Question

How many air molecules are in a 11.5×12.0×10.0 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.

Answer 1

In order to determine how many molecule of air you have, you must determine how many moles you have in the room. Before calculating the number of moles you have, convert the volume from cubic feet to liters

V_room=11.5 x 12.0 x 10.0=1380 ft³

If we convert to liters

1380 ft³ x 28.2 L / 1 ft³ = 38,916 L

Now using ideal equation we can find out the moles of gas

PV = nRT

where:

P is the pressure of the gas = 1 atm

V is the volume of the gas = 38916

n is the amount of substance of gas (in moles)

R is gas constant = = 0.0821 L atm K-1 Mol-1

T is the absolute temperature of the gas = 273.15 + 20 = 293.15

substitute in the equation and calculate n

n = 1 x 38916 / 0.0821 x 293.15 = 1616.944 Moles

Since 1 mole of a substance is defined as containing 6.022x10²³ molecules of that substance - this is known as Avogadro's number - the total number of molecules of air in the room will be

The total number of molecules in the room = 1616.944 x 6.022x10²³  = 9.738 x 10²⁶ Molecules