How many moles of gas must be forced into a 3.7L ball to give it a gauge pressure of 8.4psi at 23degrees C? The gauge pressure is relative to atmospheric pressure. Assume that atmospheric pressure is 14.6psi so that the total pressure in the ball is 23.0psi
Jessica, I think I worked this for you last night at the original post. I can try to find that if you can't locate it.
To find the number of moles of a gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the temperature from Celsius to Kelvin by adding 273:
23°C + 273 = 296 K
Now, let's convert the pressure from psi to atmospheres:
8.4 psi = (8.4 / 14.6) atmospheres ≈ 0.5753 atmospheres
The total pressure in the ball is given as 23 psi, which we'll also convert to atmospheres:
23 psi = (23 / 14.6) atmospheres ≈ 1.5753 atmospheres
Now we can rearrange the ideal gas law equation to solve for moles:
n = PV / RT
n = (1.5753 - 0.5753) atmospheres * 3.7 liters / (0.0821 L·atm/mol·K * 296 K)
n ≈ 0.6649 moles
Therefore, approximately 0.6649 moles of gas must be forced into the 3.7 L ball to achieve a gauge pressure of 8.4 psi at 23°C.