(Solved): Lime is a term that includes calcium oxide \( \mathrm{CaO} \), also called quicklime) and calcium h ...

Lime is a term that includes calcium oxide \( \mathrm{CaO} \), also called quicklime) and calcium hydroxide \( \left[\mathrm{Ca}(\mathrm{OH})_{2}\right. \), also called slaked lime]. It is used in the steel industry to remove acidic impurities, in air-pollution control to remove acidic oxides such as \( \mathrm{SO}_{2} \), and in water treatment. Quicklime is made industrially by heating limestone \( \left(\mathrm{CaCO}_{3}\right) \) above \( 2000^{\circ} \mathrm{C} \) : \[ \mathrm{CaCO}_{3}(s) \rightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) \quad \Delta H^{\circ}=177.8 \mathrm{~kJ} / \mathrm{mol} \] Slaked lime is produced by treating quicklime with water: \[ \mathrm{CaO}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}\left(() \rightarrow \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{~s}) \quad \Delta H^{\circ}=-65.2 \mathrm{~kJ} / \mathrm{mol}\right. \] The exothermic reaction of quicklime with water and the rather small specific heats of both quicklime \( \left(0.946 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right) \) and slaked lime \( \left(1.20 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\right) \) make it hazardous to store and transport lime in vessels made of wood. Wooden sailing ships carrying lime would occasionally catch fire when water leaked into the hold. (a) If a 500-g sample of water reacts with an equimolar amount of \( \mathrm{CaO} \) (both at an initial temperature of \( 25^{\circ} \mathrm{C} \) ), what is the final temperature of the product, \( \mathrm{Ca}(\mathrm{OH})_{2} \) ? Assume that the product absorbs all of the heat released in the reaction. (5 pts)