Question

Consider the process by which lead chloride dissolves in water: $$ \mathrm{PbCl}_{2}(s) \longrightarrow \mathrm{Pb}^{2+}(a q)+2 \mathrm{Cl}^{-}(a q) $$ (a) Using data from tables in Chapter 8 , calculate \(\Delta H\) for this reaction. (b) Based only on thermodynamic data, would you expect the solubility of \(\mathrm{PbCl}_{2}\) to increase if the temperature is increased?

Short answer

#Answer# (a) The enthalpy change (ΔH) for the dissolution of lead chloride (PbCl₂) in water is -122 kJ/mol. (b) The solubility of PbCl₂ is expected to decrease with increasing temperature because the dissolution process is exothermic.

Step-by-step solution

Identify the enthalpy of formation for each component

Using the enthalpy formation data provided in Chapter 8, find the enthalpy of formation for each component in the reaction: - PbCl₂(s): ΔHf(PbCl₂) = -359 kJ/mol - Pb²⁺(aq): ΔHf(Pb²⁺) = -147 kJ/mol - Cl⁻(aq): ΔHf(Cl⁻) = -167 kJ/mol

Apply Hess's Law to calculate the enthalpy change

ΔHreaction = Σ [ΔHf(products)] - Σ [ΔHf(reactants)] ΔHreaction = [1 * ΔHf(Pb²⁺) + 2 * ΔHf(Cl⁻)] - [1 * ΔHf(PbCl₂)] Plug in the values: ΔHreaction = (1 * (-147 kJ/mol) + 2 * (-167 kJ/mol)) - (1 * (-359 kJ/mol)) ΔHreaction = -481 kJ/mol + 359 kJ/mol ΔHreaction = -122 kJ/mol

Analyze the enthalpy change with respect to solubility change

Since the enthalpy change (ΔHreaction) is negative, the dissolution of PbCl₂ in water is exothermic (releases heat). According to Le Chatelier's Principle, if we increase the temperature of the system, the reaction will shift in a direction that absorbs the extra heat which, in this case, is the reverse reaction (precipitation of PbCl₂).

Answer the question about the solubility change with temperature

Based on thermodynamic data and our analysis, we can conclude that the solubility of PbCl₂ would not increase if the temperature is increased; in fact, the solubility is expected to decrease when the temperature increases since the dissolution process is exothermic.

Key concepts

Enthalpy of Formation

The enthalpy of formation, represented as \( \Delta H_f \), is a measure of the change in enthalpy when one mole of a substance is formed from its elements in their standard states. Understanding this concept is crucial for predicting how substances will interact in a reaction, including their solubility in various solvents like water.

For each substance involved in a chemical reaction, tabulated values of \( \Delta H_f \) are used to determine the overall energy change. For instance, the enthalpy of formation for the lead chloride (\( \Delta H_f(\mathrm{PbCl}_2) \) = -359 kJ/mol) reflects the energy released when one mole of lead chloride is formed from its constituent elements, lead and chlorine, under standard conditions.

When considering solubility, the enthalpy of formation for the dissolved ions, lead (II) ions (\( \Delta H_f(\mathrm{Pb^{2+}}) \) = -147 kJ/mol) and chloride ions (\( \Delta H_f(\mathrm{Cl^-}) \) = -167 kJ/mol), must also be accounted for. These values are essential to computing the overall energy change during the dissolution process.

Hess's Law

According to Hess's Law, the total enthalpy change for a reaction is the same, no matter how the reaction occurs, as long as it begins and ends with the same substances. In other words, whether a chemical change happens in one step or multiple stages, the total energy transfer is constant.

To apply this law in calculating enthalpy changes, sum up the enthalpies of formation for the products and subtract the sum of the enthalpies of formation for the reactants. Take the case of lead chloride dissolving in water: \( \Delta H_{reaction} = [\Delta H_f(\mathrm{Pb^{2+}}) + 2 \cdot \Delta H_f(\mathrm{Cl^-})] - [\Delta H_f(\mathrm{PbCl}_2)] \). By substituting the required values, we obtain the total enthalpy change for the dissolution process. This allows us to assess whether the reaction absorbs or releases energy, which directly impacts the solubility of substances like lead chloride.

Le Chatelier's Principle

Le Chatelier's Principle reveals how a system at equilibrium adjusts to changes that affect the equilibrium conditions. For example, adding or removing heat will cause the equilibrium to shift in a way that counteracts that change.

If the dissolution of a substance like lead chloride (\( \mathrm{PbCl}_2 \)) is exothermic (releases heat), Le Chatelier's Principle tells us that increasing the temperature will drive the reaction towards the reactants to absorb the extra heat. This results in the formation of more \( \mathrm{PbCl}_2 \) solid and decreases its solubility in water.

Inversely, if the reaction were endothermic (absorbing heat), raising the temperature would increase solubility, because the system would need to absorb more heat to reach equilibrium, favoring the dissolution reaction. Understanding this principle assists students in predicting the effects of temperature changes on solubility.