How Many Moles of Gas Must Be Forced into a 3.6 L Ball?
What is the required number of moles of gas?
How many moles of gas must be forced into a 3.6 L ball to give it a gauge pressure of 8.4 Psi at 23 ∘C?
Answer:
Approximately 2.27 moles of gas must be forced into the 3.6 L ball to give it a gauge pressure of 8.4 psi at 23°C.
To calculate the number of moles of gas required, we can utilize the ideal gas law equation:
PV = nRT
Where:
- P is the ball's total internal pressure (23.3 psi)
- V is the ball's volume (3.6 L)
- n is the number of moles of gas we need to find
- R is the ideal gas constant (0.0821 L atm/(mol K))
- T is the temperature in Kelvin (23°C = 296 K)
The gauge pressure must be converted to absolute pressure by adding the atmospheric pressure. We know that the total pressure in the ball is 23.3 psi, which includes the gauge pressure and the atmospheric pressure.
Next, we convert the temperature from Celsius to Kelvin by adding 273.15 to 23°C, resulting in 296 K.
By rearranging the ideal gas law equation and plugging in the given values, we can solve for the number of moles of gas (n).