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Calculate the standard enthalpy change (in kcal mol⁻¹) for the precipitation of calcium carbonate according to the reaction: Ca²+(aq) + CO3²-(aq) -> CaCO3(s). Given: standard enthalpy of formation of Ca²+(aq) = -130 kcal mol⁻¹; standard enthalpy of formation of CO3²-(aq) = -160 kcal mol⁻¹; standard enthalpy of formation of CaCO3(s) = -285 kcal mol⁻¹.

1. +5 kcal mol⁻¹
2. -5 kcal mol⁻¹
3. +10 kcal mol⁻¹
4. -10 kcal mol⁻¹

Correct answer: +5 kcal mol⁻¹

Solution

Applying Hess's law: delta_H = delta_f H(CaCO3, s) - [delta_f H(Ca²+, aq) + delta_f H(CO3²-, aq)] = -285 - (-130 + -160) = -285 - (-290) = -285 + 290 = +5 kcal mol⁻¹. The positive value indicates the precipitation is slightly endothermic under standard conditions.

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