Chemical Equilibrium II

Homework 5 Solutions have not been released yet.

• All questions are multiple-choice questions with five options (A–E). Only one answer is correct.
• Assume ideal-gas behavior throughout.
• Unless otherwise stated, equilibrium constants are dimensionless, with standard pressure $p^\circ=1\ \mathrm{bar}$ and standard concentration $c^\circ=1\ \mathrm{mol\,L^{-1}}$.
• Use $R=8.314\ \mathrm{J\,mol^{-1}K^{-1}}$ or $R=0.08314\ \mathrm{L\,bar\,mol^{-1}K^{-1}}$, as appropriate.
• Show the relevant equilibrium expressions and calculations.
• Round numerical answers appropriately.

Problem 1Easy

Calculating the Equilibrium Constant

For the reaction

$$\mathrm{H_2(g)+I_2(g)\rightleftharpoons 2HI(g)}$$

the equilibrium partial pressures are $p_{\mathrm{H_2}}=0.50\ \mathrm{bar}$, $p_{\mathrm{I_2}}=0.20\ \mathrm{bar}$, and $p_{\mathrm{HI}}=1.00\ \mathrm{bar}$.

Calculate $K_p$.

A) 5.00

B) 10.0

C) 20.0

D) 2.00

E) 40.0

Problem 2Easy

Degree of Dissociation

Initially, a vessel contains 1.00 mol of pure N₂O₄.

$$\mathrm{N_2O_4(g)\rightleftharpoons 2NO_2(g)}$$

At equilibrium, 20.0% of N₂O₄ has dissociated, and the total pressure is 3.00 bar.

Calculate $K_p$.

A) 0.250

B) 1.00

C) 2.00

D) 0.500

E) 0.125

Problem 3Easy

Calculating Kc

A 10.0 L vessel contains 2.00 mol of PCl₅, which decomposes according to:

$$\mathrm{PCl_5(g)\rightleftharpoons PCl_3(g)+Cl_2(g)}$$

At equilibrium, 0.500 mol of PCl₃ is present.

Calculate $K_c$.

A) 0.0167

B) 0.00833

C) 0.0333

D) 0.0500

E) 0.100

Problem 4Easy

Relationship Between Kp and Kc

Consider the reaction:

$$\mathrm{CO(g)+Cl_2(g)\rightleftharpoons COCl_2(g)}$$

At 300 K, the concentration-based equilibrium constant is $K_c=2.00$.

Calculate $K_p$.

A) 2.00

B) 0.0401

C) 49.9

D) 0.160

E) 0.0802

Problem 5Easy

Partial Pressure

A vessel initially contains 2.00 mol of SO₂ and 1.00 mol of O₂.

$$\mathrm{2SO_2(g)+O_2(g)\rightleftharpoons 2SO_3(g)}$$

At equilibrium, 60.0% of the initial SO₂ has reacted.

If the total equilibrium pressure is 6.00 bar, calculate the partial pressure of SO₃.

A) 1.00 bar

B) 2.00 bar

C) 3.00 bar

D) 4.00 bar

E) 5.00 bar

Problem 6Easy

Dissociation from Pressure Change

A rigid vessel initially contains pure gas A at a pressure of 1.00 bar.

The reaction is:

$$\mathrm{A(g)\rightleftharpoons 2B(g)}$$

At constant temperature and volume, the equilibrium total pressure is 1.40 bar.

Calculate the percentage of A that has dissociated.

A) 40.0%

B) 20.0%

C) 60.0%

D) 30.0%

E) 50.0%

Problem 7Easy

Equilibrium Concentrations

For the gaseous reaction

$$\mathrm{A(g)+B(g)\rightleftharpoons C(g)}$$

the initial concentrations are:

$$[A]_0=[B]_0=1.00\ \mathrm M$$

Initially, no C is present.

At equilibrium, the concentration of C is 0.400 M.

Calculate $K_c$.

A) 0.667

B) 1.67

C) 2.50

D) 0.444

E) 1.11

Problem 8Easy

Gibbs Energy and Equilibrium

At 300 K, the equilibrium constant of a gaseous reaction is:

$$K_p=10.0$$

Calculate the standard Gibbs energy change of the reaction.

A) +5.74 kJ mol⁻¹

B) −11.49 kJ mol⁻¹

C) −5.74 kJ mol⁻¹

D) 0 kJ mol⁻¹

E) +11.49 kJ mol⁻¹

Problem 9Easy

Temperature Dependence of Equilibrium

For a certain gaseous reaction:

$$K_{p,300}=2.00$$

The standard reaction enthalpy is:

$$\Delta_rH^\circ=+6.92\ \mathrm{kJ\,mol^{-1}}$$

Assuming that the reaction enthalpy is temperature-independent, calculate the equilibrium constant at 400 K.

