(a) Select a set of data points from the table below and plot those points on a graph to determine whether the gas exhibits properties of an ideal gas. Fill in blank columns in the table for any quantities you graph other than the given data. Label the axes and indicate the scale for each. Draw a best-fit line or curve through your data points.
(b) Indicate whether the gas exhibits properties of an ideal gas, and explain what characteristic of your graph provides the evidence.
(c) The students repeat their experiment with an identical container that contains half as much gas. They take data for the same values of volume and temperature as in the table. Would the new data result in a different conclusion about whether the gas is ideal? Justify your answer in terms of interactions between the molecules of the gas and the container walls.

Video Transcript

This is College Physics Answers with Shaun Dychko. A clear plastic container has some gas in it and a movable piston and some students are doing some measurements of the absolute gas pressure, the volume of gas and its temperature in Kelvin and we are going to plot some data on a graph to determine whether this gas resembles an ideal gas and I have created a Google spreadsheet and I will share a link to this in the answer and I have copied the data table here it's absolute gas pressure in, you know, newtons per meter squared (I suppose I should write that down there) and the volume in meters cubed here, the absolute temperature in Kelvin and here's the column that I have added, which is the reciprocal of the volume and so there's a formula here, which says 1 divided by the number in this column C and so this is 1 over C row 2, this is 1 over C 3 and this is 1 over C 4 and so on. Okay! We are going to create three different graphs, one for each temperature. So at 270 Kelvin, we have these pressures versus these reciprocal volumes and that's what's plotted in this graph here. And we can see that when we put a trend line in, the trend line is a nice straight line and there's a linear relationship between pressure and reciprocal of the volume and then we do the same at 290 Kelvin and so that's the graph here is plotting these pressures from here to here and these reciprocal volumes here and then likewise at 310 Kelvin, we have another linear relationship. So three linear relationships showing that pressure is linear function of 1 over volume and we expected that because when you have this PV equals nRt—ideal gas law— and you rearrange to solve for P... (let me just breakdown what I am saying here I guess) so PV equals nRT and then you divide both sides by V, you end up with this here and I put a subscript 1 on here to say this is the first case versus part (c) where we consider the second case otherwise just ignore the subscript 1 here for now. So pressure is a bunch of things divided by volume and all of these things can be summarized in a single factor m and I chose the letter m because this is resembling a linear relationship y equals mx plus b where b is 0 and x is 1 over V and m is nRT. Okay! So because the graph is linear, we have shown that the gas is following the ideal gas law in which case, it must be an ideal gas. Now in part (c), if you have half as much gas, this pressure in this second case will be some new number of moles times the gas constant times temperature over volume and this new number of moles is the old number that we had before divided by 2 and so we have one-half n 1RT over V and n 1RT over V is P 1 so we expect half the pressure and we still expect to see an ideal gas because it should still follow the same pattern, you know, with respect to having this ideal gas law apply. And in terms of... the question asks us justify your answer in terms of interactions between the molecules of the gas and the container walls. Well, there will be half as many molecules and so there will be half as many collisions with the container wall and so that's explaining why the pressure will be half but it will still follow the ideal gas law and still have a linear relationship for the slope; the slope should be... a half of what it was before so slope two will be half of slope one and because it is now n 1 over 2 RT is slope two and that's half of what m 1 was up here.