# Ideal Gas - tank sprung a leak

• format1998
In summary, the problem involves a fixed volume tank filled with an ideal gas at a given pressure and temperature. Due to a leak, some of the gas escapes and the pressure and temperature in the tank changes. The task is to determine the amount of gas that has leaked from the tank, given the final pressure and temperature. To solve this, the final number of moles of gas must be calculated using the ideal gas law, and then subtracted from the initial number of moles to get the amount of gas that has escaped.

## Homework Statement

A tank with a fixed volume of 0.0800 m3 is filled with an ideal gas at a pressure of 4.00 atmospheres and a temperature of 48.0° C. Due to a small leak, some of the gas leaks out. Later it is found that the pressure in the tank is 3.20 atmospheres when the temperature is 20.0° C. How much of the gas leaked from the tank?

## Homework Equations

PV=nRT -> n=PV/RT

## The Attempt at a Solution

I solved for the initial number of moles using the initial values
n= [(405.2E3 Pa)(0.08m3)]/[(8.314 J/mol*K)(321K)]=12.1463 mol

I thought I could get the final volume by using
(P1*V1)/T1 = (P2*V2)/T2

and after I obtain V2, I thought I could get the number of moles so that i could plug it into n=PV/RT to get the final number of moles left

and then use the initial numbers of moles and subtract the numbers of moles left in order to give me the # of moles that escaped.

But ofcourse, the answer I came up with was ridiculous. I had a higher V2 than V1, which ofcourse doesn't make sense when some of the gas supposedly leaked out into the environment.

## The Attempt at a Solution

You are just interested in knowing the number of moles of gas still in the tank - so that is the final volume. Since you know the final P, V and T, just determine the final n from that.

You can only use PV/T = constant (=nR) if n is constant. But n is obviously not constant in this case.

AM

Andrew Mason said:
Since you know the final P, V and T, just determine the final n from that.

Even though some of the gas leaked out into the environment, the final Volume of the gas remains as 0.08 m3? Is this what you mean by knowing the final Volume?

format1998 said:
Even though some of the gas leaked out into the environment, the final Volume of the gas remains as 0.08 m3? Is this what you mean by knowing the final Volume?
Yes. The pressure and temperature given (3.2 atm and 20C) is of the gas that is left in the tank after the leak occurs.

AM

format1998 said:
Even though some of the gas leaked out into the environment, the final Volume of the gas remains as 0.08 m3?

You certainly have learned that the gas always fills the whole space available in the container. Gases do not have own volume: The volume is that of the container.

ehild

Thank you to both of you :)