Hii:) anyone able to explain and help me with this question?

A fixed mass of gas is heated while kept at constant volume. Does the average distance apart change?

Thank you!

No

Explanation:

The equation of state for ideal gases tells that:

where

p is the gas pressure

V is the gas volume

n is the number of moles of the gas

R is the gas constant

T is the absolute temperature

In this problem, we have a fixed mass of gas. This means that the number of moles of the gas, , does not change; also, the volume V remains the same, and R is a constant, this means that

So, as the pressure increases, the temperature increases.

However, here we want to understand what happens to the average distance between the molecules.

We have said previously that the number of moles n does not change: and therefore, the total number of molecules in has does not change either.

If we consider one dimension only, we can say that the average distance between the molecules is

where L is the length of the container and N the number of molecules. Since the volume of the container here does not change, L does not change, and since N is constant, this means that the average distance between the molecules remains the same.