A. Calculate the ΔH^∘ value for the following reaction:...

a. Calculate the $\Delta H^{\circ}$ value for the following reaction: $$\mathrm{CH}_{4}+\mathrm{Cl}_{2} \stackrel{h \nu}{\longrightarrow} \mathrm{CH}_{3} \mathrm{Cl}+\mathrm{HCl}$$ b. Calculate the sum of the $\Delta H^{\circ}$ values for the following two propagation steps: $$\begin{array}{l} \mathrm{CH}_{3}-\mathrm{H}+\cdot \mathrm{Cl} \longrightarrow \cdot \mathrm{CH}_{3}+\mathrm{H}-\mathrm{Cl} \\ \cdot \mathrm{CH}_{3}+\mathrm{Cl}-\mathrm{Cl} \longrightarrow \mathrm{CH}_{3}-\mathrm{Cl}+\cdot \mathrm{Cl} \end{array}$$ c. Why do both calculations give you the same value of $\Delta H^{\circ} ?$

a. Calculate the $\Delta H^{\circ}$ value for the following reaction:
$$\mathrm{CH}_{4}+\mathrm{Cl}_{2} \stackrel{h \nu}{\longrightarrow} \mathrm{CH}_{3} \mathrm{Cl}+\mathrm{HCl}$$
b. Calculate the sum of the $\Delta H^{\circ}$ values for the following two propagation steps:
$$\begin{array}{l}
\mathrm{CH}_{3}-\mathrm{H}+\cdot \mathrm{Cl} \longrightarrow \cdot \mathrm{CH}_{3}+\mathrm{H}-\mathrm{Cl} \\
\cdot \mathrm{CH}_{3}+\mathrm{Cl}-\mathrm{Cl} \longrightarrow \mathrm{CH}_{3}-\mathrm{Cl}+\cdot \mathrm{Cl}
\end{array}$$
c. Why do both calculations give you the same value of $\Delta H^{\circ} ?$

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Key Concepts

Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the same regardless of the pathway taken. This principle allows one to calculate complicated reaction energies by summing the enthalpies of individual steps or using bond energies, demonstrating that the overall energy change remains constant whether the reaction occurs in one step or through intermediates.

Bond Energy Calculations

Bond energy calculations involve determining the overall energy change of a reaction by accounting for the energy required to break bonds in the reactants and the energy released upon forming bonds in the products. This method is useful when estimating reaction enthalpies, especially in processes where multiple bonds are broken and formed as seen in chain reactions or radical mechanisms.

Chain Reaction Propagation Steps

In chain reactions, the mechanism is divided into initiation, propagation, and termination steps. The propagation steps are crucial as they sustain the reaction by regenerating reactive intermediates. Analyzing the propagation steps helps illustrate the conservation of energy throughout the reaction process, making it evident why the summed enthalpy changes of these steps match the overall reaction enthalpy.

Transcript

00:01 The first part of this question asks us to calculate the delta h value for this reaction.

00:06 So remember that delta h is bonds broken minus bonds formed for an overall reaction.

00:12 So if we start by looking at the bonds that are breaking and forming in this, we are breaking the c -h bond and the methane and breaking the cl -cl bond in the chlorine.

00:25 And then we are forming, or so that's 105 to break the c -h bond and 50.

00:31 To break the cl cll bond and then we form a ccl bond and for 84 k cows per mole and we form an hcl bond for 103 k cows per mole.

00:45 So if we just do this math here, our broken is 105 plus 58 and our formed is 84 plus 103.

00:59 So if we do the math, we get 163 minus 187 for an overall delta h of negative 24 k cows per mole for this overall reaction.

01:15 And then part b asks us to calculate the sum of the delta h values for these two propagation steps.

01:22 So again, we'll start with our values for each of the bonds broken and formed.

01:28 So in this first propagation step, we're breaking ch for 105 and forming hcl for 103.

01:36 So 105 minus 103 is a total of two k -cals per mole.

01:44 And then in the next part, we are breaking clcl for 58 and forming c -cl for 84.

01:55 So 58 minus 84 is.

02:00 Negative 26 k kkals per mole.

02:02 So our overall delta h is negative 26 plus 2...

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