Question

Given the following data $$ \begin{aligned} 2 \mathrm{ClF}(g)+\mathrm{O}_{2}(g) & \longrightarrow \mathrm{Cl}_{2} \mathrm{O}(g)+\mathrm{F}_{2} \mathrm{O}(g) & \Delta H &=167.4 \mathrm{~kJ} \\ 2 \mathrm{ClF}_{3}(g)+2 \mathrm{O}_{2}(g) & \longrightarrow \mathrm{Cl}_{2} \mathrm{O}(g)+3 \mathrm{~F}_{2} \mathrm{O}(g) & \Delta H &=341.4 \mathrm{~kJ} \\\ 2 \mathrm{~F}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{~F}_{2} \mathrm{O}(g) & \Delta H &=-43.4 \mathrm{~kJ} \end{aligned} $$ calculate \(\Delta H\) for the reaction $$ \mathrm{ClF}(g)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{ClF}_{3}(g) $$

Short answer

The enthalpy change, \(\Delta H\), for the reaction $$ \mathrm{ClF}(g)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{ClF}_{3}(g) $$ is -189.1 kJ.

Step-by-step solution

Identify which reactions will be used to form the desired reaction.

First, we need to determine which reactions we need to combine to get the desired reaction: $$ \mathrm{ClF}(g)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{ClF}_{3}(g) $$ From the given reactions, we know that the above reaction is a combination of the first and third reaction.

Adjust the reactions to match the desired reaction coefficients.

We will manipulate the first and third reactions so that they can be added together to create the desired reaction equation. In this case, we will reverse the first reaction and divide the third reaction by 2. This will give us the correct stoichiometric coefficients for our target reaction. Reversed first reaction: $$ \mathrm{Cl}_{2}\mathrm{O}(g)+\mathrm{F}_{2}\mathrm{O}(g) \longrightarrow 2 \mathrm{ClF}(g)+\mathrm{O}_{2}(g) $$ and the new enthalpy is $$ \Delta H_{1}' = -167.4 \mathrm{~kJ} $$ Divide the third reaction by 2: $$ \mathrm{F}_{2}(g)+\frac{1}{2}\mathrm{O}_{2}(g) \longrightarrow \mathrm{F}_{2}\mathrm{O}(g) $$ and the new enthalpy is $$ \Delta H_{3}' = -\frac{43.4}{2} \mathrm{~kJ} = -21.7 \mathrm{~kJ} $$

Add the adjusted reactions and their enthalpy changes.

Now we will add the adjusted reactions from Step 2 to form the desired reaction, and add the corresponding enthalpies to find the enthalpy for the desired reaction. Add the adjusted reactions: $$ (\mathrm{Cl}_{2}\mathrm{O}(g)+\mathrm{F}_{2}\mathrm{O}(g) \longrightarrow 2\mathrm{ClF}(g)+\mathrm{O}_{2}(g)) + (\mathrm{F}_{2}(g)+\frac{1}{2}\mathrm{O}_{2}(g) \longrightarrow \mathrm{F}_{2}\mathrm{O}(g)) $$ This simplifies to $$ \mathrm{ClF}(g)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{ClF}_{3}(g) $$ Add the adjusted enthalpy changes: $$ \Delta H = \Delta H_{1}' + \Delta H_{3}' = -167.4 \mathrm{~kJ} - 21.7 \mathrm{~kJ} = -189.1 \mathrm{~kJ} $$

Write the answer.

The enthalpy change, \(\Delta H\), for the reaction $$ \mathrm{ClF}(g)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{ClF}_{3}(g) $$ is -189.1 kJ.

Key concepts

Hess's Law

Hess's Law is a principle in chemistry that states that the total enthalpy change for a chemical reaction is the same, no matter how the reaction occurs, in one step or multiple steps. This is because enthalpy is a state function, meaning it depends only on the initial and final states of a system, not on the path taken to get there. In essence, if you know the enthalpy change of several steps in a reaction pathway, you can add or subtract them to find the overall enthalpy change.

One way to apply Hess’s Law, as demonstrated in the step-by-step solution, is by manipulating given reactions (such as reversing reactions or dividing stoichiometric coefficients) to match a desired reaction. Then, you sum up the enthalpy changes of these modified reactions to find the enthalpy change of the target reaction. This method allows us to calculate enthalpy changes that are difficult or impossible to measure directly in a lab.

To enable easy calculations:

• Identify the reactions that, when combined, will yield the desired equation.
• Adjust the coefficients in the reactions to fit the target reaction.
• Reverse any reactions as necessary, remembering that reversing a reaction changes the sign of its enthalpy change.
• Add the adjusted enthalpy changes to find the enthalpy of the desired reaction.

Thermochemistry

Thermochemistry is the branch of chemistry that deals with the study of heat energy associated with chemical reactions and changes of state. It involves studying how energy, in the form of heat, is absorbed or released as substances undergo chemical transformations.

Enthalpy (\(H\)), a concept central to thermochemistry, is the heat content of a system at constant pressure. When we calculate the enthalpy change (\(\Delta H\)) for a reaction, we are determining how much heat is absorbed or evolved as the reaction proceeds. A negative \(\Delta H\) indicates an exothermic reaction, where heat is released, while a positive \(\Delta H\) indicates an endothermic reaction, where heat is absorbed.

Thermochemistry provides crucial insights into:

• Energy transfer among molecules and the environment during reactions.
• Understanding reaction spontaneity and feasibility in connection with kinetics and thermodynamics.
• Industrial applications, such as designing processes that optimize energy use in chemical manufacturing.

In our example, understanding the enthalpy changes are vital because they illustrate how energy is exchanged when using the given reactions to achieve the desired chemical transformation.

Stoichiometry

Stoichiometry refers to the calculation of reactants and products in chemical reactions. It is rooted in the conservation of mass, meaning that in a chemical reaction, the mass of the reactants equals the mass of the products. Stoichiometry ensures that equations are balanced, with the same number of each type of atom on both sides of the reaction.

In stoichiometry, coefficients in a chemical equation tell us the ratio in which molecules or moles of each substance react and are produced. For example, if a balanced equation reads 2\(\text{A} + 3 \text{B} \rightarrow 4\text{C}\), it means:

• 2 moles of substance A react with 3 moles of substance B.
• This reaction produces 4 moles of substance C.

In practice, stoichiometry allows chemists to:

• Determine how much of each reactant is needed to produce a desired amount of product.
• Predict how much product will be formed from known quantities of reactants.
• Ensure chemical reactions are efficient and resources are used effectively.

Applying this to the exercise, stoichiometry helps manipulate the given reactions to align with a target chemical reaction, enabling the successful application of Hess's Law to calculate the desired enthalpy change.