CHEM1001 Worksheet 11: Enthalpy Change And Equilibrium Model 1: The Equilibrium Constant Many chemical reactions lead to a mixture of reactants and products. In Worksheet 10, you studied the thermodynamics of the dimerization of NO2, a prominent air pollutant. At low temperatures, NO2 is in equilibrium with its dimer, N2O4. Starting from NO2, the formation of the dimer can be studied using one of the two equations below:

2NO2(g) N2O4(g) (A)

NO2(g) ½ N2O4(g) (B) Starting from the dimer, the formation of NO2 can be studied using one of the two equations below:

N2O4(g) 2NO2(g) (C) ½ N2O4(g ) NO2(g) (D)

You will end up with a mixture of both NO2(g) and N2O4(g) whether you start with pure NO2(g) or pure N2O4(g). Such reactions are said to reach an equilibrium in which the amount of each substance does not change. Consider a reaction such as that below which has been left long enough to reach equilibrium.

wW(g) + xX(g) yY(g) + zZ(g) The equilibrium constant in terms of concentrations, Kc, is a constant at a given temperature that defines how much of each substance there will be at equilibrium:

Kc =[! ! ]![! ! ]!

[! ! ]![! ! ]!

If Kc > 1, the mixture will contain more of the substances on the right hand side (Y and Z) of the equation. If Kc < 1, the mixture will contain more of the substances on the left hand side (W and Z) of the equation.

Critical thinking questions 1. Write down the expression for Kc for reactions A, B, C and D in Model 1.

Kc (A) =                                               Kc (B) =

                                              Kc (C) =                                               Kc (D) =

                                             

2. Looking at the equations in Q1, what is the mathematical relationship the values of Kc?

(a) Kc (A) and Kc (B) (b) Kc (A) and Kc (C)

3. At equilibrium at room temperature, [NO2(g)] = 1.60 M and [N2O4] = 0.20 M. Calculate the values of

Kc(A) and Kc(B) and Kc(C) and hence confirm your analysis in Q2.

Model 2: The Reaction Quotient The reaction quotient, Qc, for a reaction wW(g) + xX(g) yY(g) + zZ(g), is defined as follows:

Qc =[! ! ]![! ! ]!

[! ! ]![! ! ]!

It looks similar to the equilibrium constant expression. The difference is that Qc can be calculated at any time during a reaction or if a reaction is disturbed. Qc is equal to Kc only if the reaction is at equilibrium. Qc is used to predict the direction in which a reaction will move.

From model 1, at equilibrium [NO2(g)] = 1.60 M, [N2O4] = 0.20 M and Kc = 0.078 is for the reaction below: 2NO2(g) N2O4(g) (A)

Critical thinking questions 1. What do you think will happen to this reaction if more NO2 is added so that [NO2(g)] = 2.00 M?

2. What do you think will happen to this reaction if instead NO2 is removed so that [NO2(g)] = 1.00 M?

3. Calculate the values for Qc for these two experiments.

(a) [NO2(g)] = 2.00 M and [N2O4] = 0.20 M: Qc =

(b) [NO2(g)] = 1.00 M and [N2O4] = 0.20 M: Qc =

4. Using your answers to Q1-3, what happens to a reaction if

(a) Qc < Kc

(b) Qc > Kc

CHEM1101 2009-J-9 June 2009

• Consider the following reaction at equilibrium.

CH3OH(g) CO(g) + 2H2(g) Kc = 1.30 × 10–2

What is the concentration of CO(g) when [CH3OH(g)] = 3.49 × 10–1 M and [H2(g)] = 1.76 × 10–1 M?

Marks 2

Equilibrium

CHEM1101 2009-N-8 November 2009

• The value of the equilibrium constant, Kc, for the following reaction is 0.118.

2CO2(g) + N2(g) 2CO(g) + 2NO(g)

What is the equilibrium concentration of CO(g) if the equilibrium concentration of [CO2(g)] = 0.492 M, [N2(g)] = 0.319 M and [NO(g)] = 0.350 M?

Marks 2

Model 3: Equilibrium calculations Calculations concerning equilibriums can be solved using an ICE table: Initial-Change-Equilibrium.

Q. The thermal decomposition of water occurs only to a very small extent, even at high temperatures. At 1000 °C, Kc = 7.3 × 10-18 for the reaction 2H!O g ⇌  2H! g +  O! ! . If water with an initial concentration of 0.10 M is allowed to react at 1000 °C, what will the equilibrium concentrations for each of the species be? A. Set up an equilibrium table, and fill it out as follows. The information in bold is what you are given. The information in italics is what you have to determine. The steps show the working. [I] = Initial concentration, [C] = change in concentration, [E] = equilibrium concentration. 2H2O(g) ⇌ 2H2(g) + O2(g) Notes [I] 0.10 0.00 0.00 Step 1: convert moles to concentration. No products initially.

[C] -2x +2x +x Step 2: Don’t know the change in concentration, so use x according to stoichiometry. When 2x H2O is lost, 2x H2 and x O2 are made.

[E] 0.10-2x +2x +x Step 3: [E] = [I] + [C] Now, use the equilibrium concentration to determine the value of x. First, write down the expression for Kc and then substitute for each concentration from the table:

𝐾! =  [H!]![O!][H!O]!

 

𝐾! =  2𝑥 !(𝑥)0.1− 2𝑥 !  

𝐾! =  4𝑥!

0.1− 2𝑥 !  

 In theory, this requires us to solve a cubic equation to work out x. Luckily, as long as Kc is small, we can simplify it considerably.  If Kc is very small, 0.1-2x ≈ 0.1, so we can replace that in the calculation to give:  

𝐾! =  4𝑥!

0.1 !

This is then rearranged for x: 4𝑥! =  𝐾!×(0.1)! 𝑥 =  ∛(𝐾!  ×

!!×0. 1!)

𝑥 =  ∛(7.3  ×10!!"  ×  !!×(0.1)!)

𝑥 =  2.6  ×10!!

Therefore, [H2O] = 0.1-2x = 0.1 M and [H2] = 2x = 5.2 × 10-7 M and [O2] = x = 2.6 × 10-7 M. Critical thinking questions 1. Why is the change in concentration for the reactants negative while for the products it is positive?

2. If [N2] = 0.033 M, and [O2] = 0.00810 M, use the ICE method to work out the equilibrium concentration of NO if Kc = 4.8 × 10-31 for the following reaction. Use the table provided.

  N2(g)   +   O2(g)   ⇌   2NO(g)  

[I]            

[C]            

[E]             3. The water-gas shift reaction CO(g)+ H!O g ⇌  H! g +  CO!(g) has Kc = 4.06 at 500 °C. If 0.100

mol of CO(g) and 0.100 mol of H2O(g) are placed in a 1.00 L vessel, what are the concentrations at equilibrium?

4. For the reaction in Q3, suppose 0.0600 mol each of CO and H2O is mixed with 0.100 mol each of CO2

and H2 in a 1.00 L vessel. Determine the concentrations of all the substances when the mixture reaches equilibrium.

5. Gaseous H2 (0.200 mol) and I2 (0.200 mol) were placed in a 2.00 litre flask. After a period of time the

equilibrium H! g +   I! g ⇌  2HI g was established. At equilibrium, the concentration of I2 was measured to be 0.020 M. What is the value for Kc for this reaction?