Aight so with these questions it's really important that you establish a process which works for you.
For all the Ks (Ka, Kp, Kc, Kw and
k) I made individual posters which I still refer to as they are laid out better than my textbook.
What you must remember is that Kc is calculated from
equilibrium concentrations, not initial concentrations nor equilibrium/initial AMOUNTS.So at the beginning you have 0.2 mol of methyl propanoate. It reacts in a 1+1--> 1+1 ratio with water to produce propanoic acid and methanol.
The whole thing about sulfuric acid is just something to throw you off. Because sulfuric acid is acting as a catalyst, not a reactant, it doesn't go into the expression. Look at the equation; the methyl propanoate reacts with water. The solution is aqueous; therefore it contains 30cm3 water as the volume of the actual sulfuric acid in the solution is probably negligible, hence you are given that assumption
Because you have 30cm3 water in a 50cm3 solution, the concentration of H20 in the entire solution at the
start is 33.33 moldm3.
This is because 30cm3=30g water, so 30/18 (molar mass of water)= 1.67 moles. Divide this by 0.05 (dm3 volume of whole solution- says it's 50cm3 in question) and you get 33.33 moles per dm3.
Finding the initial conc of methyl propanoate is less complicated. Just divide the moles by the volume (0.2/0.05) and you get 4 moldm3.
Then for the products- you have 0.12 moles of propanoic acid
at equilibrium. This means there are 2.4 mol/dm3 because 0.12/ 0.05=2.4.
Because the ratio of the products in the equation are the same, we can assume that 2.4 moldm3 of methanol has also been produced at equilibrium.
Initially there would have been no propanoic acid or methanol- so the change in moles/dm3 is +2.4.
Because the two reactants are also in the same stoichiometric quantity as the products, we can be sure that 2.4 mol/dm3 of each reactant has been lost.
so, as 33.33-2.4= 30.93 and 4-2.4= 1.6, we now have the four equilibrium concentrations.
The equation for Kc is
Kc= ([methanol] x [propanoic acid])/([water] x [methyl propanoate]).
as such, you have (2.4 x 2.4) / (30.93 x 1.6) which should give a value shown in the spoiler
I'm not entirely sure my answer is right as I haven't done A-Level chem for a while so I'm a bit rusty. Either way I hope it helps.