Peroxycarboxylic acids are organic compounds containing the −COOOH-\text{COOOH}−COOOH functional group. Peroxypropanoic acid, CH3CH2COOOH\text{CH}_3\text{CH}_2\text{COOOH}CH3CH2COOOH, can be prepared by reacting hydrogen peroxide with propanoic acid in a heterogeneous equilibrium mixture:
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\text{H}_2\text{O}_2(\text{aq}) + \text{CH}_3\text{CH}_2\text{COOH}(\text{aq}) \rightleftharpoons \text{CH}_3\text{CH}_2\text{COOOH}(\text{aq}) + \text{H}_2\text{O}(\text{l}) \quad K_c = 0.42 \text{ dm}^3 \text{ mol}^{-1}{\char"24}$ A $500 \text{ cm}^3$ equilibrium mixture contains concentrations of $0.400 \text{ mol dm}^{-3}$ $\text{H}_2\text{O}_2(\text{aq})$ and $0.600 \text{ mol dm}^{-3}$ $\text{CH}_3\text{CH}_2\text{COOH}(\text{aq})$.Calculate the amount, in mol, of peroxypropanoic acid in the equilibrium mixture.
