Q: Which equation correctly expresses Dalton’s Law of Partial Pressures for a mixture of ideal gases?

$$p_{\text{total}} = p_A + p_B + p_C$$

Q: Which of the following is NOT a correct way to express the composition of a solution?

Partial pressure: $$p_A = x_A + p_{\text{total}}$$

Question 1

Which of the following best describes a homogeneous mixture?

Accepted Answer

A mixture in which the composition is uniform throughout and the components are not visually distinguishable.

Question 2

Which equation correctly expresses Dalton’s Law of Partial Pressures for a mixture of ideal gases?

Accepted Answer

$$p_{	ext{total}} = p_A + p_B + p_C$$

Question 3

A solution is prepared by dissolving 0.5 mol of NaCl in 1.0 kg of water. What is the molality of the solution?

Accepted Answer

0.5 mol/kg

Question 4

Which of the following is the correct expression for the chemical potential $$\mu_i of $$component $$i in a $$mixture?

Accepted Answer

$$\mu_i = \left( \frac{\partial G}{\partial n_i} \right)_{T,p,n'}$$

Question 5

If 2.00 L of He at 1.50 bar and 2.00 L of Ne at 1.50 bar are mixed in a 4.00 L container at constant temperature, what is the partial pressure of He in the final mixture?

Accepted Answer

0.75 bar

Question 6

Which of the following statements about chemical potential is TRUE for a mixture?

Accepted Answer

The chemical potential of a component in a mixture depends on the composition of the mixture.

Question 7

Given the Gibbs-Duhem equation for a binary mixture at constant $$T$$ and $$p$$: $$n_A d\mu_A + n_B d\mu_B = 0$$, what does this imply about the chemical potentials?

Accepted Answer

If the chemical potential of A increases, the chemical potential of B must decrease.

Question 8

Which of the following is NOT a correct way to express the composition of a solution?

Accepted Answer

Partial pressure: $$p_A = x_A + p_{	ext{total}}$$

Question 9

A mixture contains 0.121 mol He, 0.303 mol Ne, and 0.0403 mol Xe in a 6.00 L container at 298 K. What is the mole fraction of Ne?

Accepted Answer

0.464

Question 10

Which of the following best explains why the chemical potential of a component in a mixture is not equal to its molar Gibbs energy in the pure state?

Accepted Answer

The molecular environment and composition change in a mixture, affecting the contribution to the Gibbs energy.

Question 11

Which equation describes the total Gibbs energy $$G$$ for a binary mixture?

Accepted Answer

$$G = n_A \mu_A + n_B \mu_B$$

Question 12

Which of the following is a real-life example of a homogeneous mixture?

Accepted Answer

A glass of salt water

Question 13

If the partial pressure of gas A in a mixture is 0.501 bar and the total pressure is 1.92 bar, what is the mole fraction of gas A?

Accepted Answer

0.261

Question 14

Which of the following statements about the effect of adding 1 mole of a component to a pure substance versus a mixture is correct?

Accepted Answer

In a pure substance, the effect on Gibbs energy is the same for every mole added.

Question 15

Which of the following is the correct form of the van’t Hoff equation for osmotic pressure?

Accepted Answer

$$\Pi = iBRT$$

Question 16

Which of the following is a key difference between a pure substance and a mixture regarding chemical potential?

Accepted Answer

A pure substance has one value for chemical potential, while a mixture has a different chemical potential for each component.

Question 17

Which of the following best describes the physical meaning of the chemical potential $$\mu_i$$?

Accepted Answer

It is the change in Gibbs free energy when one additional mole of a component is added at constant temperature and pressure.

Question 18

A mixture of gases contains 0.121 mol He, 0.303 mol Ne, and 0.0403 mol Xe in a 6.00 L container at 298 K. What is the total pressure of the mixture? (Use $$R = 0.08314 L$$·bar·K$$^{-1}$$·mol$$^{-1})$$

Accepted Answer

1.92 bar

Question 19

Which of the following is the correct form of the Gibbs-Duhem equation for a binary mixture?

Accepted Answer

$$n_A d\mu_A + n_B d\mu_B = 0$$

Thermodynamics of Simple Mixtures: Definitions, Properties, and Chemical Potential

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