Question

How long does it take a person at rest to breathe one mole of air if the person breathes 77.0 ml/s of air that is measured at 25 ∘c and 755 mmhg? express your answer numerically in seconds?

Answer 1

320. seconds The ideal gas law is PV = nRT where P = pressure of the gas V = volume of the gas n = number of moles of the gas R = the ideal gas constant T = absolute temperature of the gas. Since we're going to want the volume, solve for V PV = nRT V = nRT/P 755 mmHg converts to 100658.11 Pascals 25 C = 298.15 K Let's calculate nT/P, then we'll multiply by R 1 mol * 298.15 K / 100658.11 Pa = 0.002962007 K mol/Pa The value for R in the most convenient units is 8.3144598 m^3 Pa/(K mol), so 0.002962007 K mol/Pa * 8.3144598 m^3 Pa/(K mol) = 0.024627486 m^3 So 1 mole of air at the specified temperature and pressure has a volume of 24.627 liters. The rest of the problem is now trivial. Just divide by the rate of consumption, so 24.627 l / 0.0770 l/s = 319.8374798 s Rounding the result to 3 significant figures gives 320. seconds.