Initial Pressure: Calculate Using PV=nRT

[gwiber]

1. A fixed amount of gas initially at 100 K and pressure P1 is expanded from 1 L to 100 L in a piston. The temperature, T2, of the gas at this point is 50 K. The piston is then locked at constant volume V2=100 L and half the gas is pumped out at a constant temperature of T2 . The observed pressure, P3, after half the gas is removed under these conditions is 0.03 atm. What was the initial pressure, P1 ?



2. PV = nRT

The Attempt at a Solution

 

[ptolema]

You need to use combined gas law here. First, use combined gas law for P3 and P2 to determine P2. Then you can use P2 with combined gas law to find P1.

 

[amal]

Start from the last step. Here, V and T are constant. So, use $\frac{P_{1}}{n_{1}}=\frac{P_{2}}{n_{2}}$. Then use $\frac{P_{1}V_{1}}{T_{1}}=\frac{P_{2}V_{2}}{T_{2}}$ to get final answer.