The equilibrium constant
In a nutshell
The equilibrium constant, Kc, can be calculated from the ratio of the concentrations of the reactants and products. The value is given at a certain temperature. The units can vary depending on the equilibrium reaction.
Equations
This is a general expression for Kc. You will need to be able to write Kc expressions for any given reaction.
Kc=[Reactants]m[Products]n
n=Numberofproductmoles
m=Numberofreactantmoles
There is a calculation to find the concentration. This involves knowing the volume and moles.
WORD EQUATION | SYMBOL EQUATION |
concentration=volumemoles | c=Vn |
Variable units
quantity name | symbol | unit name | unit |
concentration | | mole per decimetre cubed | moldm−3 |
| | | |
| | decimetre cubed | |
Equilibrium constant, Kc
The equilibrium constant shows which reaction the equilibrium is closer to. It can be calculated at a given temperature with the known molar concentrations of the reactants and products at equilibrium.
This definition is usually applied for homogeneous equilibria. All the reactants and products are in the same physical state.
Writing the Kc expression:
Kc=[Reactants]m[Products]n
Procedure
1. | In the numerator, write the products separately in square brackets. |
2. | Write the number of moles each product has in the power form for each product. |
3. | In the denominator, write the reactants separately in square brackets. |
4. | Write the number of moles each reactant has in the power form for each reactant. |
Example
2NO(g)+O2(g)⇌2NO2(g)
Write the Kc expression for the above reaction.
Kc=[NO]2[O2][NO2]2
Note: The square brackets, [ ], indicate concentration.
Kc units
The units for the equilibrium constant, Kc, can vary depending on the reaction. You need to figure out the units every single time you calculate Kc.
Procedure
1. | In the numerator, write the concentration units all to the power of the total product moles. |
2. | In the denominator, write the concentration units all to the power of the total reactant moles. |
3. | Simplify it fully. |
Example
2NO(g)+O2(g)⇌2NO2(g)
The Kc expression is:
Kc=[NO]2[O2][NO2]2
Insert the concentration units into the equation:
Kc=[moldm−3]2[moldm−3][moldm−3]2
The simplified version by canceling out any common units is:
Kc=moldm−31=mol−1dm3
The units for Kc are mol−1dm3.
Calculating Kc
You can calculate the value of the equilibrium constant, Kc, with known equilibrium concentrations. Sometimes you have to work out the equilibrium concentrations first.
procedure
1. | Write the balanced chemical equation. |
2. | Write the moles before equilibrium. |
3. | Calculate the moles after equilibrium. |
4. | Calculate the concentration using the equation: concentration=volumemoles |
5. | Write down the Kc expression. |
6. | Insert concentration values into the Kc equation to calculate Kc. |
Example
0.30mole of phosphorous (V) bromide reacts at 550K in a reaction tube of 6.00dm3. The equilibrium mixture has 0.080mole of bromine. Calculate Kc, including units.
PBr5(g)⇌PBr3(g)+Br2(g)
The equation is balanced. Note down the moles before equilibrium. The moles before are mentioned in the question:
PBr5molesbeforeequilibrium=0.30mol
Note down the moles after equilibrium. The moles of bromine after equilibrium is mentioned in the question:
Br2molesafterequilibrium=0.080mol
Calculate the moles after equilibrium for the reactants. Both products, Br2 and PBr3, have 1mole in the balanced equation. This means they have a 1:1 ratio. Therefore, the moles produced after equilibrium will be the same:
Br2molesafterequilibrium=PBr3molesafterequilibrium=0.080mol
Calculate the moles for PBr5 after equilibrium. Since 0.080moles of Br2 was produced, that means 0.080moles of PBr5 reacted:
PBr5molesafterequilibrium=0.30−0.080=0.22mol
Calculate the concentration of each species. The concentration of each species can be calculated using the moles after equilibrium and the volume given in the question:
[PBr5]=6dm30.22mol=0.036moldm−3
[Br2]=6dm30.080mol=0.013moldm−3
[PBr3]=6dm30.080mol=0.013moldm−3
Write down the Kc expression:
Kc=[PBr5][PBr3][Cl2]
Insert the concentration values to calculate Kc:
Kc=(6dm30.22molmoldm−3)(6dm30.080molmoldm−3)×(6dm30.080molmoldm−3)=0.00485moldm−3
The Kc value is 0.00485moldm−3 .
Finding concentration with known Kc
When given a known value of Kc, you can use the equation to solve for the concentration.
Procedure
1. | Write the Kc expression. |
2. | Insert the values you are given. |
3. | Rearrange and solve for unknown concentration. |
Experimental data and Kc
The equilibrium constant, Kc, can be calculated from experimental data made in the laboratory. An experiment between iron(II) sulfate solution and silver nitrate solution at 298K will reach equilibrium.
You can titrate it to work out the equilibrium concentrations of the Fe2+ ions. Then you'll be able to work out the other equilibrium concentrations and Kc.
Example
400cm3 of 0.2moldm−3 iron(III) sulfate solution and 400cm3 of 0.2moldm−3 silver nitrate solution were left together in a flask at 298K until equilibrium was reached. A sample was titrated and it was found that the equilibrium concentration for Fe2+ was 0.0411moldm−3. What is the value of Kc?
Fe2+(aq)+Ag+(aq)⇌Fe3+(aq)+Ag(s)
The balanced equation is heterogeneous, you can ignore the solid silver.
Work out the initial concentration for Fe2+ and Ag+. You half the concentration because the reactants have the same number of moles but in double the volume since they're mixed together:
InitialconcentrationofFe2+andAg+=20.2moldm−3=0.1moldm−3
Write the concentrations for Fe2+ and Ag+at equilibrium:
Fe2+equilibriumconcentration=Ag+equilibriumconcentration=0.0411moldm−3
Calculate the concentration for Fe3+ at equilibrium:
Fe3+equilibriumconcentration=Initialconcentration−Reactantsequilibriumconcentration
Fe3+equilibriumconcentration=0.1−0.0411=0.0589moldm−3
Insert the equilibrium concentration values into the Kc equation:
Kc=[Fe2+][Ag+][Fe3+]=0.0411moldm−3×0.0411moldm−30.0589moldm−3=34.9mol−1dm3
Ag(s) is ignored in the Kc expression because it's a solid. The value of Kc is 34.9mol−1dm3.
Kc value
You can only calculate one Kc value at a given temperature. The Kc value will change if you change the temperature.
Catalysts don't affect the value of Kc.