Equilibrium (1) Calculation of an equilibrium constant Kc

Edexcel A level Chemistry (2017)

Topic 10: Equilibrium I:

Here is the fifth learning objective:

10/I/4. To be able to deduce an expression for Kc , for homogeneous and heterogeneous systems, in terms of equilibrium concentrations

There is a mathematical model that fits an equilibrium reaction.

If   wA    +     xB         ⇋      yC      +     zD   then

        

   
=    K_c

K_c   is called the equilibrium constant.

It is constant at constant temperature.

And [C]^y is the equilibrium concentration of species C in the chemical equation raised to the power of its stoichiometric coefficient y.

Example 1: A gaseous Homogenous Equilibrium

Ammonia and the Haber process

The overall reaction vessel equation is:

N₂ (g) +   3H₂ (g)   ⇌  2NH₃ (g)  ΔH = –92kJ/mol

=   K_c  

at constant temp.

where eqm refers to the equilibrium concentrations of each species in the equilibrium.

The units of the equilibrium constant are:

which leaves the units of the equilibrium constant as

or  mol^–2.dm⁶

so the units of K_c change according to the chemical change involved.

Example 2: A aqueous homogenous equilibrium

Esterification:

CH₃CH₂OH(l)  +  CH₃COOH(l)   ⇌   CH₃COOCH₂CH₃(l)  +  H₂O(l)

Here K_c has no units.

Example 3: A heterogeneous equilibrium.

A heterogeneous reaction is one in which the reactants and/or products are not all in the same physical state at room temperature and pressure.

CaCO₃ (s)        ⟶        CaO(s)     +        CO₂(g)

In this example, the solids do not have a vapour pressure or a concentration so they cannot be included in the equilibrium expression.

Therefore:    K_c     =     [CO₂(g)]_eqm

K_c has units of mol.dm-³

There are Labs available to use to calculate experimentally a value of an equilibrium constant.

Measuring an equilibrium constant Kc

AS the specification for the Edexcel A level suggests

“Possible experiments include investigating equilibrium systems, such as iron(III) – thiocyanate,….”

In this experiment, the slow redox reaction between silver ions and iron(III) ions is studied.

The equilibrium is convenient to study because it establishes itself reasonably quickly i.e. over a few days and we can get at its value using a precipitation titration.

Ag+ (aq)    +      Fe ²⁺ (aq)       ⇌        Ag(s)        +         Fe ³⁺  (aq)

Samples of the resulting equilibrium mixture containing silver ions are titrated with potassium thiocyanate solution (KCNS).

The titration results are used to calculate K_c from the expression:

                 

The reaction between silver ions and potassium thiocyanate is at first a precipitation of insoluble silver thiocyanate (AgCNS)

KCNS(aq)     +     AgNO₃ (aq)       ⟶   KNO₃(aq)    +      AgCNS

But when all the silver ions have been precipitated from the equilibrium mixture the thiocyante ions react with iron(III) ions in the resultant equilibrium mixture to give the deep red colour of the iron(III) thiocyanate complex.

Fe³⁺      +      CNS^–        ⟶         Fe(CNS)²⁺

We assume that the equilibrium cannot re-establish itself fast enough in the time we do the titration.

A Practical Script

Preparation:

• Place 25ml of a solution of 0.10M silver nitrate in a dry 100ml conical flask.

• Add 25ml of a solution of 0.10M iron(II) sulphate to the same flask.

• Stopper and shake the flask and leave to stand overnight.

Practical:

• After equilibrium has been established, use a pipette to transfer 10.0ml of the solution to another conical flask.  Ensure that the pipette does not pick up or disturb the silver precipitate in the flask.

• Titrate the 10ml sample of the equilibrium mixture with 0.020M potassium thiocyanate.

• Look for the end point when the first permanent red colour is seen in the conical flask. 

• It should be possible for you to repeat the titration twice.

• Calculate the average titre from the “best” of your results.

• Calculate the concentration of free silver ions at equilibrium from your titration results and call this value x.

Calculation of Kc:

At equilibrium [Ag⁺_(aq)]_eqm  =  [Fe²⁺_(aq)]_eqm =   x

And [Fe³⁺_(aq)] _eqm = [Fe²⁺_(aq)] _initial  –  x  i.e. 0.05  –  x

Fill in this table:

	[Fe2+(aq)]	[Ag+(aq)]	Ag(s)	[Fe3+(aq)]
Initial concentrations	0.05	0.05	0.00	0.00
Equilibrium concentrations	x	x		0.05–x

Use  

                                                    

And calculate K_c  

(in 2007 I calculated K_c to be 55 mol^-1.dm³  at 21^oC)

Questions:

1. Why is Ag(s) irrelevant to your calculation?

2. Why are the units of K_c  mol^-1.dm³ ?

3. Why leave the reaction mixture overnight and why must the flask be sealed with a stopper?