Body temperature is about 308 K. On a cold day, what volume of air at 273 K must a person with a lung capacity of 2.00 L breathe in to fill the lungs?

Question

Quizplus · Accepted Answer

To solve this problem, we can use the ideal gas law:

PV = nRT

where P is the pressure of the gas, V is its volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature in Kelvin.

Assuming the pressure stays constant, we can rearrange this formula to solve for the volume:

V = nRT/P

We know that the lung capacity of the person is 2.00 L. Assuming they breathe in air at normal atmospheric pressure (1 atm), we can plug in the other values:

V = nRT/P
2.00 L = n(0.0821 L atm/mol K)(308 K)/1 atm

Solving for n, we get:

n = (2.00 L)(1 atm)/(0.0821 L atm/mol K)(308 K) = 0.0904 mol

Now we can use this value to find the volume of air at 273 K (0°C):

V = nRT/P
V = (0.0904 mol)(0.0821 L atm/mol K)(273 K)/1 atm
V ≈ 1.77 L

Therefore, the best answer is C) 1.77 L.

Body Temperature Is About 308 K