Calculating the Number of Moles of Air in a Soccer Ball

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?

The total ball pressure is the sum of gauge pressure and atmospheric pressure. We know that atmospheric pressure is 101.325 kPa, so the total ball pressure is 61 kPa + 101.325 kPa = 162.325 kPa.

Now we will use the ideal gas equation:

PV = nRT

Where:

• P = pressure = 162.325 kPa
• V = 5.2 L
• R = gas constant = 8.314 kPa  L / mol K
• T = 32°C = 305.15 K
• n = moles = ?

Therefore, to calculate the number of moles:

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

How did we calculate the number of moles of air in the soccer ball?

We calculated the number of moles using the ideal gas equation, which involves the pressure, volume, gas constant, and temperature of the air inside the soccer ball.