Larisa Pumps Up a Soccer Ball: How Many Moles of Air Are in the 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?

Answer Choices:

A. 0.13 mol

B. 0.33 mol

C. 1.2 mol

D. 3.2 mol

Answer:

B. 0.33 mol

Explanation:

We are given:

Gauge pressure, P = 61 kPa (1 atm = 101.325 kPa) = 0.602 atm

Volume, V = 5.2 liters

Temperature, T = 32°C, but K = °C + 273.15 thus, T = 305.15 K

We are required to determine the number of moles of air. We are going to use the concept of the ideal gas equation.

According to the ideal gas equation, PV = nRT, where P is the pressure, V is the volume, R is the ideal gas constant (0.082057 L.atm mol.K), n is the number of moles, and T is the absolute temperature.

Total pressure = Atmospheric pressure + Gauge pressure

Total ball pressure = 1 atm + 0.602 atm = 1.602 atm

Therefore:

n = (1.602 atm × 5.2 L) / (0.082057 × 305.15 K) = 0.3326 moles ≈ 0.33 moles

Therefore, there are 0.33 moles of air in the ball.

How much gauge pressure does Larisa pump up the soccer ball to?

Larisa pumps up the soccer ball to a gauge pressure of 61 kilopascals, which is equivalent to 0.602 atm.