A) 2.00

B) 4.00

C) 1.00

D) 8.00

E) 3.00

Problem 10Easy

Equilibrium Composition

A vessel initially contains 1.00 mol of pure A.

$$\mathrm{A(g)\rightleftharpoons B(g)}$$

At equilibrium, the total pressure is 2.00 bar and $K_p=3.00$.

Calculate the equilibrium partial pressure of B.

A) 1.00 bar

B) 1.25 bar

C) 0.500 bar

D) 1.50 bar

E) 1.75 bar

Problem 11Olympiad

Compression After Equilibrium

A rigid vessel initially contains 4.00 mol of gas A and 1.00 mol of helium. The following reaction takes place:

$$2A(g)\rightleftharpoons B(g)+3C(g)$$

At constant temperature, the initial total pressure is 2.00 bar. After equilibrium is established, the total pressure increases to 3.00 bar.

The vessel is then compressed isothermally to exactly half its original volume, and a new equilibrium is established.

Helium does not participate in the reaction.

What is the mole percentage of C at the new equilibrium?

A) 27.3%

B) 38.5%

C) 43.3%

D) 50.0%

E) 56.3%

Problem 12Olympiad

Equilibrium from Gas Density

A vessel contains an initial mixture of 92.0 g of N₂O₄ and 8.00 g of helium.

The following equilibrium is established at 350 K:

$$\mathrm{N_2O_4(g)\rightleftharpoons 2NO_2(g)}$$

At equilibrium, the total pressure is 4.00 bar, and the experimentally determined average molar mass of the gaseous mixture is $28.5714\ \mathrm{g\,mol^{-1}}$.

The mixture is then compressed isothermally until its new equilibrium total pressure is 8.00 bar.

Assume that no gas escapes and no other reactions occur.

What is the mole percentage of NO₂ in the final mixture?

A) 15.7%

B) 20.0%

C) 22.8%

D) 28.6%

E) 33.3%

Problem 13Olympiad

Thermodynamic Equilibrium and Inert Gas Addition

Consider the hypothetical gaseous reaction:

$$\mathrm{A(g)+B(g)\rightleftharpoons 2C(g)}$$

The standard reaction Gibbs energy at 400 K and standard reaction enthalpy are:

$$\Delta_rG^\circ_{400}=+4.611\ \mathrm{kJ\,mol^{-1}}$$ $$\Delta_rH^\circ=+26.0\ \mathrm{kJ\,mol^{-1}}$$

Assume that the standard reaction enthalpy is independent of temperature.

A vessel is charged with the following gases at 600 K:

The initial amounts are:

• Gas A: 2.00 mol
• Gas B: 3.00 mol
• Gas C: 1.00 mol
• Helium: 1.00 mol

The system is allowed to reach equilibrium.

Additional helium is then introduced while maintaining the temperature and total pressure constant, until the total number of gas moles is exactly twice its value immediately before helium addition.

What is the final mole percentage of C?

A) 10.0%

B) 16.7%

C) 20.0%

D) 28.6%

E) 40.0%

Problem 14Olympiad

Reconstructing an Equilibrium Constant

At a certain temperature, the following equilibrium is established:

$$\mathrm{N_2(g)+3H_2(g)\rightleftharpoons 2NH_3(g)}$$

A vessel initially contains 2.00 mol of N₂, 6.00 mol of H₂, 1.00 mol of NH₃, and 1.00 mol of helium.

At equilibrium, the total pressure is 8.00 bar and the mole fraction of NH₃ is 0.400.

In a second vessel at the same temperature, an initial mixture containing only 2.00 mol NH₃ and 1.00 mol He is allowed to reach equilibrium.

The volume of the second vessel is adjusted such that exactly 80.0% of the initial NH₃ decomposes at equilibrium.

What is the equilibrium total pressure in the second vessel?

A) 0.401 bar

B) 0.803 bar

C) 1.25 bar

D) 3.21 bar

E) 8.00 bar

Problem 15Olympiad

Determining Reaction Enthalpy from Pressure Measurements

A rigid vessel initially contains 2.00 mol of SO₃ and 1.00 mol of helium.

The following equilibrium is established:

$$\mathrm{2SO_3(g)\rightleftharpoons 2SO_2(g)+O_2(g)}$$

At 400 K, exactly 20.0% of the initial SO₃ has decomposed, and the total equilibrium pressure is 3.00 bar.

The same sealed vessel is subsequently heated to 500 K. After a new equilibrium is established, its total pressure is measured to be 4.336 bar.

Assume that the standard reaction enthalpy is constant over this temperature interval.

Calculate the standard reaction enthalpy for the reaction as written.

A) +49.4 kJ mol⁻¹

B) +79.1 kJ mol⁻¹

C) +98.8 kJ mol⁻¹

D) −98.8 kJ mol⁻¹

E) +123.5 kJ mol⁻¹