Question

What is the enthalpy change for the unknown reaction? $$ \begin{array}{l} \mathrm{Pb}(\mathrm{s})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{PbCl}_{2}(\mathrm{~s}) \Delta H=-359 \mathrm{~kJ} \\ \mathrm{PbCl}_{2}(\mathrm{~s})+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{PbCl}_{4}(\ell) \Delta H=? \\ \mathrm{~Pb}(\mathrm{~s})+2 \mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{PbCl}_{4}(\ell) \Delta H=-329 \mathrm{~kJ} \end{array} $$

Short answer

The enthalpy change for the unknown reaction is 30 kJ.

Step-by-step solution

Identify Known Reactions

First, identify the given reactions and their enthalpy changes.1. \( \mathrm{Pb}(\mathrm{s}) + \mathrm{Cl}_2 (\mathrm{g}) \rightarrow \mathrm{PbCl}_2 (\mathrm{s}) \) with \( \Delta H = -359 \mathrm{~kJ} \)2. \( \mathrm{Pb}(\mathrm{s}) + 2 \mathrm{Cl}_2 (\mathrm{g}) \rightarrow \mathrm{PbCl}_4 (\ell) \) with \( \Delta H = -329 \mathrm{~kJ} \)3. The unknown reaction: \( \mathrm{PbCl}_2 (\mathrm{s}) + \mathrm{Cl}_2 (\mathrm{g}) \rightarrow \mathrm{PbCl}_4 (\ell) \) with an unknown \( \Delta H \).

Calculate Using Hess's Law

Hess's Law states that the total enthalpy change for a reaction is the same, no matter how it is carried out in steps. We can set up the equations to solve for the unknown enthalpy.The overall reaction is: \( \mathrm{Pb}(\mathrm{s}) + 2 \mathrm{Cl}_2 (\mathrm{g}) \rightarrow \mathrm{PbCl}_4 (\ell) \).To achieve this using the given reactions:- Start with \( \mathrm{Pb}(\mathrm{s}) + \mathrm{Cl}_2 (\mathrm{g}) \rightarrow \mathrm{PbCl}_2 (\mathrm{s}) \) with \( \Delta H = -359 \mathrm{~kJ} \).- Follow with \( \mathrm{PbCl}_2 (\mathrm{s}) + \mathrm{Cl}_2 (\mathrm{g}) \rightarrow \mathrm{PbCl}_4 (\ell) \) with unknown \( \Delta H \).

Set Up Equation

Based on Hess's Law, the sum of the two reactions should equal the direct reaction's \( \Delta H \):\[ -359 \mathrm{~kJ} + \Delta H = -329 \mathrm{~kJ} \]Solve for \( \Delta H \) to find the enthalpy change for the unknown reaction.

Solve Equation

Rearrange and solve the equation:\[ \Delta H = -329 \mathrm{~kJ} + 359 \mathrm{~kJ} \]\[ \Delta H = 30 \mathrm{~kJ} \]

Key concepts

Understanding Enthalpy Change

Enthalpy change, denoted as \( \Delta H \), represents the heat absorbed or released in a chemical reaction at constant pressure. It is an important concept in thermochemistry that helps predict whether a reaction is exothermic or endothermic. An exothermic reaction releases heat to the surroundings, resulting in a negative \( \Delta H \). Conversely, an endothermic reaction absorbs heat, giving a positive \( \Delta H \).

In the context of Hess's Law, the enthalpy change is independent of the path taken by the reaction. This means that you can split reactions into multiple steps and still calculate the same overall enthalpy change, as each step's contribution is considered. By understanding \( \Delta H \), students can better grasp energy changes occurring during chemical reactions, predicting how much energy a reaction will absorb or give off.

Exploring Thermochemistry

Thermochemistry is the branch of chemistry that studies the relationship between chemical reactions and energy changes. A core focus is on how heat is involved in chemical processes. This field uses concepts like enthalpy, entropy, and free energy to understand and predict reaction behavior.

One of its key principles is the conservation of energy, which states that energy cannot be created or destroyed, only transformed or transferred. This principle allows chemists to calculate how much energy certain reactions require or produce. Hess's Law is an essential tool within thermochemistry, enabling chemists to determine the enthalpy change for complex reactions by breaking them down into simpler steps with known energy changes.

• By using Hess's Law, you can add or subtract enthalpy values of known reactions to find unknown enthalpies for related reactions.
• Thermochemistry provides ways to measure these energy changes, often involving calorimetry, to obtain precise data for calculations.

Basics of Chemical Equation Balancing

Balancing chemical equations is crucial for ensuring that the same amount of each element is present on both sides of the equation. This practice reflects the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction.

In a balanced equation, the number and type of atoms are the same for the reactants and products. This balance is vital for accurately calculating enthalpy changes since the stoichiometry of the reaction is directly linked to the energy change.

• An accurate coefficient for each molecule ensures the correct mole ratio, aligning calculations with the actual chemical amounts involved.
• Balancing helps in determining the exact proportion of reactants needed and predicting the amount of products formed.

Using this knowledge, students can ensure they correctly determine energy changes and the consumption or production of energy in reactions as exemplified in Hess's Law application.