A common question is where you need to determine Kc for a reaction given Kc for some other, related, reaction. These often look tricky but are very quick to do if you know how to do them.
Have a look at the three reactions and Kc below:
Can you see the relationship between reaction (1) and (2)?
To get the second reaction, we have to reverse the first reaction. This means that the top and bottom of the Kc fraction switch around as products become reactants and vice versa.
Can you see the relationship between reaction (1) and (3)?
To get the third reaction, we have to halve all the co-efficients in the first reaction. This halves all the powers in the Kc fraction.
If we know all the equilibrium concentrations, we can simply plug them back into the new Kc expression and use that to determine the new Kc value and unit.
However, sometimes we don’t have the equilibrium concentrations and have we have to think a bit more carefully about how the new Kc value and its unit relates to the original Kc value and its unit.
You might know from Maths (at GCSE or A Level), that swapping the top and bottom of a fraction is the same as calculating the reciprocal i.e., 1 / x. Similarly, halving the power of something is the same as calculating the square root of it.
This means that if Kc = 16 for Reaction 1,
then Kc = 1/16 for Reaction 2
and Kc = 4 for Reaction 3
All three of these Kc’s are unitless since the number of moles of products = number of moles of reactants. However, in the more general case where Kc does have a unit, the units would change in exactly the same way as the values:
| Example The equilibrium D + 2 E -> F has Kc = 100 mol-2 dm6 |
| Calculate Kc for the following equilibriums:
1/2 D + E -> 1/2 F In this reaction, all the co-efficients are halved, so we must take the square root of the Kc value AND the unit, i.e., Kc = 10 mol-1 dm3
2 D + 4 E -> 2 F In this reaction, all the co-efficients are doubled, so we must take the square of the Kc value AND the unit, i.e., Kc = 10,000 mol-4 dm12
F -> D + 2E In this reaction, all reactants and products are reversed, so we must take the reciprocal of the Kc value AND the unit, i.e., Kc = 0.01 mol2 dm-6
1/2 F -> 1/2 D + E In this reaction, all reactants and products are reversed AND all the co-efficients are halved, so we must take the reciprocal AND the square root of the Kc value AND the unit, i.e., Kc = 0.1 mol dm-3 |