Question

Using the following data, calculate the standard heat of formation of \(\operatorname{ICl}(g)\) in \(\mathrm{kJ} / \mathrm{mol}\) : $$ \begin{aligned} \mathrm{Cl}_{2}(g) & \longrightarrow 2 \mathrm{Cl}(g) & \Delta H^{\circ} &=242.3 \mathrm{~kJ} \\ \mathrm{I}_{2}(g) & \longrightarrow 2 \mathrm{I}(g) & \Delta H^{\circ} &=151.0 \mathrm{~kJ} \\ \mathrm{ICl}(g) & \longrightarrow \mathrm{I}(g)+\mathrm{Cl}(g) & \Delta H^{\circ} &=211.3 \mathrm{~kJ} \\ \mathrm{I}_{2}(s) & \Delta H^{\circ}=62.8 \mathrm{~kJ} \end{aligned} $$

Short answer

The standard heat of formation of ICl(g) is \(-14.65 \mathrm{~kJ/mol}\).

Step-by-step solution

Identify the direct reaction pathway

First, we have to identify the direct reaction pathway from reactants to products for ICl(g). We can see that we need 1/2 I2(g), 1/2 Cl2(g), and ICl(g) reactions.

Determine the stoichiometric coefficients

In this step, we will determine the stoichiometric coefficients for our direct reaction pathway. The balanced equation for the formation of ICl(g) is: $$ \frac{1}{2} \mathrm{I}_{2}(g) + \frac{1}{2} \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{ICl}(g) $$

Calculate the standard heat of formation

To calculate the standard heat of formation, we will add or subtract the \(\Delta H^{\circ}\) of each reaction in our direct pathway, making sure to multiply each \(\Delta H^{\circ}\) by its respective stoichiometric coefficient from Step 2. The equation we need to follow is: $$ \Delta H_{f}^{\circ}(\mathrm{ICl}(g)) = \frac{1}{2}\Delta H^{\circ}(\mathrm{I}_{2}(g)) + \frac{1}{2}\Delta H^{\circ}(\mathrm{Cl}_{2}(g)) - \Delta H^{\circ}(\mathrm{ICl}(g)) $$ Using the provided data: $$ \Delta H_{f}^{\circ}(\mathrm{ICl}(g)) = \frac{1}{2}(151.0 \mathrm{~kJ}) + \frac{1}{2}(242.3 \mathrm{~kJ}) - 211.3\mathrm{~kJ} $$

Calculate the final answer

Evaluate the expression to find the standard heat of formation for ICl(g): $$ \Delta H_{f}^{\circ}(\mathrm{ICl}(g)) = 75.5\mathrm{~kJ} + 121.15\mathrm{~kJ} - 211.3\mathrm{~kJ} = -14.65\mathrm{~kJ} $$ Thus, the standard heat of formation of ICl(g) is -14.65 kJ/mol.

Key concepts

Stoichiometric Coefficients

Stoichiometric coefficients play a pivotal role in chemical reactions, especially when it comes to calculating thermodynamic quantities like the standard heat of formation. These coefficients indicate the proportion of each reactant and product involved in a reaction. For any balanced chemical equation, stoichiometric coefficients ensure that the law of conservation of mass is upheld and the number of atoms for each element is the same on both sides of the equation.

• In this exercise, the stoichiometric coefficients for iodine (\(I_2 ext{(g)}\)) and chlorine (\(Cl_2 ext{(g)}\)) were determined as \(\frac{1}{2}\), meaning that half a mole of each gas is needed to form one mole of iodine monochloride (\(ICl ext{(g)}\)).
• These coefficients help in scaling the enthalpy change (\(\Delta H\)) for the reaction, appropriately reflecting the change per mole of \(ICl ext{(g)}\).

Understanding stoichiometric coefficients allows us to accurately use given reaction data in thermochemical calculations, which is essential for predicting the enthalpy changes in chemical reactions.

Direct Reaction Pathway

The concept of a direct reaction pathway simplifies the process of calculating thermodynamic changes by outlining a straightforward path from reactants to the desired products.
It essentially allows chemists to break down complex reactions into a series of simpler steps for which data is available.

• In this context, creating \(ICl ext{(g)}\) involves determining a direct pathway from the elements \(I_2 ext{(g)}\) and \(Cl_2 ext{(g)}\) to the product.
• Instead of dealing directly with solid iodine, understanding the gaseous pathway helps us use more commonly available \(\Delta H^\circ\) values of intermediate steps.

By using a direct reaction pathway, the task of compiling accurate thermochemical calculations becomes much more manageable, as it allows for the use of available thermodynamic data.

Thermochemistry Calculations

Thermochemistry calculations are crucial for understanding the heat changes that accompany chemical reactions. In this exercise, calculating the standard heat of formation involves combining the \(\Delta H^\circ\) values from various reactions using stoichiometric coefficients.

This is achieved with the equation:\[\Delta H_{f}^{\circ}(ICl(g)) = \frac{1}{2}\Delta H^{\circ}(I_2(g)) + \frac{1}{2}\Delta H^{\circ}(Cl_2(g)) - \Delta H^{\circ}(ICl(g))\]

• Each term in this equation represents an enthalpy change that associates with transforming the reactants into products along the identified pathway.
• Using the values from the given data, we substitute them into this equation and find the value of \(\Delta H_{f}^{\circ}(ICl(g))\), which simplifies into evaluating simple arithmetic calculations.

The resulting value of \(-14.65\text{kJ/mol}\) reflects the energy change when one mole of \(ICl\) is formed, giving a comprehensive understanding of the thermodynamic aspects of the reaction. By mastering these calculations, students are able to predict not just energy changes but also aspects like reaction feasibility and direction in thermochemical contexts.