Passage
During deep underwater dives, scuba divers must overcome the external ambient pressure in order to expand their chests to inhale. To assist underwater breathing, air from scuba tanks is administered at high pressures to keep divers' lungs inflated. Scuba tanks are often filled with a mixture of N₂ and O₂ gas. Due to the increased pressure of the gases in the lungs, a greater amount of the gases are dissolved into the bloodstream during underwater dives. At a body temperature of 37°C, the solubility of N₂ gas in blood is 6.0 × 10⁻³ mol/L⋅atm and the solubility of O₂ gas is 1.3 × 10⁻² mol/L⋅atm.If a diver ascends too quickly after an extended dive, there is an increased risk of vascular bubble formation. Due to the decrease in ambient pressure, the excess gas dissolved in the blood may come out of solution as gas bubbles and cause a number of adverse effects. This condition is known as decompression sickness, or "the bends." To avoid this problem, scuba divers limit their rate of ascension to allow the excess gas dissolved in their blood to be safely removed through respiration. Because gas bubbles are good reflectors of sound, these bubbles can be detected using Doppler ultrasonic flowmetry after the diver has surfaced.
Adapted from M. Spencer, Journal of Applied Physiology. ©1976 American Physiology Society.
-A diver is using a tank filled with 20% O₂ and 80% N₂ (by volume) . If the pressure in the lungs is 5 atm, what is the expected equilibrium concentration of N₂ dissolved in the diver's blood? (Note: Assume that the mixtures of the gases in the lungs and tank are equal.)

Question

Quizplus · Accepted Answer

11ecba2d_12bf_8ae4_a3bf_171b0bd3d49a_MD0008_00 The amount of N₂ dissolved in the blood is in equilibrium with the partial pressure of N₂ in the gas phase. The partial pressure (P_gas) of a gas is the hypothetical pressure it would exert if it was the only gas occupying the same volume (Dalton law of partial pressures): where X_gas is the mole fraction of the gas, the ratio of the number of moles of a substance to the total number of moles present. An ideal gas's mole fraction is equal to its fraction of the total volume. Therefore, the partial pressure of N₂ is 80% of the total pressure (5 atm): The equilibrium between the gas partial pressure and the amount dissolved in solution is described by the Henry law of solubility: where C is the concentration of the dissolved gas, and k_H is the solubility coefficient specific to the gas and solution at a given temperature. Using 6.0 × 10⁻³ mol/atm for k_H and 4 atm for P, the concentration of dissolved N₂ is: (Choice A) The concentration of O₂ in the blood is 1.3 × 10⁻² mol/L. However, the question asks for the concentration of N₂. (Choice C) If the total pressure (5 atm) is used as the partial pressure of N₂, the incorrectly calculated concentration is 3.0 × 10⁻² mol/L. Educational objective: The partial pressure of a specific gas in a mixture is its hypothetical individual pressure (Dalton law of partial pressures). The partial pressure of a gas can be calculated from its mole fraction, which is equal to its fraction of the total volume. The gas partial pressure determines the concentration of the gas dissolved in solution by the Henry law of solubility (C = k_HP_gas).

Passage During Deep Underwater Dives, Scuba Divers Must Overcome the External