Consider two identical containers, one contains 1.5 moles of nitrogen gas at 250K and the other contains 1.5 moles of nitrogen gas at 350K. Which of the following statements is TRUE? *
0 points

The pressure exerted by the nitrogen gas (N2) is the same in both containers
The average speed of the nitrogen gas (N2) molecules is higher in container #1 than in container #2
The rate at which nitrogen gas (N2) molecules collide with the container walls is lower in container #1 than in container #2
The average kinetic energy of the nitrogen gas (N2) molecules is the same in both containers

We want to see which of the given statements is true for the identical containers with nitrogen gas.

The correct statement is:

"The rate at which nitrogen gas (N2) molecules collide with the container walls is lower in container #1 than in container #2"

Remember the ideal gas equation:

P*V = n*R*T

Where P is the pressure, V is the volume, n is the number of moles, R is a constant, and T is the temperature.

Both gases are in identical containers, so both have the same volume. Also both containers have 1.5 moles of nitrogen, so n is the same number for both containers, and R is a constant, so it is the same for both.

The thing that is different is the temperature, for container 1 we have a temperature of 250K, while for container 2 we have a temperature of 350K, then we can write two pressure equations:

[tex]P_1 = \frac{n*R}{V}*(250k)\\\\P_2 = \frac{n*R}{V}*(350k)[/tex]

Where n*R/V is a constant term.

Then is really clear to see that the pressure exerted by nitrogen will be larger in container 2, because it increases linearly with the temperature and the temperature is larger in container 2.

Also remember that increases in temperature manifest as an increase in the kinetic energy of the molecules of the gas, thus, the container with a larger temperature will have molecules with larger kinetic energy (thus, larger mean velocity)

From the given statements, the only one that is true is:

"The rate at which nitrogen gas (N2) molecules collide with the container walls is lower in container #1 than in container #2"

This collision with the walls is a representation of pressure, this says that container 1 has less pressure than container 2, which is true.

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