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 airpollution 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 \(2000^{\circ}
\mathrm{C}\) :
$$
\begin{aligned}
\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) \\
\Delta H^{\circ} &=177.8 \mathrm{~kJ} / \mathrm{mol}
\end{aligned}
$$
Slaked lime is produced by treating quicklime with water:
$$
\begin{aligned}
\mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow
\mathrm{Ca}(\mathrm{OH})_{2}(s) \\
\Delta H^{\circ} &=-65.2 \mathrm{~kJ} / \mathrm{mol}
\end{aligned}
$$
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 \(\left.25^{\circ}
\mathrm{C}\right)\), 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. (b) Given that the standard enthalpies of
formation of \(\mathrm{CaO}\) and \(\mathrm{H}_{2} \mathrm{O}\) are \(-635.6
\mathrm{~kJ} / \mathrm{mol}\) and \(-285.8 \mathrm{~kJ} / \mathrm{mol}\),
respectively, cal-
culate the standard enthalpy of formation of \(\mathrm{Ca}(\mathrm{OH})_{2}\).
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