Consider the following intermediate chemical equations. 3 equations. 1: upper C upper H subscript 4 (g) right arrow upper C (s) plus 2 upper H subscript 2 (g). Delta H 1 equals 74.8 kilojoules. 2: upper C upper C l subscript 4 (g) right arrow upper C (s) plus 2 upper C l subscript 2 (g). Delta H 2 equals 95.7 kilojoules. Upper H subscript 2 (g) plus upper C l subscript 2 (g) right arrow 2 upper H upper C l (g). Delta H subscript 3 equals negative 92.3 kilojoules. What is the enthalpy of the overall chemical reaction Upper C upper H subscript 4 (g) plus 4 upper C l subscript 2 (g) right arrow upper C upper C l subscript 4 (g) plus 4 upper H upper C l (g).? -205.7 kJ -113.4 kJ -14.3 kJ 78.0 kJ

To determine the enthalpy of the overall chemical reaction, we can use Hess's Law, which states that the total enthalpy change for a chemical reaction is the same regardless of the number of steps in which the reaction is carried out.

The overall chemical reaction is:

\[ \mathrm{CH_4(g) + 4Cl_2(g) \rightarrow CCl_4(g) + 4HCl(g)} \]

We must manipulate the given intermediate reactions to get this overall equation. Firstly, let us write down the given intermediate reactions and their enthalpy changes:

1. \[ \mathrm{CH_4(g) \rightarrow C(s) + 2H_2(g)} \quad \Delta H_1 = +74.8 \, \text{kilojoules} \]

2. \[ \mathrm{CCl_4(g) \rightarrow C(s) + 2Cl_2(g)} \quad \Delta H_2 = +95.7 \, \text{kilojoules} \]

3. \[ \mathrm{H_2(g) + Cl_2(g) \rightarrow 2HCl(g)} \quad \Delta H_3 = -92.3 \, \text{kilojoules} \]

We must reverse reaction 2 to match the form of the overall equation and multiply reaction 3 by two to account for the 4 moles of HCl being produced:

Reversed reaction 2 (also change sign of ΔH_2):

\[ \mathrm{C(s) + 2Cl_2(g) \rightarrow CCl_4(g)} \quad \Delta H_2^\prime = -95.7 \, \text{kilojoules} \]

Multiplied reaction 3 by two:

\[ \mathrm{2H_2(g) + 2Cl_2(g) \rightarrow 4HCl(g)} \quad \Delta H_3^* = 2 \times (-92.3) = -184.6 \, \text{kilojoules} \]

Summing these modified reactions:

\[ \mathrm{CH_4(g) \rightarrow C(s) + 2H_2(g)} \quad +74.8 \, \text{kilojoules} \] \[ \mathrm{C(s) + 2Cl_2(g) \rightarrow CCl_4(g)} \quad -95.7 \, \text{kilojoules} \] \[ \mathrm{2H_2(g) + 2Cl_2(g) \rightarrow 4HCl(g)} \quad -184.6 \, \text{kilojoules} \]

When we sum up the reactions, we get the overall reaction:

\[ \mathrm{CH_4(g) + 4Cl_2(g) \rightarrow CCl_4(g) + 4HCl(g)} \]

We also sum the ΔH values to find the enthalpy for the overall reaction:

\[ \Delta H_{\text{overall}} = +74.8 \, \text{kilojoules} - 95.7 \, \text{kilojoules} - 184.6 \, \text{kilojoules} = -205.5 \, \text{kilojoules} \]

So, the enthalpy of the overall chemical reaction is approximately -205.5 kJ, which is closest to the first option given:

\[ \boxed{-205.7 \, \text{kilojoules}} \]

(Note: There is a slight difference between the calculated -205.5 kJ and the option -205.7 kJ. This discrepancy might be due to rounding errors or approximations in the given ΔH values.)

Extra: Enthalpy (\( \Delta H \)) is a measure of heat change during a chemical reaction at constant pressure. It is a state function, which means its value depends only on the state of the reactants and products and not on the path taken between them. If \( \Delta H \) is positive, the reaction is endothermic (absorbs heat), and if it is negative, the reaction is exothermic (releases heat).

Hess's Law is a very useful principle because it allows chemists to determine the enthalpy change of a reaction even when it cannot be measured directly. By using known enthalpies of related reactions, one can calculate the enthalpy of a target reaction. In practice, it means that you can add or subtract chemical equations and their associated enthalpy changes, just as if you were dealing with mathematical equations, to derive the enthalpy change for a new reaction equation.

In school, students often practice Hess's Law by manipulating given chemical equations, ensuring that when they sum up these equations, the intermediates cancel out, leaving the desired overall reaction. Through this process, they learn about the conservation of matter, stoichiometry, and the thermodynamics of reactions.