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 10-L scuba tank is initially filled with 2,800 g of N₂ gas. At room temperature (25°C) , what is the pressure in the tank? (Note: Use R = 0.0821 L⋅atm/mol⋅K.)

Question

Quizplus · Accepted Answer

11ecba2d_12c1_5fab_a3bf_d1fabade9b95_MD0008_00 The relationship between pressure (P), volume (V), number of moles (n), and temperature (T) of an ideal gas is given by the ideal gas law: 11ecba2d_12c1_5fac_a3bf_c9a9666b22e1_MD0008_00 where R is the universal gas constant, given as 0.0821 L⋅atm⋅mol⁻¹⋅K⁻¹. The mass of N₂ is converted to moles using its molar mass. From the periodic table, the atomic mass of N is 14 g/mol. Therefore, the molar mass of N₂ is (2)(14 g/mol) = 28 g/mol. Dividing the total mass of N₂ in the tank (2,800 g) by its molar mass gives the moles of N₂: 11ecba2d_12c1_5fad_a3bf_ef16523bbbe9_MD0008_00 The value of R is given with units of inverse kelvin (K⁻¹). Therefore, the given temperature (25°C) is converted from Celsius to kelvin: 11ecba2d_12c1_86be_a3bf_3b19e3d6cc1c_MD0008_00 11ecba2d_12c1_86bf_a3bf_db5200a5e391_MD0008_00 This value is approximated as 300 K. Rearranging the ideal gas law equation to solve for P and using these values, 11ecba2d_12c1_86c0_a3bf_95cc1f88e15e_MD0008_00 11ecba2d_12c1_86c1_a3bf_655540dc9c29_MD0008_00 (Choice D) If the molar mass of N (14 g/mol) is used instead of the molar mass of N₂ (28 g/mol), the pressure would be incorrectly calculated as 480 atm. Education objective: For an ideal gas, the relationship between its pressure P, volume V, number of moles n, and temperature T is PV = nRT, where R is the universal gas constant. This equation is known as the ideal gas law, and it can be rearranged to solve for pressure.

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