Question

Question:A 1-L sample of CO initially at STP is heated to 546⁰C, and its volume is increased to 2-L. (a) What effect do these changes have on the number of collisions of the molecules of the gas per unit area of the container wall? (b) What is the effect on the average kinetic energy of the molecules? (c) What is the effect on the root mean square speed of the molecules?

Short answer

1. The collision will not change.
2. The average kinetic energy increases.
3. The root mean square increases by $\sqrt{2}$ times.

Step-by-step solution

Define Gas

A gas is made up of particles with no definite volume or structure.

Explanation of the effect

1. The number of collisions between the gas molecules per unit area of the container wall does not change. Therefore, it remains constant.

Explanation of the effect on average kinetic energy

b. The temperature goes up. As a result, because kinetic energy is related to temperature, the average kinetic energy rises as well. Therefore, the temperature increases.

Explanation of the effect on root mean square

c. The root mean square is obtained as:

$\begin{array}{c}{\mathrm{u}}_{\mathrm{r}\mathrm{m}\mathrm{s}}=\sqrt{\frac{2\mathrm{K}{\mathrm{E}}_{\mathrm{a}\mathrm{v}\mathrm{g}}}{\mathrm{m}}}\\ ={\mathrm{u}}_{\mathrm{r}\mathrm{m}\mathrm{s}}\alpha \sqrt{2\mathrm{K}{\mathrm{E}}_{\mathrm{a}\mathrm{v}\mathrm{g}}}.\end{array}$

Therefore, the root mean square increases by the value of $\sqrt{2}$ times.