Question

An air mattress is filled with 16.5 moles of air. The air inside the mattress has a temperature of 295 K and a gauge pressure of 3.5 kilopascals. What is the volume of the air mattress?
The volume of the air mattress is__liters.

Answer 1

PV=nRT
3.5×X=16.5×0.082×295
X= 114 L
The volume of the air mattress is 114 liters.

Answer 2

Explanation:

According to ideal gas equation, product of pressure and volume equals n times R times T.

Mathematically,         PV = nRT

where       P = pressure

                 V = volume

                 n = number of moles

                 R = gas constant

                 T = temperature

Therefore, it is given that no. of moles is 16.5 mol, pressure is 3.5 kilopascal equals 0.035 atm (as 1 Kpa = 0.01 atm), temperature is 295 K and R = 0.082 $LatmK^{-1}mol^{-1}$.

Hence, calculate the volume as follows.

                                   PV = nRT

                          $0.035 atm \times V = 16.5 mol \times 0.082 L atmK^{-1}mol^{-1} \times 295 K$

                                 V = $\frac{399.135 L atm}{0.035 atm}$

                                     = 11403.85 L

Hence, we can conclude that the volume of the air mattress is 11403.85 liters.