How many moles of air must escape from a 12-m × 10-m × 3-m room when the temperature is raised from 5°C to 25°C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

Question

Quizplus · Accepted Answer

We can use the ideal gas law, PV=nRT, to solve for the number of moles of air that must escape. Since the pressure remains unchanged, we can simplify the equation to V/n=RT/P. We can calculate the initial volume of the room as V=12m x 10m x 3m = 360 m^3. Given the temperature change from 5°C to 25°C, the change in temperature is ΔT = 20°C = 20 K. R is the gas constant, which is 8.31 J/mol K. Therefore, we have:

V/n = (8.31 J/mol K)(298 K)/ (1 atm x 101,325 Pa/atm x 360 m^3)
n = V(1 atm x 101,325 Pa/atm)/(8.31 J/mol K)(298 K) = 1.1 x 10^13 mol

Therefore, approximately 1.1 x 10^13 moles of air must escape from the room. The closest answer choice is B.

How Many Moles of Air Must Escape from a 12-M