Ah, so these graphs are interesting. Let's take a look at the axes. We have a graph of the expression (PV / RT) vs. pressure (atm). Pressure, we get, and it's on the x-axis, so it should be the independent variable. So we've got samples of gases in some chamber and we vary the pressure and then collect data and plot whatever this expression (PV / RT) represents using the data. Easy! But what does (PV / RT) represent?
Seeing the expression (PV / RT) you should think of the ideal gas law, because all four of those variables are present. The law is of course PV = nRT, and so solving for the expression from the graph we see that (PV / RT) = n. Aha! So the y-axis is number of moles! We're good right? Except wait...
The number of moles shouldn't change in response to pressure right? It's not like we have a hole in the gas chamber and we're leaking gas... So what's the deal? It's the ideal gas law, remember? The number of moles absolutely should be constant no matter how we vary the pressure, as long as were doing so on an ideal gas. In reality there are no ideal gases, so we can't expect that.
So what does this mean for the graph? Well since the x-y graph represents some function f(x) = y and the value of y should be constant for an ideal gas, if we plotted the curve for a hypothetical gas "idealium" we should see a straight horizontal line running parallel to the x-axis. That means any line plotted that isn't perfectly horizontal represents a real gas, exhibiting behavior deviating from that which we would ideally expect. Unsurprisingly, we see that all four gases plotted (real gases, in fact) do so.
Right! Now that we understand the graph, let's turn to the question. The question stem tells us up front that the CO2 plot "actually" represents data collected from CO2 at 313 K. Why the "actually?" What temperature should we have expected? Well, thinking about conducting experiments with gases, and noticing that all plot lines on the graph start from 1.0 on the y-axis, we should probably have expected data from a CO2 sample at STP! That is, 1 mol CO2 at ~ 273 K (we're varying pressure so we can't be locked in at 1 atm). So why did we need to raise the temperature up to 313 K to gather data for CO2? Hmm... Let's check out the answer choices:
(a) CO2 liquefies under low pressure at 300 K.
(b) CO2 liquefies under high pressure at 300 K.
(a) and (b) both refer to a phase change that would make data collection impossible; we can't collect data on gas behavior if our sample stops being a gas, right? So they both sound reasonable so far. Think about the condensation process that would take place as gaseous CO2 condensed to form liquid CO2; it's exothermic (so occurring a lower temperature than what we actually had to use makes sense) and from a kinetic perspective represents molecules gathering and staying closer together. (a) and (b) differ in their stated pressure conditions, so which one better describes conditions allowing molecules to gather and stay closer together? Higher pressure of course! So (a) can't be right over (b). Let's look at the others.
(c) At 300K CO2 behaves like an ideal gas.
Couple things to note here: You should know that the real gas that most closely approximates ideal behavior is helium, and you should know why. CO2 is a bulky molecule compared to He and so probably isn't a good bet in general to ever exhibit ideal behavior. You should also know that ideal behavior is more closely approximated by real gases when the conditions align with the postulates of ideal gas theory (low pressure, high temperature). Thus, CO2 shouldn't behave more ideally at a lower temperature. (c) is out.
(d) At 300K CO2 deviates from ideal behavior.
CO2 deviates from ideal behavior in the graph anyway, that's what we're looking at! So if it behaves non-ideally at 313 K and we were fine with using that temp., similar behavior at 300K can't be a good excuse for avoiding that temperature.
Of all the choices, (b) is the best answer.
