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

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.