Question

Larisa pumps up a soccer ball until it has a gauge pressure of 61 kilopascals. The volume of the ball is 5.2 liters. The air temperature is 32°C, and the outside air is at standard pressure. How many moles of air are in the ball?

Answer 1

The total ball pressure is sum of gauge pressure and atmospheric pressure

We know that atmospheric pressure = 101.325 kPa

so the total ball pressure = 61 kPa + 101.325 kPa = 162.325 kPa

Now we will use ideal gas equation as

PV = nRT

P = pressure = 162.325 kPa

V = 5.2 L

R = gas constant = 8.314 kPa L / mol K

T = 32 C = 273.15 + 32 = 305.15 K

n = moles = ?

Moles = PV / RT = 162.325 kPa X 5.2 / 305.15 X 8.314 = 0.332 moles