Kc and Equilibrium Problems

(4 types)

Additional KEY TermsICE table

• Solve 4 types of problems involving equilibrium constants.

1. Plug and solve

*Always make sure the equation is balanced, FIRST*

At 225°C, a 2.0 L container holds 0.040 moles of N2, 0.15 moles of H2 and 0.50 moles of NH3. If the system is at equilibrium, calculate KC.

1. Change all into concentrations - mol/L

2. Write the equilibrium law for the reaction

N2(g) + 3 H2(g) 2 NH3(g)

0.040 mol N2

2.0 L= 0.020 M N2

= 0.075 M H2

= 0.25 M NH3

3. Substitute the concentrations and calculate K.(Note: no units for K)

The equilibrium concentrations of N2 and NO are 1.40 mol/L and 5.20 mol/L respectively. Calculate the KC.

According to Eq stoichiometry – the same amount of O2 will be produced as N2.

2 NO(g) N2(g) + O2(g)

1.40 M5.20 M 1.40 M

Kc =

[N2][O2] [NO]2

Kc =

[1.40][1.40] [5.20]2

= 0.0725

and solve2. Rearrange

At 210°C, the Kc is 64.0 The equilibrium concentrations of N2 and O2 are 0.40 mol/L and 0.60 mol/L, respectively. Calculate the equilibrium concentration of NO.

1. Write out the Eq Law.

2. Rearrange for [NO].

N2(g) + O2(g) 2 NO(g)

3. Substitute concentrations then solve.

At 10.0°C, the Kc is 215.0 The equilibrium concentrations of SO2 is 9.40 mol/L. Calculate the [S] and [O2] at equilibrium.

SO2(g) S(g) + O2(g)

Values should be the same amount for S and O2 – assign the unknown “x”

x M9.40 M x M

Kc =

[S][O2] [SO2]

= Kc [S][O2] [SO2]

[x][x] = 215 [9.40]

= Kc [S][O2] [SO2]

[x]2 = 2021√ √x = 45.0 M

[S]eq and [O2] eq = 45.0 M

3. Simple I.C.E. Tables

1.00 M of hydrogen and 1.00 M of fluorine are allowed to react at 150.0°C. At equilibrium, the [HF] is 1.32 M. Calculate KC.

H2(g) + F2(g) 2 HF(g)

[Eqlbm] 1.320.340.34

[Initial] 1.00 M 1.00 M 0

[Change] - 0.66 - 0.66 + 1.32

Tip #1 – the changes in concentration match the stoichiometry of the reaction.

1 1

[Eq] 1.320.340.34

H2(g) + F2(g) 2 HF(g)

Initially 2.0 mol of SO2, 1.0 mol of O2 are mixed in a 3.0 L reaction container. At equilibrium, 0.20 mol of O2 are found to remain. Calculate the Kc.

2 SO3 (g) 2 SO2 (g) + O2 (g)

[E] 0.15 0.0670.52

[I] 0 0.67 mol/L 0.33 mol/L

[C] - 0.52+ 0.52 - 0.26

Tip #2 – make sure the +/- reflect the appropriate side being made or used up

Kc = 0.00557 Kc = 5.6 x 10-3

[E] 0.15 0.0670.52

Kc =

[SO2]2[O2] [SO3]2

2 SO3 (g) 2 SO2 (g) + O2 (g)

Kc =

[0.15]2[0.067] [0.52]2

Tip #3 – Write Eq Law for equation as written.

4. HARD I.C.E. Tables

[E] 6.0 - x 2x6.0 - x

6.0 moles of N2 and O2 gases are placed in a 1.0 L container, what are all the concentrations at equilibrium? The Kc is 6.76.

N2(g) + O2(g) 2 NO(g)

[I] 6.0 mol/L 0 6.0 mol/L

[C] - x - x + 2x

Tip #4 – use x values to match the stoichiometry changes of the reaction.

1 1

Get rid of the square by taking the square root of both sides.

Substitute known values.

Isolate, and solve for x.

[I]

[C]

[E]

6.0 mol/L 0 6.0 mol/L

- 3.4 - 3.4 2(3.4)

6.82.6 2.66.0 - x 2x6.0 - x

- x - x + 2x

H2 (g) + I2 (g) 2 HI (g)

2.0 moles of HI were placed in a 1.0 L flask at 430ºC. (Kc = 54.3) Calculate the equilibrium concentrations.

[I]

[C]

[E]

0 0 2.0

+ x + x - 2x

2.0 - 2x+ x+ x

Kc = [HI]2

[H2][I2]

54.3 = [2.0 - 2x]2

[+ x][+ x]

Kc = [HI]2

[H2][I2]

7.37 = 2.0 – 2x x

7.37 x = 2.0 – 2x

√ √

7.37 x + 2x = 2.0

9.37 x = 2.0

x = 0.21

[I]

[C]

[E]

0 0 2.0

+ x + x - 2x

2.0 - 2x+ x+ x

0.21 0.21 - 0.42

1.580.210.21

The Kc for the reaction 5.3 x 10 -2 at 0ºC. Initially, 2.5 mol each particle was injected into a 1 L reaction vessel. Find the Eq concentrations.

2.5 + x 2.5 + x 2.5 - 2x

-2x+ x+ x2.5 mol/L 2.5 mol/L2.5 mol/L

[E]

[C]

[I]

H2 (g) + Cl2 (g) 2 HCl (g)

Tip #5 – use the Kc value to predict the changes in the reaction.

5.3 x 10 -2 = [2.5 - 2x]2

[2.5 + x][2.5 + x]

Kc = [HCl]2

[H2][Cl2]

√5.3 x 10 -2 = [2.5 - 2x]2

[2.5+x]2 √

√

0.23 = 2.5 – 2x 2.5+ x

x = 0.86 mol/L x = 1.92

2.23

0.58 + 0.23x = 2.5 - 2x

2.5 mol/L 2.5 mol/L2.5 mol/L

[E]

[C]

[I]

+ 0.86 + 0.86 2(0.86)

0.8 mol/L3.4 mol/L3.4 mol/L

2.23 x = 1.92

Additional KEY TermsICE table

CAN YOU / HAVE YOU?

• Solve 4 types of problems involving equilibrium constants.