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.