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Chapter 6: Problem 63

A coffee-cup calorimeter initially contains \(125 \mathrm{~g}\) water at \(24.2^{\circ} \mathrm{C}\). Potassium bromide \((10.5 \mathrm{~g})\), also at \(24.2^{\circ} \mathrm{C}\), is added to the water, and after the KBr dissolves, the final temperature is \(21.1^{\circ} \mathrm{C}\). Calculate the enthalpy change for dissolving the salt in \(\mathrm{J} / \mathrm{g}\) and \(\mathrm{kJ} / \mathrm{mol}\). Assume that the specific heat capacity of the solution is \(4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\) and that no heat is transferred to the surroundings or to the calorimeter.

Short Answer

Expert verified
The enthalpy change for dissolving potassium bromide in water is approximately \(-34.43 \, \mathrm{J/g}\) and \(-120.6\, \mathrm{kJ/mol}\).

Step by step solution

01

Calculate the heat absorbed by the potassium bromide

We'll start by determining the heat absorbed by the potassium bromide during the dissolving process. To do this, we'll use the formula: heat absorbed (q) = mass (m) × specific heat capacity (C) × temperature change (ΔT). The temperature change can be found by subtracting the initial temperature from the final temperature.
02

Calculate the heat absorbed by water found in the calorimeter

Now, let's calculate the heat absorbed by water in the calorimeter using the same formula as in Step 1. It's important to note that the heat should be negative since the water cools down.
03

Determine the total heat absorbed

Next, let's find the total heat absorbed by adding the heat absorbed by potassium bromide and water.
04

Calculate enthalpy change in J/g

To find the enthalpy change in Joules per gram (J/g), we need to divide the total heat absorbed by the mass of potassium bromide.
05

Calculate the molar mass of potassium bromide

To convert our enthalpy change from J/g to kJ/mol, first, we need to find the molar mass of potassium bromide. The molar mass can be calculated by adding the molar masses of potassium (K) and bromine (Br), which are 39.10 g/mol and 79.90 g/mol, respectively.
06

Calculate enthalpy change in kJ/mol

Now that we have the molar mass of potassium bromide, we can calculate the enthalpy change in kilojoules per mole (kJ/mol) by multiplying the enthalpy change in J/g by the molar mass of potassium bromide and converting the units to kJ/mol. Following these steps, you can calculate the enthalpy change for dissolving the salt in both J/g and kJ/mol.

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Most popular questions from this chapter

Photosynthetic plants use the following reaction to produce glucose, cellulose, and so forth: $$ 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \stackrel{\text { Sunlight }}{\longrightarrow} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) $$ How might extensive destruction of forests exacerbate the greenhouse effect?

Nitromethane, \(\mathrm{CH}_{3} \mathrm{NO}_{2}\), can be used as a fuel. When the liquid is burned, the (unbalanced) reaction is mainly $$ \mathrm{CH}_{3} \mathrm{NO}_{2}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) $$ a. The standard enthalpy change of reaction \(\left(\Delta H_{\mathrm{rxn}}^{\circ}\right)\) for the balanced reaction (with lowest whole- number coefficients) is \(-1288.5 \mathrm{~kJ}\). Calculate \(\Delta H_{\mathrm{f}}^{\circ}\) for nitromethane. b. A \(15.0\) - \(\mathrm{L}\) flask containing a sample of nitromethane is filled with \(\mathrm{O}_{2}\) and the flask is heated to \(100 .{ }^{\circ} \mathrm{C}\). At this temperature, and after the reaction is complete, the total pressure of all the gases inside the flask is 950 . torr. If the mole fraction of nitrogen \(\left(\chi_{\text {nitrogen }}\right)\) is \(0.134\) after the reaction is complete, what mass of nitrogen was produced?

The combustion of \(0.1584 \mathrm{~g}\) benzoic acid increases the temperature of a bomb calorimeter by \(2.54^{\circ} \mathrm{C}\). Calculate the heat capacity of this calorimeter. (The energy released by combustion of benzoic acid is \(26.42 \mathrm{~kJ} / \mathrm{g}\).) A \(0.2130\) -g sample of vanillin \(\left(\mathrm{C}_{8} \mathrm{H}_{8} \mathrm{O}_{3}\right)\) is then burned in the same calorimeter, and the temperature increases by \(3.25^{\circ} \mathrm{C}\). What is the energy of combustion per gram of vanillin? Per mole of vanillin?

Are the following processes exothermic or endothermic? a. When solid \(\mathrm{KBr}\) is dissolved in water, the solution gets colder. b. Natural gas \(\left(\mathrm{CH}_{4}\right)\) is burned in a furnace. c. When concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}\) is added to water, the solution gets very hot. d. Water is boiled in a teakettle.

Given the following data $$ \begin{aligned} \mathrm{Ca}(s)+2 \mathrm{C}(\text { graphite }) & \longrightarrow \mathrm{CaC}_{2}(s) & \Delta H &=-62.8 \mathrm{~kJ} \\ \mathrm{Ca}(s)+\frac{1}{2} \mathrm{O}_{2}(g) & \longrightarrow \mathrm{CaO}(s) & \Delta H &=-635.5 \mathrm{~kJ} \\ \mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) & \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q) & \Delta H &=-653.1 \mathrm{~kJ} \\ \mathrm{C}_{2} \mathrm{H}_{2}(g)+\frac{5}{2} \mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) & \Delta H &=-1300 . \mathrm{kJ} \\ \mathrm{C}(\text { graphite })+\mathrm{O}_{2}(g) & \mathrm{CO}_{2}(\mathrm{~g}) & \Delta H &=-393.5 \mathrm{~kJ} \end{aligned} $$ calculate \(\Delta H\) for the reaction $$ \mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{C}_{2} \mathrm{H}_{2}(g) $$
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