Introduction to Equilibrium

Writing Equilibrium Expressions

Example Problem: 1

Write the equilibrium expression for the following homogeneous reactions.

a. N_2(g) + O_2(g) $⟺$ 2 NO_(g)

b. N₂O_4(g) $⟺$ 2 NO_(g)

c. FeSCN²⁺_(aq) $⟺$ Fe³⁺_(aq) + SCN^1-_(aq)

d. 2 PBr_3(g) + 3 Cl_2(g) $⟺$ 2 PCl_3(g) + 3 Br_2(g)

Example Problem: 2

Write the equilibrium expression for the following heterogeneous reactions.

a. 2 NH_3(g) + CO_2(g) $⟺$ N₂CH₄O_(s) + H₂O_(g)

b. 2 NBr_3(s) $⟺$ N_2(g) + 3 Br_2(g)

c. 2 KClO_3(s) $⟺$ 2 KCl_(s) + 3 O_2(g)

d. Cr₂O₇^2-_(aq) + 3 H₂O_(l) $⟺$ 2 CrO₄²⁺_(aq) + 2 H₃O⁺_(aq)

Manipulation of the Equilibrium Expression

Example Problem: 3

At a given temperature, K = 0.013 for the reaction:

N_2(g) + 3 H_2(g) $⟺$ 2 NH_3(g)

calculate values of K for the following reactions at this temperature

a. $\frac{1}{2}$ N_2(g) + $\frac{3}{2}$ H_2(g) $⟺$ NH_3(g)

b. 2 NH_3(g) $⟺$ N_2(g) + 3 H_2(g)

c. NH_3(g) $⟺$ $\frac{1}{2}$ N_2(g) + $\frac{3}{2}$ H_2(g)

d. 2 N_2(g) + 6 H_2(g) $⟺$ 4 NH_3(g)

Statements that best describe equilibrium

For the reaction given in the video. what can we conclude about this reaction?

Which is the best Kc expression for the reaction, in light of all common conventions:

Reaction Quotients and predicting the directions of reactions

Example Problem: 4

The equilibrium constant, K, is 2400 at a certain temperature for the reaction:

2 NO(g) $⟺$ N_2(g) + O_2(g)

For which of the following sets of conditions is the system at equilibrium? For those that are not at equilibrium, in which direction will the system shift?

a. a 1.0 L flask contains 0.024 mol NO, 2.10 mol N₂ and 2.6 mol O₂

b. a 2.0 L flask contains 0.032 mol NO, 0.62 mol N₂ and 4.0 mol O₂

c. a 3.0 L flask contains 0.060 mol NO, 2.4 mol N₂ and 1.7 mol O₂

The Relationship between K_c and K_p

Example Problem: 5

Write the equations for the conversions of Kc to Kp for each of the following reactions.

a. N_2(g) + 3 H_2(g) $⟺$ 2 NH_3(g)

b. H_2(g) + I_2(g) $⟺$ 2 HI_(g)

c. 2 SO_2(g) + O_2(g) $⟺$ 2 SO_3(g)

d. C₃H_8(g) + 5 O_2(g) $⟺$ 3 CO_2(g) + 4 H₂O_(g)

Introduction to RICE Table Notes

Example Problem: 6

Nitrosyl bromide decomposes into nitrogen monoxide and elemental bromine. What is the algebraic (substituted) Kc expression for the system charged with 2.0 M NOBr and allowed to come to equilibrium?

2 NOBr_(g) $⟺$ 2 NO_(g) and Br_2(g)

Example Problem: 7

Into an empty vessel COCl_2(g) is introduced at 1.0 atm pressure whereupon it dissociates until equilibrium is established:

2 COCl_2(g) $⟺$ C_(graphite) + CO_2(g) + 2 Cl_2(g)

If x represents the partial pressure of CO_2(g) at equilibrium, what is the values of the equilibrium constant, K_p, in respect to x.

Le Chatielier's Principle of gases and Pressure

Example Problem: 8

For the reaction:

4 NH_3(g) + 5 O_2(g) $⟺$ 4 NO_(g) + 6 H₂O_(g); $Δ$ H = -904 kJ

a. What effect will compressing the system (decreasing the volume) have on this reaction?

b. Considering only equilibrium effects (ignoring kinetic effects due to E_a), what effects will cooling the system have?

