cramps and dark urine after short sprints, yet can ride for hours at an easy pace. Clinicians performed an ischemic forearm test: with a cuff stopping blood flow to the forearm, the patient squeezed a hand grip hard for one minute; the cuff was then released. Blood was drawn from a forearm vein before exercise and two minutes after it. Ammonia, which muscle releases by deaminating AMP during intense effort, rises whether or not glycolysis works, so it confirms that the effort was adequate. A healthy volunteer served as the control (Table 2). A later muscle biopsy found no M subunits.

Table 2. Venous blood in the ischemic forearm test

A Cyclist Who Cannot Sprint: The Isozymes of Lactate Dehydrogenase

Lactate dehydrogenase (LDH) catalyzes the last step of anaerobic glycolysis:

$\text{pyruvate} + \text{NADH} + \text{H}^+ \rightleftharpoons \text{lactate} + \text{NAD}^+ \qquad \Delta G^{\circ\prime} = -25\ \text{kJ/mol}$

Active LDH is a tetramer built from two kinds of subunit: M, encoded by the LDHA gene and dominant in skeletal muscle, and H, encoded by LDHB and dominant in heart. Heart muscle takes up lactate from the blood, runs the reaction in reverse, and oxidizes the resulting pyruvate in its mitochondria. In one study, the two pure tetramers were compared at low pyruvate concentrations (Table 1).

Table 1. Pyruvate affinity of the two pure LDH tetramers

A 19-year-old cyclist reports cramps and dark urine after short sprints, yet can ride for hours at an easy pace. Clinicians performed an ischemic forearm test: with a cuff stopping blood flow to the forearm, the patient squeezed a hand grip hard for one minute; the cuff was then released. Blood was drawn from a forearm vein before exercise and two minutes after it. Ammonia, which muscle releases by deaminating AMP during intense effort, rises whether or not glycolysis works, so it confirms that the effort was adequate. A healthy volunteer served as the control (Table 2). A later muscle biopsy found no M subunits.

Table 2. Venous blood in the ischemic forearm test