# Calculating the Number of Moles of Air in a Soccer Ball

## Question:

## Answer:

0.66 mol## Explanation:

**Given Data:**

Gauge Pressure (P): 61 kPa

Volume (V): 5.2 liters

Air Temperature (T): 32°C

Standard Pressure: 101 kPa

Universal Gas Constant (R): 4.186 J/(mol K)

**Conversion:**

To use the ideal gas law equation (PV = nRT), we need to convert the given units to standard SI units:

1 kPa = 10^3 Pa

1 liter = 10^(-3) m^3

Temperature in Kelvin (T): 32°C + 273 = 305 K

**Calculations:**

1. Convert pressure to Pascals:

P = 61 kPa + 101 kPa = 162 kPa = 162 x 10^3 Pa

2. Convert volume to cubic meters:

V = 5.2 liters = 5.2 x 10^(-3) m^3

3. Substitute the values into the ideal gas law equation:

n = (162 x 10^3) x (5.2 x 10^(-3)) / (4.186 x 305) mol

n ≈ 0.66 mol

Therefore, there are approximately 0.66 moles of air in the soccer ball pumped up by Larisa under the given conditions.