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Chapter 7: Problem 13

How much heat, in kilojoules, is associated with the production of \(283 \mathrm{kg}\) of slaked lime, \(\mathrm{Ca}(\mathrm{OH})_{2} ?\) $$\mathrm{CaO}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(1) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s}) \quad \Delta H^{\circ}=-65.2 \mathrm{kJ}$$

Short Answer

Expert verified
The total heat energy released in joules. Remember that if the answer is negative, this means that energy is released.

Step by step solution

01

Calculating the number of moles

Firstly, we need to calculate the number of moles in 283 kg of \( \mathrm{Ca}(\mathrm{OH})_2 \) by using the molar mass of \( \mathrm{Ca}(\mathrm{OH})_2 \), which is 74.093 g/mol. Therefore, the number of moles (n) can be calculated by using the formula \( n = \frac{mass}{molar mass} \), where mass = 283000 g (since 1 kg = 1000 g).
02

Determining the total heat of reaction

Now that we have the number of moles of \( \mathrm{Ca}(\mathrm{OH})_2 \), we can calculate the total heat energy released. Given that \( \Delta H = -65.2 \) kJ/mol, the total heat energy (Q) can be calculated by using the formula \( Q = n \Delta H \).
03

Calculating the total heat energy

Substitute the values into the formula. The sign would remain negative as the heat is released and not absorbed. This will give you the final answer in kilojoules.

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Most popular questions from this chapter

A 0.205 g pellet of potassium hydroxide, \(\mathrm{KOH}\), is added to \(55.9 \mathrm{g}\) water in a Styrofoam coffee cup. The water temperature rises from 23.5 to \(24.4^{\circ} \mathrm{C}\). [Assume that the specific heat of dilute \(\mathrm{KOH}(aq)\) is the same as that of water.] (a) What is the approximate heat of solution of \(\mathrm{KOH}\) expressed as kilojoules per mole of \(\mathrm{KOH}?\) (b) How could the precision of this measurement be improved without modifying the apparatus?

The method of Exercise 97 is used in some bomb calorimetry experiments. A 1.148 g sample of benzoic acid is burned in excess \(\mathrm{O}_{2}(\mathrm{g})\) in a bomb immersed in 1181 g of water. The temperature of the water rises from 24.96 to \(30.25^{\circ} \mathrm{C}\). The heat of combustion of benzoic acid is \(-26.42 \mathrm{kJ} / \mathrm{g} .\) In a second experiment, a \(0.895 \mathrm{g}\) powdered coal sample is burned in the same calorimeter assembly. The temperature of \(1162 \mathrm{g}\) of water rises from 24.98 to \(29.81^{\circ} \mathrm{C}\). How many metric tons (1 metric ton \(=1000 \mathrm{kg}\) ) of this coal would have to be burned to release \(2.15 \times 10^{9} \mathrm{kJ}\) of heat?

Thermite mixtures are used for certain types of welding, and the thermite reaction is highly exothermic. $$\begin{array}{r} \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Al}(\mathrm{s}) \longrightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Fe}(\mathrm{s}) \\ \Delta H^{\circ}=-852 \mathrm{kJ} \end{array}$$ \(1.00 \mathrm{mol}\) of granular \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) and \(2.00 \mathrm{mol}\) of granular Al are mixed at room temperature \(\left(25^{\circ} \mathrm{C}\right),\) and a reaction is initiated. The liberated heat is retained within the products, whose combined specific heat over a broad temperature range is about \(0.8 \mathrm{Jg}^{-1}\) \(^{\circ} \mathrm{C}^{-1} .\) (The melting point of iron is \(1530^{\circ} \mathrm{C} .\) ) Show that the quantity of heat liberated is more than sufficient to raise the temperature of the products to the melting point of iron.

A 1.397 g sample of thymol, \(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{O}(\mathrm{s})\) (a preservative and a mold and mildew preventative), is burned in a bomb calorimeter assembly. The temperature increase is \(11.23^{\circ} \mathrm{C},\) and the heat capacity of the bomb calorimeter is \(4.68 \mathrm{kJ} /^{\circ} \mathrm{C}\). What is the heat of combustion of thymol, expressed in kilojoules per mole of \(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{O} ?\)

What will be the final temperature of the water in an insulated container as the result of passing \(5.00 \mathrm{g}\) of steam, \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}),\) at \(100.0^{\circ} \mathrm{C}\) into \(100.0 \mathrm{g}\) of water at \(25.0^{\circ} \mathrm{C} ?\left(\Delta H_{\mathrm{vap}}^{\circ}=40.6 \mathrm{kJ} / \mathrm{mol} \mathrm{H}_{2} \mathrm{O}\right)\).
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