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?
A.
0.13 mol
B.
0.33 mol
C.
1.2 mol
D.
3.2 mol

Answer 1

Answer:

B.  0.33 mol

Explanation:

We are given;

Gauge pressure, P = 61 kPa (but 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 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.

• Therefore, to find the number of moles we replace the variables in the equation.
• Note that the total ball pressure will be given by the sum of atmospheric pressure and the gauge
• Therefore;
• Total pressure = Atmospheric pressure + Gauge pressure  

       We know atmospheric pressure is 101.325 kPa or 1 atm

Total ball pressure = 1 atm + 0.602 atm

                               = 1.602 atm

That is;

PV = nRT

n = PV ÷ RT

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.