Butanedioic acid and methanol react together in the presence of an acid catalyst to form dimethyl butanedioate (C6H10O4\text{C}_6\text{H}_{10}\text{O}_4C6H10O4) and water as shown:
C4H6O4(l)+2CH3OH(l)⇌C6H10O4(l)+2H2O(l) \text{C}_4\text{H}_6\text{O}_4\text{(l)} + 2\text{CH}_3\text{OH(l)} \rightleftharpoons \text{C}_6\text{H}_{10}\text{O}_4\text{(l)} + 2\text{H}_2\text{O(l)} C4H6O4(l)+2CH3OH(l)⇌C6H10O4(l)+2H2O(l)Write an expression for the equilibrium constant, KcK_cKc, for the reaction. Explain why the total volume of the mixture does not need to be measured to allow a correct value for KcK_cKc to be calculated.
A small amount of catalyst was added to a mixture of 0.350 mol0.350\text{ mol}0.350 mol of butanedioic acid and 0.640 mol0.640\text{ mol}0.640 mol of methanol. The mixture was left to reach equilibrium at a constant temperature. At equilibrium, 0.220 mol0.220\text{ mol}0.220 mol of methanol was found to remain.
Calculate the equilibrium amount, in mol, of:
At a different temperature, a different equilibrium mixture was analysed and found to contain 0.250 mol0.250\text{ mol}0.250 mol of butanedioic acid, 0.800 mol0.800\text{ mol}0.800 mol of dimethyl butanedioate, and 1.50 mol1.50\text{ mol}1.50 mol of water. The value of KcK_cKc at this temperature is 20.020.020.0.
Calculate the amount, in mol, of methanol present in this new equilibrium mixture. Give your answer to 3 significant figures.
