How many moles of gas must be forced into a 4.8L tire to give it a gauge pressure of 30.8psi at 30 degrees celsius? The gauge pressure is relative to atmospheric pressure. Assume that atmospheric pressure is 14.5L so that the total pressure in the tire is 45.3psi.
What formula do I use?
n=PV/RT where p=guage+atmospheric pressure
Ok thank you so much!
To determine the number of moles of gas required to reach a specific gauge pressure, we can use the Ideal Gas Law equation: PV = nRT.
Here's how to use the formula in this problem:
1. Convert the provided atmospheric pressure from psi to the appropriate unit of pressure. In this case, it is important to keep the units consistent, so we should convert both psi and liters to the unit of pressure that matches the gas constant (R).
The provided atmospheric pressure is 14.5 psi. The gas constant R is 0.0821 L·atm/(mol·K), so we need to convert psi to atm. Divide 14.5 psi by 14.7 psi/atm to get 0.9866 atm.
2. Convert the tire gauge pressure from psi to atm. The gauge pressure is given as 30.8 psi. Again, divide 30.8 psi by 14.7 psi/atm to get 2.0959 atm.
3. Convert the temperature from degrees Celsius to Kelvin. The temperature provided is 30 °C. To convert Celsius to Kelvin, add 273.15 to the Celsius value. So, 30 °C + 273.15 = 303.15 K.
4. Plug the values into the Ideal Gas Law equation (PV = nRT) and solve for n (the number of moles of gas):
n = (PV) / (RT)
n = [(2.0959 atm + 0.9866 atm) × 4.8 L] / [(0.0821 L·atm/(mol·K)) × 303.15 K]
Calculate the value on the right side of the equation and divide it by the value on the left side to get the number of moles (n) required.
n = [(3.0825 atm × 4.8 L) / (24.81615 L·atm/(mol·K))] = 0.5956 moles
So, approximately 0.596 moles of gas must be forced into the 4.8L tire to give it a gauge pressure of 30.8psi at 30 degrees Celsius.