Which of the following effects will make the ratio (PV) / (nRT) less than 1 for a real gas?

a) The gas molecules are large enough to occupy a substantial amount of space.
b) A large number of molecules have speeds greater than the average speed.
c) The gas molecules have a very low molecular weight.
d) The gas molecules attract one another.
e) The gas molecules repel each other.

Well, let's clown around with this question and have some fun!

The correct answer is actually "d) The gas molecules attract one another." Ain't that just the saddest thing? When gas molecules start getting all touchy-feely with each other, the pressure drops and the volume increases, making the ratio (PV) / (nRT) less than 1 for real gases. They're like, "Hey buddy, come closer!" and the other molecules are like, "No way, man! Personal space!" It's a real gas soap opera.

As for the other options, they don't really affect the ratio. Molecule size, fast speeds, low molecular weight, or even repelling each other won't make the ratio less than 1. It's all about that good old attraction game they play.

Well, I hope I didn't gas you out with my clownish explanations! Remember, when gas molecules start cuddling up, the ratio (PV) / (nRT) gets all wacky. Stay gas-tastic!

The effect that will make the ratio (PV) / (nRT) less than 1 for a real gas is:

d) The gas molecules attract one another.

When gas molecules attract each other, it results in lower pressure and a reduced volume compared to an ideal gas. This causes the ratio (PV) / (nRT) to be less than 1.

To determine which effect will make the ratio (PV) / (nRT) less than 1 for a real gas, let's analyze each given option:

a) The gas molecules are large enough to occupy a substantial amount of space.
- This effect would actually increase the ratio (PV) / (nRT), as the gas molecules occupying more space would result in a higher pressure (P) for the same number of molecules (n) and temperature (T). Therefore, option (a) is not the correct answer.

b) A large number of molecules have speeds greater than the average speed.
- The speed distribution of gas molecules follows the Maxwell-Boltzmann distribution, with most molecules having speeds close to the average speed. If a large number of molecules have speeds greater than the average, it would lead to an increase in pressure (P). Therefore, this effect would increase the ratio (PV) / (nRT) rather than making it less than 1. Thus, option (b) is also not correct.

c) The gas molecules have a very low molecular weight.
- Having a low molecular weight means that the gas molecules are lighter and therefore have a higher average speed. Since the ratio (PV) / (nRT) is directly proportional to average speed, a higher average speed would increase the ratio rather than making it less than 1. Thus, option (c) is not correct.

d) The gas molecules attract one another.
- This effect would actually decrease the pressure (P) because the gas molecules are attracting each other instead of colliding with the walls of the container. As a result, the ratio (PV) / (nRT) would be smaller than if there were no attractive forces between the molecules. Therefore, option (d) is a possible correct answer.

e) The gas molecules repel each other.
- Repulsive forces between gas molecules would cause them to occupy a larger volume, resulting in a lower pressure (P). Consequently, the ratio (PV) / (nRT) would be smaller than if there were no repulsive forces. Thus, option (e) is another possible correct answer.

In conclusion, both options (d) and (e) could make the ratio (PV) / (nRT) less than 1 for a real gas.

I think most of this covered in discussions of the "imperfect gas" and the van der Waals equation.