The graph below shows the change in pressure as the temperature increases for a 1-mol sample of a gas confined to a 1-L container. The four plots correspond to an ideal gas and three real gases: CO2, N2, and Cl2. (b) Use the van der Waals constants in Table 10.3 to match the labels in the plot (A, B, and C) with the respective gases 1CO2, N2, and Cl22.

Video transcript

Hello. In this problem, we are asked to consider the following graph, which shows how pressure changes against temperature. Each gas represents one mole of the substance contained in a one liter vessel. On the other hand, the four lines denote an ideal gas and three real gasses, Xenon neon and Krypton, referring to the Vander wal's constants given below were asked to match gasses, X, y and Z. With the gasses, Xenon, neon and Krypton. So vander Waals equation can be written in terms of pressure, pressure then is equal to the molds times of gas constant times temperature divided by the volume minus moles times the Vander wal's constant B minus mole squared times abandoned wells constant A divided by volume squared. And so we have been told that N is equal to one mole and our volume is equal to one leader. So substituting tuning those into the Van der Waals equation, we get them, pressure is equal to R. T. Since mold is one divided by one minus B minus and is one again. So that's just A and volume is one. So it's one squared times 85 by one squared. We now consider the ideal gas equation in terms of pressure, Then moles and volume are again equal to one. So we get this is equal to R. T. You can see that these take the form of a straight line, so we have Y because M X plus B. Where our slope is equal to R Over 1 -7. And were plotting pressure vs temperature. In this case, our slope is just equal to our so looking and comparing the equation for the ideal gas law and that Evander walls law, we see that will approach a real gas when B and A are small and then the soap will be closer to our and intercept will be closer to zero. So when we look at the van der Waals constants that were given neon has the smallest Vander wal's constance for A and B, followed by that for krypton and then xenon. So gas X then, which is closer to ideal. As we see the ideals in the dash blue line gas X is very close to that. So that would be neon and then the green would be krypton and the yellow would be xenon. So these are three gasses and this corresponds to answer B. Thanks for watching. Hope this helps