Problem 71 - General Chemistry: Principles and Modern Applications

Question

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

Step-by-Step Solution

Answer

The enthalpy change, \(\Delta H^{\circ}\), of the target reaction is -84.45 kJ.

Step 1: Identify the Target Reaction

The reaction to be solved for is the transformation of ethylene gas and chlorine gas into dichloroethane liquid, given by \(C_2H_4(g) + Cl_2(g) → C_2H_4Cl_2(l)\). This is the target reaction and we need to find \(\Delta H^{\circ}\) for it.

Step 2: Rearrange and Combine the Known Reactions

The given reactions are: 1) \(4 HCl(g) + O_2(g) → 2 Cl_2(g) + 2 H_2O(l)\)with \(\Delta H^{\circ} = -202.4 kJ\)2) \(2 HCl(g) + C_2H_4(g) + 0.5 O_2(g) → C_2H_4Cl_2(l) + H_2O(l)\)with \(\Delta H^{\circ} = -318.7 kJ\)To match the target reaction, we need to manipulate the given reactions. Let's reverse the first reaction and halve it, which also reverses its enthalpy sign and halves the magnitude. Then, subtract the modified first reaction from the unmodified second reaction.

Step 3: Solve for \(\Delta H^{\circ}\)

After the above manipulations, the resultant reaction is the target reaction and its \(\Delta H^{\circ}\) can be obtained by adding the enthalpy changes of the modified reactions, that is, half the reverse of the first reaction's \(\Delta H^{\circ}\) and the second reaction's \(\Delta H^{\circ}\).

Key Concepts

Chemical Reactions

Chemical reactions involve the transformation of substances, resulting in the formation of new products. These reactions can be represented using chemical equations, which show the reactants on the left side and the products on the right side. In the example given, the reaction \( \text{C}_2\text{H}_4(g) + \text{Cl}_2(g) \rightarrow \text{C}_2\text{H}_4\text{Cl}_2(l) \) involves the combination of ethylene gas and chlorine gas to form dichloroethane liquid.
This is a type of synthesis reaction, where two or more simple substances combine to form a more complex product. The process of these transformations is governed by the principles of stoichiometry, which determine the proportions of each reactant and product.
Understanding the nature of reactants and the conditions under which they react is crucial to predicting the outcomes of chemical reactions. Factors such as temperature, pressure, and catalyst presence can significantly affect the reaction rate and product yields.

Hess's Law

Hess's Law is a principle in chemistry that helps in calculating the enthalpy change \( \Delta H \) for a reaction. It states that the total enthalpy change for a chemical reaction is the same, irrespective of the route taken. This means you can use a series of intermediate steps to arrive at the enthalpy change of the overall reaction.
In the exercise provided, Hess’s Law is applied by manipulating and combining the given reactions to arrive at the desired reaction and its enthalpy change. For example, to find the enthalpy of formation for the reaction \( \text{C}_2\text{H}_4(g) + \text{Cl}_2(g) \rightarrow \text{C}_2\text{H}_4\text{Cl}_2(l) \), known reactions were rearranged and their enthalpies adjusted.
The versatility of Hess's Law allows chemists to determine enthalpy changes that are difficult to measure directly. By breaking complex reactions into simpler steps, its application makes thermodynamic calculations more manageable.

Thermodynamics

Thermodynamics, particularly its branch focused on chemical reactions, examines the energy changes that occur during reactions. The key aspect of thermodynamics in chemistry is understanding how energy is absorbed or released.
The concept of enthalpy, which is a measure of total energy within a chemical system at constant pressure, plays a vital role in this analysis. In reactions, enthalpy change \( \Delta H \) reflects the difference in energy between products and reactants.
Thermodynamics also introduces the idea of spontaneity, predicting whether a reaction will occur under given conditions. Factors like temperature, entropy, and Gibbs free energy are used to assess this. Through these principles, thermodynamics provides a framework that helps predict and interpret the energy flow in chemical processes.

Enthalpy in Chemistry

Enthalpy is a thermodynamic property that signifies the heat content of a chemical system. It is crucial in understanding how energy flows in reactions. The enthalpy change \( \Delta H \) is typically measured in kilojoules per mole (kJ/mol) and indicates how much heat is absorbed or released.
In chemical reactions, if \( \Delta H \) is negative, the reaction releases heat, termed an exothermic reaction. Conversely, a positive \( \Delta H \) indicates heat absorption, characteristic of endothermic reactions.
Enthalpy changes are essential for understanding reaction energetics and are used extensively in designing reactions and processes in industrial applications. By calculating the enthalpy changes, chemists can predict temperature changes during reactions and the feasibility of reactions under specific conditions. Moreover, enthalpy changes help in planning efficient energy use in chemical plants and environmental conservation by evaluating process energy demands.