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Chapter 7: Problem 39

A 0.75 g sample of \(\mathrm{KCl}\) is added to \(35.0 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) in a Styrofoam cup and stirred until it dissolves. The temperature of the solution drops from 24.8 to \(23.6^{\circ} \mathrm{C}\) (a) Is the process endothermic or exothermic? (b) What is the heat of solution of KCl expressed in kilojoules per mole of KCl?

Short Answer

Expert verified
(a) The process is endothermic. (b) The molar heat of solution of KCl is -17.32 kJ/mol.

Step by step solution

01

Identifying the type of process

The process is endothermic or exothermic based on whether the temperature drops or rises respectively. Given that the temperature drops from \(24.8^{\circ} \mathrm{C}\) to \(23.6^{\circ} \mathrm{C}\), it's clear that it's an endothermic reaction.
02

Calculating change in temperature

\(\Delta T = T_f - T_i =(23.6^{\circ} \mathrm{C} - 24.8^{\circ} \mathrm{C}) = -1.2^{\circ} \mathrm{C} \). Where \(T_i\) and \(T_f\) are the initial and final temperatures respectively.
03

Converting grams to moles

The number of moles of KCl = mass/molar mass = 0.75 g / 74.5513 g/mol = 0.01006 mol.
04

Calculate the heat gained

Using the formula \(q=mc\Delta T\). The specific heat capacity of water (\(c\)) is usually given as 4.18 J/gC. The mass of water (\(m\)) is given as 35g and \(\Delta T\) as calculated in step 2 is -1.2C. Therefore, \(q = 35g * 4.18 J/gC * -1.2C = -174.36 J\).
05

Convert J to kJ and then divide by moles of solute

This will give the heat of solution of KCl in kJ/mol. Since 1 Joule = 0.001 kJ, first convert J to kJ (-174.36 J = -0.17436 kJ) and then divide by number of moles. That is \(-0.17436kJ / 0.01006mol = -17.32 kJ/mol \)

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Most popular questions from this chapter

Hot water and a piece of cold metal come into contact in an isolated container. When the final temperature of the metal and water are identical, is the total energy change in this process (a) zero; (b) negative; (c) positive; (d) not enough information.

How much heat, in kilojoules, is evolved in the complete combustion of (a) \(1.325 \mathrm{g} \mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g})\) at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{atm} ;\) (b) \(28.4 \mathrm{L} \mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g})\) at \(\mathrm{STP} ;(\mathrm{c})\) \(12.6 \mathrm{LC}_{4} \mathrm{H}_{10}(\mathrm{g})\) at \(23.6^{\circ} \mathrm{C}\) and \(738 \mathrm{mmHg} ?\) Assume that the enthalpy change for the reaction does not change significantly with temperature or pressure. The complete combustion of butane, \(\mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g}),\) is represented by the equation $$\begin{array}{r} \mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g})+\frac{13}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{CO}_{2}(\mathrm{g})+5 \mathrm{H}_{2} \mathrm{O}(1) \\ \Delta H^{\circ}=-2877 \mathrm{kJ} \end{array}$$

Several factors are involved in determining the cooking times required for foods in a microwave oven. One of these factors is specific heat. Determine the approximate time required to warm \(250 \mathrm{mL}\) of chicken broth from \(4^{\circ} \mathrm{C}\) (a typical refrigerator temperature) to \(50^{\circ} \mathrm{C}\) in a \(700 \mathrm{W}\) microwave oven. Assume that the density of chicken broth is about \(1 \mathrm{g} / \mathrm{mL}\) and that its specific heat is approximately \(4.2 \mathrm{Jg}^{-1}\) \(^{\circ} \mathrm{C}^{-1}\).

Some of the butane, \(\mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g}),\) in a \(200.0 \mathrm{L}\) cylinder at \(26.0^{\circ} \mathrm{C}\) is withdrawn and burned at a constant pressure in an excess of air. As a result, the pressure of the gas in the cylinder falls from 2.35 atm to 1.10 atm. The liberated heat is used to raise the temperature of 132.5 L of water in a heater from 26.0 to 62.2 ^ C. Assume that the combustion products are \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) exclusively, and determine the efficiency of the water heater. (That is, what percent of the heat of combustion was absorbed by the water?)

James Joule published his definitive work related to the first law of thermodynamics in \(1850 .\) He stated that "the quantity of heat capable of increasing the temperature of one pound of water by \(1^{\circ} \mathrm{F}\) requires for its evolution the expenditure of a mechanical force represented by the fall of 772 lb through the space of one foot." Validate this statement by relating it to information given in this text.
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