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Chapter 5: Problem 58

A 2.20-g sample of phenol $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)$ was burned in a bomb calorimeter whose total heat capacity is \(11.90 \mathrm{~kJ} /{ }^{\circ} \mathrm{C} .\) The temperature of the calorimeter plus contents increased from 21.50 to $27.50^{\circ} \mathrm{C} .(\mathbf{a})$ Write a balanced chemical equation for the bomb calorimeter reaction. (b) What is the heat of combustion per gram of phenol and per mole of phenol?

Short Answer

Expert verified
The balanced chemical equation for the combustion of phenol is: \(C_6H_5OH + 7O_2 \rightarrow 6CO_2 + 3H_2O\). The heat of combustion per gram of phenol is 32.45 kJ/g, and the heat of combustion per mole of phenol is 3053.35 kJ/mol.

Step by step solution

01

Write the balanced chemical equation for the combustion of phenol.

Combustion reactions involve the reaction of a substance with oxygen gas, producing carbon dioxide and water as the products. For phenol, the chemical equation for its combustion can be written as: C6H5OH + O2 → CO2 + H2O To balance the equation, we need to adjust the coefficients of each element so that the number of atoms on each side of the equation is equal. The balanced chemical equation is: C6H5OH + 7O2 → 6CO2 + 3H2O
02

Calculate the total heat gained by the calorimeter.

The total heat capacity of the calorimeter is 11.90 kJ/°C. The temperature increased from 21.50°C to 27.50°C, a difference of 6.00°C. To find the total heat gained by the calorimeter, we use the formula: Total heat gained = Heat capacity * Temperature change Total heat gained = 11.90 kJ/°C * 6.00°C = 71.40 kJ
03

Calculate the heat of combustion per gram of phenol.

We are given that 2.20 g of phenol was burned. To find the heat of combustion per gram of phenol, we divide the total heat by the mass of phenol: Heat of combustion per gram = Total heat gained / Mass of phenol Heat of combustion per gram = 71.40 kJ / 2.20 g = 32.45 kJ/g
04

Determine the molar mass of phenol.

To find the molar mass of phenol (C6H5OH), we can sum up the molar masses of the individual atoms in the molecule: Molar mass of phenol = 6 * (Molar mass of C) + 5 * (Molar mass of H) + 1 * (Molar mass of O) + 1 * (Molar mass of H) Molar mass of phenol = 6 * (12.01 g/mol) + 5 * (1.01 g/mol) + 1 * (16.00 g/mol) + 1 * (1.01 g/mol) = 94.11 g/mol
05

Calculate the heat of combustion per mole of phenol.

Now that we have the molar mass of phenol and the heat of combustion per gram, we can find the heat of combustion per mole: Heat of combustion per mole = Heat of combustion per gram * Molar mass of phenol Heat of combustion per mole = 32.45 kJ/g * 94.11 g/mol = 3053.35 kJ/mol The heat of combustion per gram of phenol is 32.45 kJ/g, and the heat of combustion per mole of phenol is 3053.35 kJ/mol.

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Most popular questions from this chapter

(a) According to the first law of thermodynamics, what quantity is conserved? (b) What is meant by the internal energy of a system? (c) By what means can the internal energy of a closed system increase?

(a) Which releases the most energy when metabolized, \(1 \mathrm{~g}\) of carbohydrates or \(1 \mathrm{~g}\) of fat? (b) A particular chip snack food is composed of \(12 \%\) protein, \(14 \%\) fat, and the rest carbohydrate. What percentage of the calorie content of this food is fat? (c) How many grams of protein provide the same fuel value as \(25 \mathrm{~g}\) of fat?

Consider the following reaction: $$ 2 \mathrm{CH}_{3} \mathrm{OH}(g) \longrightarrow 2 \mathrm{CH}_{4}(g)+\mathrm{O}_{2}(g) \quad \Delta H=+252.8 \mathrm{~kJ} $$ (a) Is this reaction exothermic or endothermic? (b) Calculate the amount of heat transferred when \(24.0 \mathrm{~g}\) of \(\mathrm{CH}_{3} \mathrm{OH}(g)\) is decomposed by this reaction at constant pressure. (c) For a given sample of \(\mathrm{CH}_{3} \mathrm{OH},\) the enthalpy change during the reaction is \(82.1 \mathrm{~kJ}\). How many grams of methane gas are produced? (d) How many kilojoules of heat are released when \(38.5 \mathrm{~g}\) of \(\mathrm{CH}_{4}(g)\) reacts completely with \(\mathrm{O}_{2}(g)\) to form \(\mathrm{CH}_{3} \mathrm{OH}(g)\) at constant pressure?

The hydrocarbons cyclohexane $\left(\mathrm{C}_{6} \mathrm{H}_{12}(l), \Delta H_{f}^{\circ}=-156\right.$ \(\mathrm{kJ} / \mathrm{mol}\) ) and 1-hexene $\left(\mathrm{C}_{6} \mathrm{H}_{12}(l), \Delta H_{f}^{\circ}=-74 \mathrm{~kJ} / \mathrm{mol}\right)$ have the same empirical formula. (a) Calculate the standard enthalpy change for the transformation of cyclohexane to 1-hexene. (b) Which has greater enthalpy, cyclohexane or 1-hexene? (c) Without doing a further calculation and knowing the answer to (b), do you expect cyclohexane or 1-hexene to have the larger combustion enthalpy?

For the following processes, calculate the change in internal energy of the system and determine whether the process is endothermic or exothermic: (a) A balloon is cooled by removing \(0.655 \mathrm{~kJ}\) of heat. It shrinks on cooling, and the atmosphere does \(382 \mathrm{~J}\) of work on the balloon. (b) A 100.0-g bar of gold is heated from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\) during which it absorbs \(322 \mathrm{~J}\) of heat. Assume the volume of the gold bar remains constant.
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