A gas is expanded from an initial volume of 10 L at 0.92 atm at 23 °C to a final volume of 30 L. During the expansion the gas cools to 12 °C. What is the final pressure?

Question

Chemistry

Atticus Marks

6 April, 08:34

A gas is expanded from an initial volume of 10 L at 0.92 atm at 23 °C to a final volume of 30 L. During the expansion the gas cools to 12 °C. What is the final pressure?

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Boris · Answer 1

Recall the ideal gas law:

PV = nRT where P is pressure in atm, V is volume in liters, n is moles, R is the ideal gas constant, and T is temperature in Kelvin.

The ideal gas constant R = 0.0821 L*atm / (mol*K)

When we calculate our final pressure, we are going to want to rewrite the equation for P in terms of moles, volume, and temperature.

P = nRT / V

We know that at the second temperature, the V = 30 L, and T = 285.15 degrees K (convert 12deg celcius to kelvin). The only information we are missing is the number of moles.

We know that n₁ = n₂; that is, the number of moles in the container is constant no matter the pressure, temperature, or volume. So we can use the data we're given for the initial conditions to solve for the number of moles.

Rewriting the ideal gas law gives us:

n = PV/RT

Under the initial conditions, P = 0.92 atm, T = 296.15 K, and V = 10 L.

Plug these values in and solve for the number of moles, which you can then plug into the original equation with the final temperature and volume, to solve for the final pressure.

P (final) = nRT/V

This should be enough information to solve the problem.