how to find the volume of a gas

Question

A quantity of an unknown gas is placed in a volume-adjustable cylinder. The temperature is
36.0ºC and the volume is set at 8.1 L. Then the temperature is raised to 250.0ºC and the volume is
adjusted so that the pressure is the same as before. What is the new volume?

Answer 1

To solve this problem, we can use Charles's law, which shows us how the volume of gas will change as we change the temperature of the system. Charles's law is written as:

 

V1 / T1 = V2 / T2

 

Since we know the starting volume is 8.1L, we would say that V1 = 8.1L. We know that the starting temperature is 36C, so we convert to kelvin by adding 273 and say that T1 = 36+273. Then, we shift the temperature up to 250C; this is our second temperature! We can now write T2 = 250+273, because we have to convert to Kelvin again for Charles's law to work. Once we fill in this information, the only variable left is V2, which is the quantity of interest. 

 

Let's rearrange the equation to solve for V2 by multiplying both sides of the equation by T2 to give:

 

V1T2 / T1 = V2

 

If we plug in our information we get:

 

(8.1L * (250+273)) / (36+273) = V2

 

Simply plug and chug to solve!

 

We check this conceptually to see that V2 will come out in liters by looking at the units. In the equation above we have:

 

(Liters * Kelvin) / Kelvin

 

Since Kelvin on top and Kelvin on the bottom cancel each other out, the only remaining unit is liters, the unit of our answer!

 

Hope that helps!

Answer 2

Since the pressure is constant. You would not have to worry about it in the equation. The things that change would be temperature and volume. This means that you would have to use Charles' law to solve this. 

 

Charles' law is V1/T1=V2/T2 make sure that the temperature is in Kelvin =C+273

 

in this case your equation would be 8.1L/309K=V2/523K. Solve for V2.