Ethanoic acid and propane-1,3-diol react together to form a diester (C7H12O4\text{C}_7\text{H}_{12}\text{O}_4C7H12O4) and water as shown:
2CH3COOH(l)+HO(CH2)3OH(l)⇌C7H12O4(l)+2H2O(l) 2\text{CH}_3\text{COOH(l)} + \text{HO(CH}_2)_3\text{OH(l)} \rightleftharpoons \text{C}_7\text{H}_{12}\text{O}_4\text{(l)} + 2\text{H}_2\text{O(l)} 2CH3COOH(l)+HO(CH2)3OH(l)⇌C7H12O4(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 0.640 mol0.640\text{ mol}0.640 mol of ethanoic acid and 0.350 mol0.350\text{ mol}0.350 mol of propane-1,3-diol. The mixture was left to reach equilibrium at a constant temperature. At equilibrium, 0.220 mol0.220\text{ mol}0.220 mol of ethanoic acid 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 propane-1,3-diol, 1.50 mol1.50\text{ mol}1.50 mol of diester, and 2.00 mol2.00\text{ mol}2.00 mol of water. The value of KcK_cKc at this temperature is 6.006.006.00.
Calculate the amount, in mol, of ethanoic acid present in this new equilibrium mixture. Give your answer to 3 significant figures.