Calculating the Number of Moles of Air in a Soccer Ball

Question:

How many moles of air are in the soccer ball pumped up by Larisa until it has a gauge pressure of 61 kilopascals, with a volume of 5.2 liters at an air temperature of 32°C?

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.

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