How Much Gas Leaked from the Tank?

[format1998]

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. Please help! Any & all help is much appreciated! Thank you in advance for your time...

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Andrew Mason]

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

 

[format1998]

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?

 

[Andrew Mason]

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

 

[ehild]

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

 

[format1998]

Thank you to both of you :)