Which graph could represent the
result of pressure times volume, 𝑃𝑉, for an ideal gas versus its volume at
We want to construct a graph of the
pressure times volume versus the volume for an ideal gas, which means that the
pressure times volume should go on the 𝑦-axis and the volume should go on the
𝑥-axis. Since we’re interested in the
behavior of an ideal gas, we can use the ideal gas law to create an expression that
we can graph. We want an expression where the
pressure times volume will be on one side of the equation, where we can graph it as
𝑦, and the volume should be on the other side of the equation, where we can graph
it as 𝑥.
Just looking at the ideal gas law,
we already have the pressure times volume on one side of the equation. But the volume isn’t present on the
other side of the equation. This may seem a little strange at
first. But all this means is that the
pressure times volume and the volume are independent of each other. Before we graph, let’s take a look
at the right-hand side of the equation.
The question tells us that we’re at
a constant temperature. So 𝑇 is a constant. 𝑅 is the gas constant. So that’s a constant as well. 𝑛 is the amount of the gas that we
have in moles. Assuming we have a sample of gas in
a container, this would be constant too. Since everything on the right-hand
side of the equation was a constant, we can combine them into one constant, which
I’ll call 𝐶. Now, this looks quite a bit like
Boyle’s law, which tells us that the pressure and the volume are inversely
proportional to one another. Or you can express it as the
pressure times the volume is equal to a constant.
Now, we’re ready to graph. If you’re a little confused about
what 𝑃𝑉 equals 𝐶 should look like, you can imagine graphing something where 𝑦 is
also equal to a constant, such as 𝑦 equals five. This would be a straight horizontal
line, which matches answer choice B, which is the correct graph to represent the
pressure times volume of an ideal gas versus its volume.