Question

Magnesium burns in air to produce a bright light and is often used in fireworks displays. The combustion of magnesium can be described by the following thermochemical equation: \(2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s) \quad \Delta H^{\circ}=-1203 \mathrm{~kJ}\) How much heat (in kilojoules) is liberated by the combustion of \(6.54 \mathrm{~g}\) of magnesium?

Short answer

The combustion of 6.54 grams of magnesium liberates 326.51 kilojoules of heat.

Step-by-step solution

Calculate moles of Magnesium

First, calculate the number of moles of magnesium (Mg) using its molar mass (24.31 grams/mole). Use the formula: moles of Mg = mass of Mg / molar mass of Mg.

Apply the stoichiometry of the reaction

Determine how the moles of magnesium relate to the heat released using the stoichiometry of the reaction given by the thermochemical equation.

Calculate the heat released

Multiply the moles of magnesium by the heat released per mole of magnesium as given by the reaction's \(\Delta H^\circ\) value to find the total heat liberated.

Key concepts

Thermochemical Equation

When we examine the combustion of magnesium, we encounter a thermochemical equation, which is essentially a chemical equation that includes the heat of reaction—termed enthalpy change (\( \Delta H^\circ \) ). In this equation,

\(2 \mathrm{Mg}(s) + \mathrm{O}_2(g) \longrightarrow 2 \mathrm{MgO}(s)\) indicates that two moles of solid magnesium react with one mole of diatomic oxygen gas to produce two moles of magnesium oxide in solid form. The \( \Delta H^\circ \) value of -1203 kJ tells us the reaction is exothermic, releasing that amount of heat when two moles of magnesium completely combust. Understanding this equation is crucial as it provides the foundation for our calculations and hints at the proportional relationship between the reacting substances and the energy exchange.

Stoichiometry

Stoichiometry, a central concept in chemistry, involves using balanced chemical equations to calculate the quantities of reactants and products involved in a chemical reaction. In the context of magnesium combustion, stoichiometry allows us to understand the proportional relationships that govern how reactants are consumed and products are formed. Specifically, the balanced equation shows a 2:1:2 mole ratio between magnesium, oxygen, and magnesium oxide. This stoichiometric information tells us that for every two moles of magnesium reacting, we can expect a corresponding release of -1203 kJ of heat energy (as indicated by the thermochemical equation).

In practical terms, stoichiometry enables us to scale this relationship to any amount of reactants—so long as we maintain the ratios dictated by the balanced equation, we can predict the amount of products and energy changes.

Heat of Reaction

Heat of reaction, or enthalpy change \( \Delta H \), is a term describing the heat absorbed or released during a chemical reaction at constant pressure. In an exothermic reaction like the combustion of magnesium, heat is released, which is noted by a negative \( \Delta H \).

For our example, the heat of reaction is -1203 kJ, which relates to two moles of magnesium. This is a significant piece of information because it allows us to calculate the energy change for any given amount of magnesium. We can predict that burning less than two moles of magnesium will release less heat, proportional to the amount burned—a concept inherently linked to stoichiometry. When dealing with enthalpy changes, it's important to relate the quantity to standard conditions, denoted by the degree sign in \( \Delta H^\circ \).

Moles Calculation

Calculating moles is a fundamental task in chemistry for quantitatively describing amounts of substances. Given a mass, we can determine the number of moles by using the substance's molar mass as a conversion factor. For magnesium, the molar mass is 24.31 grams/mole. Using the formula \(\text{moles of Mg} = \frac{\text{mass of Mg}}{\text{molar mass of Mg}}\), and the given mass of 6.54 g, we determine the moles of magnesium involved in the reaction.

Once we have the moles, we link this quantity to the heat of reaction using stoichiometry to calculate the heat released. This step is critical because the amount of heat produced in a reaction is directly related to the amount of the reactant—magnesium, in this case—that undergoes combustion.