How many air molecules are in a 14.0×12.0×10.0 ft room? assume atmospheric pressure of 1.00 atm, a room temperature of 20.0 ∘c,

Question

sdas [7]

2 years ago

12

How many air molecules are in a 14.0×12.0×10.0 ft room? assume atmospheric pressure of 1.00 atm, a room temperature of 20.0 ∘c,

and ideal behavior. volume conversion:there are 28.2 liters in one cubic foot?

Physics

2 answers:

erastova [34] · Answer 1 · 2022-08-28T15:37:06+03:00

First, let's find the total volume of the room (and of the gas):
$V=(14.0 ft\cdot 12.0 ft \cdot 10.0 ft)\cdot 28.0 \frac{L}{ft^3}=47040 L$

Then we can use the ideal gas law to find the number of moles of the gas, n:
$pV=nRT$
where
p= 1.00 atm is the pressure
V= 47040 L is the volume of the gas
n is the number of moles
$R=0.082 atm L K^{-1} mol^{-1}$ is the gas constant
$T=20.0^{\circ}=293 K$ is the temperature

Using these data and re-arranging the formula, we find
$n= \frac{pV}{RT}=1957.9 mol$

Then we know that 1 mol of gas contains $N_A = 6.022 \cdot 10^{23}$ molecules (Avogadro number), so the total number of molecules of the air in the problem is
$N= n N_A = (1957.9 mol)(6.022 \cdot 10^{23} mol^{-1})=1.18 \cdot 10^{27}$ molecules.