# IMAT 2018 Q50 [Ideal Gases]

A sealed container contains 1.00 mol of hydrogen gas, which behaves as an ideal gas.

Which of the following changes increase(s) the total kinetic energy of the hydrogen gas molecules initially within the container?

1. Changing the amount of hydrogen from 1.0 mol to 1.2 mol whilst keeping the pressure and volume constant.

2. Changing the pressure from 1.0 atm to 1.2 atm whilst keeping the volume and number of moles constant.

3. Changing the volume from 1.0 L to 1.2 L whilst keeping the pressure and number of moles constant.

A. 3 only
B. 2 and 3 only
C. 1, 2 and 3
D. 1 and 2 only
E. 1 only

Key to solving this question:

Kinetic Theory of Matter (Collision Theory)

The average kinetic energy of the particles is directly related to the temperature of the system.

Each particle has different Kinetic Energy (KE) because of the random nature of motion - the average of the KE values relates directly to temperature (K)

We must remember that increasing temperature increases kinetic energy (KE), they are directly proportional to each other. Higher temperature means particles have higher energy. To find out if the temperature is going to change based on the parameters in this question, we need to use the ideal gas equation: PV=nRT

1) P and V are constant, increasing concentration from 1.0 mol to 1.2 mol Hydrogen will decrease kinetic energy.

Why?

PV=nRT, we are focused on n and T here. n represents the concentration here and T represents temperature. When P and V are constant, n and T become inversely proportional, if one increases the other must decrease in order to maintain our constant pressure and volume. In 1), we are asked to increase ‘n’, and since we have explained that T and n are inversely proportional, increasing n will result in a decrease in T. A decrease in T results in a decrease in kinetic energy, since they are directly proportional to each other. There 1) does not cause a decrease in KE.

2) Here V and n are constant, while we are increasing pressure.

PV = nRT, but if V, n, and R (already a constant) are going to remain unchanged, then the equation becomes P ∝ T since they are the only things changing here (∝ means proportional to). This would mean that increasing P will result in an increase of T, and therefore an increase in kinetic energy. So 2) results in an increase in KE.

3) Pressure and moles are constant. Increasing V.

PV = nRT, but becomes V ∝ T because P, n, R are all constant. Similar to 2), we can see that increasing V will also increase T, and therefore will result in an increase in KE.

\fcolorbox{red}{grey!30}{Since 2) and 3) are correct, the answer must be B.}