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Chapter 7: Problem 138

The standard molar heats of combustion of C(graphite) and \(\mathrm{CO}(\mathrm{g})\) are -393.5 and \(-283 \mathrm{kJ} / \mathrm{mol}\) respectively. Use those data and that for the following reaction $$\mathrm{CO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{COCl}_{2}(\mathrm{g}) \quad \Delta H^{\circ}=-108 \mathrm{kJ}$$ to calculate the standard molar enthalpy of formation of \(\mathrm{COCl}_{2}(\mathrm{g})\).

Short Answer

Expert verified
The standard molar enthalpy of formation of \(COCl_{2}(g)\) is \(175 kJ/mol\).

Step by step solution

01

Identify Given Data

Begin by identifying and writing down the given information. The standard molar heats of combustion of C(graphite) and \(CO(g)\) are \(-393.5 kJ/mol\) and \(-283 kJ/mol\) respectively. The reaction \(CO(g) + Cl_{2}(g) \rightarrow COCl_{2}(g)\) has a heat of reaction \(\Delta H^{\circ} = -108 kJ\).
02

Write The Heat Formation Reactions

The standard molar enthalpy of formation of a compound is the heat absorbed or evolved when 1 mole of the compound is formed from its elements in their standard states. Write heat formation reactions for the known substances: \(C(graphite) + 0.5O_{2}(g) \rightarrow CO(g)\) with \(\Delta H_{f_1} = -283 kJ/mol\), and \(C(graphite) + O_{2}(g) \rightarrow CO_{2}(g)\) with \(\Delta H_{f_2} = -393.5 kJ/mol\).
03

Use Hess's Law To Write The Desired Reaction

Hess's Law states that the heat of any reaction depends only on the initial and final states and is independent of the path or nature of the reaction. The thermochemical equation desired is \(C(graphite) + O_{2}(g) + Cl_{2}(g) \rightarrow COCl_{2}(g)\), from which we'll find \(\Delta H_{f_3}\). By liberally applying Hess's Law, we can subtract the heat enthalpy of formation for \(CO(g)\) from the heat of reaction supplied to isolate the heat enthalpy for \(COCl_{2}(g)\). \(\Delta H_{f_3} = \Delta H_{R} - \Delta H_{f_1}\).
04

Calculate The Enthalpy of Formation

Substitute the known values into the equation from Step 3: \(\Delta H_{f_3} = -108 kJ - (-283 kJ/mol) = 175 kJ/mol\).

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Most popular questions from this chapter

Refer to Example \(7-3 .\) Based on the heat of combustion of sucrose established in the example, what should be the temperature change \((\Delta T)\) produced by the combustion of \(1.227 \mathrm{g} \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) in a bomb calorimeter assembly with a heat capacity of \(3.87 \mathrm{kJ} /^{\circ} \mathrm{C} ?\)

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 $$\begin{array}{r} \mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g})+\frac{13}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{CO}_{2}(\mathrm{g})+5 \mathrm{H}_{2} \mathrm{O}(1) \\ \Delta H^{\circ}=-2877 \mathrm{kJ} \end{array}$$

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.

A plausible final temperature when \(75.0 \mathrm{mL}\) of water at \(80.0^{\circ} \mathrm{C}\) is added to \(100.0 \mathrm{mL}\) of water at \(20^{\circ} \mathrm{C}\) is (a) \(28^{\circ} \mathrm{C} ;\) (b) \(40^{\circ} \mathrm{C} ;\) (c) \(46^{\circ} \mathrm{C} ;\) (d) \(50^{\circ} \mathrm{C}\)

For the reaction \(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}(1)\) determine \(\Delta H^{\circ},\) given that $$\begin{array}{r} 4 \mathrm{HCl}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{Cl}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(1) \\ \Delta H^{\circ}=-202.4 \mathrm{kJ} \end{array}$$ $$\begin{aligned} 2 \mathrm{HCl}(\mathrm{g})+\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \\ \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}(1)+\mathrm{H}_{2} \mathrm{O}(1) & \Delta H^{\circ}=-318.7 \mathrm{kJ} \end{aligned}$$
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