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 ?

I would use PV = nRT and solve for n = numbr of moles of the gas at the third stage (you know P, V, R, and T)

Then double that amount to find moles at stage and solve for P2. Then I believe you can use (P1V1/T1) = (P2V2./T2) and solve for P at the first stage.

I can't solve this question

To solve this problem, we can apply the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.

First, let's solve for the number of moles of gas using the initial conditions:
PV = nRT1
n = PV / RT1

Now, let's use the given information to find the initial pressure, P1. We know that the gas is expanded from 1 L to 100 L while the temperature changes from T1 = 100 K to T2 = 50 K.

n = PV / RT1
n = (P1 * 1L) / (R * 100 K) (1L is the initial volume)
n = (P1 * 1) / (R * 100) (since the volume is in liters)
n = P1 / (100 R)

n = PV / RT2
n = (P3 * V2) / (R * T2) (P3 and V2 are the observed pressure and volume after half the gas is removed)

n = (0.03 atm * 100 L) / (R * 50 K) (substituting the given values)
n = (3 atm L) / (R * 50)

Since both expressions for n represent the same number of moles of gas, we can set them equal to each other:

P1 / (100 R) = (3 atm L) / (R * 50)

To simplify this equation, we can cancel out the R terms:

P1 / 100 = 3 / 50

Now, we can solve for P1:

P1 = (3 / 50) * 100
P1 = 6 atm

Therefore, the initial pressure, P1, is 6 atm.