Problem 78 - Chemistry The Molecular Science

Question

Calorimetric measurements show that the reaction of magnesium with chlorine releases \(26.4 \mathrm{~kJ}\) per gram of magnesium reacted. (a) Write a balanced chemical equation for the reaction. (b) Calculate the standard formation enthalpy of magnesium chloride.

Step-by-Step Solution

Answer

(a) \( \text{Mg} + \text{Cl}_2 \rightarrow \text{MgCl}_2 \); (b) \(-641.784 \mathrm{~kJ/mol}\).

Step 1: Determine the Reaction

The reaction between magnesium and chlorine is a synthesis reaction where magnesium and chlorine combine to form magnesium chloride. The unbalanced chemical equation is \( \text{Mg} + \text{Cl}_2 \rightarrow \text{MgCl}_2 \).

Step 2: Balance the Chemical Equation

In this equation, one magnesium (Mg) atom combines with one chlorine molecule (Cl₂) to form magnesium chloride (MgCl₂). The balanced chemical equation is \( \text{Mg}(s) + \text{Cl}_2(g) \rightarrow \text{MgCl}_2(s) \).

Step 3: Use Energy Released to Find Enthalpy Change

Since \(26.4 \mathrm{~kJ}\) of energy is released per gram of magnesium reacted, calculate the enthalpy change using the molar mass of magnesium \(24.31 \mathrm{~g/mol}\). Enthalpy change \(= 26.4 \times 24.31 \approx 641.784\mathrm{~kJ/mol}\).

Step 4: Calculate the Standard Enthalpy of Formation

The standard formation enthalpy \( \Delta H_f^\circ \) for magnesium chloride can be considered equivalent to the enthalpy change calculated since we start with elemental forms of magnesium and chlorine. The enthalpy of formation for \( \text{MgCl}_2 \) is \( \Delta H_f^\circ = -641.784 \mathrm{~kJ/mol} \) (negative sign indicates exothermic reaction).

Key Concepts

Calorimetry

Calorimetry is a technique used in thermochemistry to measure the amount of heat involved in chemical reactions or physical changes. It plays a crucial role in understanding energetic exchanges between substances. When magnesium reacts with chlorine to form magnesium chloride, calorimetric measurements can help determine the energy released during this reaction by measuring temperature changes in the calorimeter.

• In calorimetry, the heat absorbed or released by the reaction is equivalent to the temperature change observed in the calorimeter, taking into account the specific heat capacity and mass of the solution or surroundings.
• This technique is essential for calculating reaction enthalpies, especially when you cannot measure them directly.

Since the reaction between magnesium and chlorine was noted to release 26.4 kJ of heat per gram of magnesium, this information assists in further calculations of enthalpies and reaction predictions. Understanding calorimetry allows chemists to assess the feasibility, safety, and energy efficiency of chemical processes.

Enthalpy Calculation

Enthalpy, a key concept in thermochemistry, refers to the heat content of a system at constant pressure. Calculating enthalpy changes (∆H) helps in understanding whether a reaction absorbs or releases energy.

To calculate the enthalpy change for a reaction:

• Identify the energy change per unit (usually per mole or gram).
• Utilize the known values of substances involved—such as molar mass.

To compute the enthalpy change for the reaction between magnesium and chlorine, multiply the energy released per gram by the molar mass of magnesium.
Enthalpy changes are calculated as:\[ \Delta H = \text{Energy released per unit} \times \text{Molar mass} \]For magnesium reacting with chlorine, the enthalpy is approximately \(-641.784 \text{kJ/mol}\), indicating an exothermic process. Understanding enthalpy calculations helps in evaluating the energy profiles of chemical reactions, providing insights into reaction spontaneity and equilibrium.

Balancing Chemical Equations

Balancing chemical equations is a fundamental step in performing any chemical calculation. It involves ensuring that the number of atoms for each element is the same on both sides of the equation. This is critical, as it reflects the law of conservation of mass.
When balancing the reaction of magnesium with chlorine:

• Start with the unbalanced equation: \(\text{Mg} + \text{Cl}_2 \rightarrow \text{MgCl}_2\).
• Observe that each side contains one magnesium atom and two chlorine atoms.
• Thus, no additional steps are needed to balance the equation as it already satisfies equal atom numbers across reactants and products.

Balancing equations helps ensure the correctness of stoichiometric calculations, allowing chemists to precisely predict the amounts of reactants and products. This practice underpins all calculations like enthalpy changes since it accurately reflects the materials' transformations during a reaction.