Example Problem: 9

The decomposition of the inter-halogen compound bromine chloride proceeds in carbon tetrachloride according to the following reaction, at 298 K,

2 BrCl $⟺$ Br_2(g) + Cl_2(g)

Kc = 0.145 for this process. The initial concentration are BrCl, 0.05 M; Br₂, 0.035 M; Cl₂, 0.30 M. What maybe concluded regarding the behavior of the system from this information"

Example Problem: 10

1. For the following reaction at at particular high temperature:

CO_(g) + H₂O_(g) $⟺$ CO_2(g) + H_2(g)

the concentration of the reactants and products at equilibrium are CO_(g), 0.060 M; H₂O_(g), 0.120 M; CO_2(g), 0.150 M, and H_2(g), 0.300M. Calculate the value of the equilibrium constant, K_c, at this temperature

2. The the following equilibrium is established in a sealed container at 25^oC:

N₂O_4(g) $⟺$ 2 NO_2(g)

The equilibrium pressures of N₂O₄ and NO₂ are 1.74 atm and 0.512 atm, respectively. Calculate the equilibrium constant, K_p, at 25^oC

Example Problem: 11

1. The equilibrium between N₂O₄ and NO₂ has a Kp value of 47.9 at 400^oC.

N₂O_4(g) $⟺$ 2 NO_2(g)

If the partial pressure of N₂O₄ in a sealed reaction vessel is 0.335 atm at equilibrium, then what is the partial pressure of NO₂ in the vessel?

2. The reaction between sulfur dioxide and molecular oxygen has a Kc value of 1.7x10⁶ at 700K.

2 SO_2(g) + O_2(g) $⟺$ 2 SO_3(g)

If this reaction is carried out in a sealed reaction vessel and the equilibrium concentration of O₂ and SO₃ are 2.1x10^-3M and 3.8 M, respectively, then what is the concentration of SO₂ in the vessel at equilibrium?

Example Problem: 12

Butane exists as two isomers n-butane and isobutane. If the Kp is 2.5 at 25^oC.

butane in equilibrium with isobutane

What will be the partial pressure of each isomer if the total pressure of the system is 3.75 atm.

Example Problem: 13

1. If 0.500 M of H₂ and 0.5 M I₂ react at high temperatures at a constant volume of 1.00 L, and the amount of HI present at equilibrium is 0.900 mol, from this information determine the the concentration of H₂ and I₂ at equilibrium. Determine the Kc from the data.

H_2(g) + I_2(g) $⟺$ 2 HI_(g)

Example Problem: 14

Suppose that 0.150 mol of SO₃ is placed in a 1.00 L flask and allowed to come to equilibrium at a high temperature. When equilibrium is achieved 0.0076 mol of SO₃ remains. Calculate the value of the equilibrium constant for the reaction.

2 SO_3(g) $⟺$ 2 SO_2(g) + O_2(g)

Example Problem: 15

Consider the reactions:

CO_(g) + H₂O_(g) $⟺$ H_2(g) + CO_2(g)

you want to calculate the concentrations of all four species at equilibrium, if the initial concentration of CO_(g) is 0.0125 M and H₂O_(g) is 0.0125 M. The value of Kc is 9.0.

The Quadratic Formula in Equilibrium Calculations

Sometimes, the equilibrium expression that results from the RICE tables will be a quadratic equation, meaning that is involves an x² term, thus requires a specific mathematical technique to solve. The following problem is an example:

Example Problem: 16

In organic chemistry for the synthesis of aspirin, we test for the salicylate ion ("Sal"). It can form a purple complex with iron(III) ions. The following equation describes the complexation reaction:

Fe³⁺_(aq) + Sal^-_(aq) $⟺$ [Fe(Sal)]²⁺_(aq) Kc = 14.8

What is the equilibrium concentrations of each species in a mixture that initially contains 0.10 M Fe³⁺ with 0.050 M salicylate (Sal^-)?