Problem 80 - Chemistry The Molecular Science

Question

When \(43.2 \mathrm{~g} \mathrm{Mg}\) reacts with sufficient sulfur, \(615 \mathrm{~kJ}\) is transferred to the surroundings. Calculate the standard formation enthalpy for \(\mathrm{MgS}\).

Step-by-Step Solution

Answer

The standard formation enthalpy for MgS is approximately -345.7 kJ/mol.

Step 1: Understand the Reaction

To find the standard enthalpy of formation for magnesium sulfide (MgS), we need to understand the reaction. Magnesium (Mg) reacts with sulfur (S) to form MgS. This reaction is exothermic as it releases 615 kJ of energy.

Step 2: Determine Moles of Reactant

Calculate the number of moles of magnesium used. The molar mass of magnesium is 24.305 g/mol. Use the formula: \( n = \frac{\text{mass}}{\text{molar mass}} \).\[ n = \frac{43.2 \text{ g}}{24.305 \text{ g/mol}} \approx 1.778 \text{ mol Mg} \]

Step 3: Calculate Enthalpy Change Per Mole

The total energy released is 615 kJ for 1.778 moles of Mg. Calculate the enthalpy change per mole using\[ \Delta H_f = \frac{-615 \text{ kJ}}{1.778 \text{ mol}} \approx -345.7 \text{ kJ/mol} \].

Step 4: Define the Formation Enthalpy

The standard formation enthalpy for MgS is the enthalpy change when one mole of MgS is formed from its elements in their standard states. The calculation shows that the standard enthalpy of formation for MgS is \( -345.7 \text{ kJ/mol} \).

Key Concepts

Exothermic Reaction

An exothermic reaction is a chemical reaction that releases energy, usually in the form of heat. This happens when the total energy of the products is less than the total energy of the reactants. In the case of magnesium reacting with sulfur to form magnesium sulfide (MgS), a significant amount of energy, 615 kJ, is released to the surroundings.

There are some key points to understand about exothermic reactions:

• Energy is released due to the formation of chemical bonds in the products.
• These reactions often result in an increase in temperature of the surroundings.
• They are characterized by a negative enthalpy change, indicating energy is released rather than absorbed.

Understanding these concepts will help you recognize and predict whether a reaction will release energy and how such energy changes affect chemical processes.

Molar Mass

Molar mass is an important concept in chemistry, referring to the mass of one mole of a substance. It is expressed in grams per mole (g/mol). For magnesium, the molar mass is 24.305 g/mol, which means that each mole of magnesium weighs 24.305 grams. When solving chemical equations or reactions, calculating molar mass is crucial.

Here’s why understanding molar mass is essential:

• It allows you to convert between the amount of substance in grams and the amount in moles.
• Accurate molar mass calculations are necessary for determining the proportions of reactants and products in chemical reactions.
• It helps in calculating other important properties such as concentration and gas volumes in chemistry.

By knowing the molar mass, we can accurately calculate how many moles are present in a given mass of a substance, as shown in the example with magnesium.

Enthalpy Change Per Mole

Enthalpy change per mole, often denoted as \( \Delta H \), is a key concept for understanding the energy changes in chemical reactions. Specifically, it refers to the change in enthalpy when one mole of a reaction takes place. In the case of the reaction forming magnesium sulfide, the enthalpy change per mole is calculated by dividing the total energy released by the number of moles of the reactant.

Let’s break it down further:

• The enthalpy change per mole provides insight into the energy efficiency of a reaction.
• A negative value indicates that the reaction releases energy, as observed in exothermic reactions.
• Understanding enthalpy change per mole can help predict reaction behavior and stability.

This concept is instrumental in thermodynamics and aids in the design and evaluation of chemical processes by quantifying how much energy is needed or released.