Q: A sample of 100 g of pure $$O_2$$ gas is placed in a $$600\ \mathrm{cm}^3$$ container at $$150^\circ C. $$What is the pressure of the gas? (Molar mass of $$O_2 = 32$$\ \mathrm{g/mol}$$, R = 8.31$$\ \mathrm{J/(mol\cdot K)}$$)

$$1.83 \times 10^7$\ \mathrm{Pa}$$

Question 1

Which of the following is a state function in thermodynamics?

Accepted Answer

Internal Energy (U)

Question 2

A sample of 100 g of pure $$O_2$$ gas is placed in a $$600\ \mathrm{cm}^3$$ container at $$150^\circ C. $$What is the pressure of the gas? (Molar mass of $$O_2 = 32$$\ \mathrm{g/mol}$$, R = 8.31$$\ \mathrm{J/(mol\cdot K)}$$)

Accepted Answer

$$1.83 	imes 10^7$\ \mathrm{Pa}$$

Question 3

Which of the following best describes the difference between state functions and path functions?

Accepted Answer

State functions depend only on the initial and final states, while path functions depend on the process taken.

Question 4

The mean free path $$\lambda of a $$gas molecule is given by $$\lambda = \frac{k_B T}{2\pi d^2$ P}. If $$the pressure is doubled while temperature and molecular diameter remain constant, what happens to the mean free path?

Accepted Answer

It is halved.

Question 5

If the root-mean-square speed ($$v_{rms}) of $$the molecules in an ideal gas is doubled, by what factor does the temperature change?

Accepted Answer

It increases by a factor of 4.

Question 6

Which of the following is NOT an assumption of the ideal gas model?

Accepted Answer

There are strong attractive forces between molecules.

Question 7

A cube has a side length of $$10\ \mathrm{cm}. $$What is its volume in liters?

Accepted Answer

1 liter

Question 8

Which law states that for a fixed amount of gas at constant temperature, the pressure is inversely proportional to the volume?

Accepted Answer

Boyle's Law

Question 9

The average kinetic energy of a gas molecule is given by $$K_{ave} = \frac{3}{2} k_B T. $$What happens to the average kinetic energy if the temperature is tripled?

Accepted Answer

It triples.

Question 10

Which of the following quantities is NOT a macroscopic thermodynamic variable?

Accepted Answer

Molecular speed

Question 11

If 1 mole of an ideal gas at STP occupies $$22.4\ \mathrm{L}$$, how many molecules are present in $$1\ \mathrm{L} of $$the gas?

Accepted Answer

$$2.69 	imes 10$$^{22}$$

Question 12

Which of the following is the correct expression for the ideal gas law in terms of the number of molecules $$N$$?

Accepted Answer

$$pV = Nk_B T$$

Question 13

A gas is compressed isothermally. Which of the following statements is true?

Accepted Answer

The internal energy of the gas remains constant.

Question 14

Which of the following best describes the physical meaning of the Boltzmann constant $$k_B$$?

Accepted Answer

It relates the average kinetic energy of particles to temperature.

Question 15

If the temperature of a fixed amount of an ideal gas is increased, which of the following must necessarily increase?

Accepted Answer

The speed of the gas molecules

Question 16

Which of the following is a derived state function that represents the maximum reversible work obtainable from a system at constant temperature and pressure?

Accepted Answer

Gibbs free energy ($$G)$$

Question 17

A gas sample is taken through two different paths from state A to state B. Which of the following quantities will be the same for both paths?

Accepted Answer

Change in internal energy ($$\Delta U)$$

Question 18

Which of the following is the best explanation for why the three-body problem is difficult to solve exactly?

Accepted Answer

The system is highly sensitive to initial conditions and cannot be solved analytically.

Question 19

Which of the following is the correct value for Avogadro's number ($$N_A$$)?

Accepted Answer

$$6.022 	imes 10$$^{23}$$

Question 20

Which of the following is NOT a condition for the ideal gas law to be a good approximation for a real gas?

Accepted Answer

The gas is at a temperature below its condensation point.

Thermodynamics and the Kinetic Theory of Gases: Foundations and Applications

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