Question 1

Which of the following is NOT an assumption of the kinetic-molecular theory for an ideal gas?

Accepted Answer

Molecules attract each other strongly at all times.

Question 2

The Maxwell–Boltzmann distribution function $$f(v)$$ describes the probability that a randomly chosen molecule has a speed between $$v$$ and $$v + dv. $$Which mathematical expression best represents the behavior of $$f(v)$$ for large values of $$v$$?

Accepted Answer

$$f(v) \sim \$$exp(-mv^2$$/2kT)$$

Question 3

In the experiment shown in the first image, what is the primary purpose of the rotating disks?

Accepted Answer

To select molecules of a specific speed for detection.

Question 4

According to the Maxwell–Boltzmann distribution, what happens to the most probable speed $$v_{mp} as $$the temperature of the gas increases?

Accepted Answer

$$v_{mp}$$ increases.

Question 5

Which of the following statements about the distribution of molecular speeds in a gas is correct?

Accepted Answer

The fraction of molecules with speeds greater than $$v_A is $$given by the area under $$f(v)$$ for $$v \u003e v_A.$$

Question 6

If the temperature of a gas is increased from $$T_1 to$$ $$T_3$$, as shown in the third image, what happens to the shape of the Maxwell–Boltzmann distribution curve?

Accepted Answer

The curve flattens and shifts to higher speeds.

Question 7

A gas sample is contained in a rigid, fixed-volume container. If the temperature is doubled, what happens to the average kinetic energy of the molecules?

Accepted Answer

It doubles.

Question 8

Which of the following best describes an elastic collision between gas molecules?

Accepted Answer

The total kinetic energy is conserved.

Question 9

In the context of the kinetic-molecular theory, why are gas molecules considered 'point particles'?

Accepted Answer

Because their size is much smaller than the average distance between molecules.

Question 10

A scientist measures the speed distribution of molecules in a gas using the apparatus shown in the first image. If the slits are narrowed, what effect does this have on the measurement?

Accepted Answer

It allows for more precise selection of molecular speeds.

Question 11

Which equation gives the most probable speed $$v_{mp}$$ for molecules in an ideal gas?

Accepted Answer

$$v_{mp} = \sqrt{\frac{2kT}{m}}$$

Question 12

If a gas sample is cooled, what happens to the fraction of molecules with speeds greater than a fixed value $$v_A$$?

Accepted Answer

It decreases.

Question 13

Which of the following is a real-world application of the Maxwell–Boltzmann distribution?

Accepted Answer

Predicting the rate of chemical reactions in the atmosphere.

Question 14

A container of gas is placed in a laboratory oven and heated. Which statement best describes the effect on the molecular speed distribution?

Accepted Answer

The distribution flattens and the peak moves to higher speeds.

Question 15

Which of the following best explains why the Maxwell–Boltzmann distribution is not symmetric about the most probable speed $$v_{mp}$$?

Accepted Answer

Because the distribution is skewed due to the exponential decay at high speeds.

Question 16

In the context of the kinetic-molecular theory, what is the significance of the Avogadro number $$N_A$$?

Accepted Answer

It represents the number of molecules in a mole.

Question 17

A student claims that increasing the volume of a gas container while keeping temperature constant will increase the average speed of the molecules. Is this correct?

Accepted Answer

No, because the average speed depends only on temperature.

Question 18

Which of the following best describes the relationship between temperature and the width of the Maxwell–Boltzmann speed distribution?

Accepted Answer

Higher temperature results in a wider distribution.

Question 19

In a real-world scenario, why is it important that collisions between gas molecules are elastic?

Accepted Answer

Elastic collisions ensure that the total kinetic energy is conserved, allowing the gas to maintain its temperature.

Kinetic Molecular Theory and Molecular Speed Distributions

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