Chemistry exercise about gas laws

Question

A sample of gas has an initial volume of 545 mL and an initial temperature of 298 K. If the volume is changed to 495 mL, what is the new temperature? Assume pressure and amount remain constant. Express your answer to three significant figures.

I know i have to change the mL to L.

Answer 1

You will actually not have to convert to L.

For equations like this you will need to use the ideal gas law PV=nRT.

First we ask what is changing?

The equation tells us that the volume changes and asks us to find the new temperature. We know that temp (T) and volume (V) will change.

Second ask what values stay the same?

In this equation we are told that the amount of gas doesn't change so n is a constant in this scenario.

We are told that P does not change, so P is a constant in this scenario.

R is always a constant.

We can rearrange the ideal gas law so that all of the values that stay the same are on one side and all of the values that change are on the other side.

PV=nRT dividing both sides by P*T yeilds:

V/T=nR/P Becuase n, R, and P are constants we know that nR/P is constant. Therefore

V/T = (constant) at any given time.

We don't need to calculate what this constant is. Because the ratio of volume to temperature (V/T) is constant in this scenario, we know that the V/T before the expansion is the same as V/T after the expansion.

V₁/T₁=V₂/T₂

Now you can plug un your V₁ and T₁ from before the expansion and V₂ from after the expansion to solve for the Temperature after the expansion.

Because this is a ratio, it doesn't matter what your units are as long as long as they are measured in absolute units. This means that volume can be measured in any unit (gal, mL, L, cubic feet, ect), but temperature must be in °K.