\(\mathrm{CCl}_{4},\) an important commercial solvent, is prepared by the reaction of \(\mathrm{Cl}_{2}(\mathrm{g})\) with a carbon compound. Determine \(\Delta H^{\circ}\) for the reaction $$ \mathrm{CS}_{2}(1)+3 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{CCl}_{4}(1)+\mathrm{S}_{2} \mathrm{Cl}_{2}(1) $$ Use appropriate data from the following listing. $$\begin{aligned} \mathrm{CS}_{2}(\mathrm{l})+3 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{SO}_{2}(\mathrm{g}) & \\ \Delta H^{\circ}=&-1077 \mathrm{kJ} \end{aligned}$$ $$2 \mathrm{S}(\mathrm{s})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{S}_{2} \mathrm{Cl}_{2}(1) \quad \Delta H^{\circ}=-58.2 \mathrm{kJ}$$ $$\mathrm{C}(\mathrm{s})+2 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{CCl}_{4}(1) \quad \Delta H^{\circ}=-135.4 \mathrm{kJ}$$ $$\mathrm{S}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{SO}_{2}(\mathrm{g}) \quad \Delta H^{\circ}=-296.8 \mathrm{kJ}$$ $$\mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{SO}_{2} \mathrm{Cl}_{2}(1) \quad \Delta H^{\circ}=+97.3 \mathrm{kJ}$$ $$\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g}) \quad \Delta H^{\circ}=-393.5 \mathrm{kJ}$$ $$\begin{aligned} \mathrm{CCl}_{4}(1)+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{COCl}_{2}(\mathrm{g})+\mathrm{Cl}_{2} \mathrm{O}(\mathrm{g}) & \\ \Delta H^{\circ}=&-5.2 \mathrm{kJ} \end{aligned}$$

Step by step solution

01

Identify Related Reactions

The first step is to examine the list of reactions and locate those that involve the same substances as those in the reaction of interest. Four reactions can be found that involve these substances: CS2(l) with O2(g) to form CO2(g) and SO2(g), \(\Delta H^{\circ}=-1077 \; kJ\); S(s) with Cl2(g) to form S2Cl2(l), \(\Delta H^{\circ}=-58.2 \; kJ\); C(s) with Cl2(g) to form CCl4(l), \(\Delta H^{\circ}=-135.4 \; kJ\); and S(s) with O2(g) to form SO2(g), \(\Delta H^{\circ}=-296.8 \; kJ\).

02

Manipulate Reactions to Match Desired Reaction

Next, it is necessary to manipulate these reactions so that they can be added together to yield the desired reaction. To do this, reverse the first reaction and double the second and fourth reactions.

03

Calculate \(\Delta H^{\circ}\) of Desired Reaction

After flipping and/or multiplying as necessarily, we add all adjusted reactions and their respective enthalpies. If done correctly, the chemical equations should combine neatly to give the overall desired reaction. Adding the adjusted \(\Delta H^{\circ}\) values together will then yield the \(\Delta H^{\circ}\) of the desired reaction. After these calculations, we find \(\Delta H^{\circ}_{desired} = -1077kJ + 2(-58.2kJ) + (-135.4kJ) + 2(-296.8kJ) = -1922.6kJ\).

04

Double Check the Result

It's always a good idea to double-check the results. Make sure that the manipulated reactions add up to give the correct stoichiometric coefficients for the desired reaction, and verify that the calculated \(\Delta H^{\circ}\) for the desired reaction is reasonable. Always pay attention to the sign of \(\Delta H^{\circ}\), as it indicates whether the reaction is exothermic (negative) or endothermic (positive).

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