Question

A gas is heated from 238.3 K to 281.8 K and the volume is increased from 14.4 Liters to 48.5 Liters by moving a large piston within a cylinder. If the original pressure was 1.00 ATM, what would the final pressure be?

Answer 1

To solve this problem, we can use the ideal gas law, which states:

PV = nRT

Where: P = Pressure V = Volume n = Number of moles R = Gas constant T = Temperature (in Kelvin)

In this case, we have the initial and final states of the gas and want to find the final pressure. We can assume that the number of moles and the gas constant remain constant.

For the initial state: P1 = 1.00 ATM V1 = 14.4 Liters T1 = 238.3 K

For the final state: V2 = 48.5 Liters T2 = 281.8 K

Let's first calculate the initial number of moles (n1) using the initial conditions:

PV = nRT

n1 = (P1 * V1) / (R * T1)

Now, we can find the final pressure (P2) using the final conditions:

P2 = (n1 * R * T2) / V2

Substituting the values:

P2 = (n1 * R * T2) / V2 P2 = ((P1 * V1) / (R * T1)) * (R * T2 / V2) P2 = (P1 * V1 * T2) / (V2 * T1)

Now, we can plug in the values to calculate P2:

P2 = (1.00 ATM * 14.4 Liters * 281.8 K) / (48.5 Liters * 238.3 K)

Calculating this expression gives us:

P2 ≈ 1.73 ATM

Therefore, the final pressure would be approximately 1.73 ATM.