Question

Consider the following reaction: $$ 2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g)-\longrightarrow 2 \mathrm{MgO}(s) \quad \Delta H=-1204 \mathrm{~kJ} $$ (a) Is this reaction exothermic or endothermic? (b) Calculate the amount of heat transferred when \(2.4 \mathrm{~g}\) of \(\mathrm{Mg}(s)\) reacts at constant pressure. (c) How many grams of \(\mathrm{MgO}\) are produced during an enthalpy change of \(-96.0 \mathrm{~kJ} ?\) (d) How many kilojoules of heat are absorbed when \(7.50 \mathrm{~g}\) of \(\mathrm{MgO}(s)\) is decomposed into \(\mathrm{Mg}(s)\) and \(\mathrm{O}_{2}(g)\) at constant pressure?

Short answer

(a) This reaction is exothermic. (b) The amount of heat transferred when $2.4 \, \text{g}$ of Mg reacts is $60.2 \, \text{kJ}$. (c) $3.2 \, \text{g}$ of MgO is produced when the enthalpy change is $-96.0 \, \text{kJ}$. (d) The heat absorbed when $7.5 \, \text{g}$ of MgO is decomposed into Mg(s) and O₂(g) at constant pressure is $112.4 \, \text{kJ}$.

Step-by-step solution

(a) Determine the type of reaction

The ΔH value is given as -1204 kJ which means that heat is being released. Since heat is released during this reaction, it is called exothermic.

(b) Calculate the amount of heat transferred

We are given 2.4 g of Mg. First, we'll convert this mass into moles. The molar mass of Mg is approximately 24.3 g/mol. So, \( \frac{2.4 \, \text{g}}{24.3 \, \text{g/mol}} = 0.1 \, \text{mol} \) of Mg. The stoichiometric ratio between Mg and the heat released is 2:1204 kJ. Now, we'll calculate the heat transferred by using the ratio: Heat transferred = \( \frac{0.1 \, \text{mol}}{2 \, \text{mol}} × 1204 \, \text{kJ} = 60.2 \, \text{kJ} \) The amount of heat transferred when 2.4 g of Mg reacts is 60.2 kJ.

(c) Calculate MgO produced with an enthalpy change of -96.0 kJ

We are given an enthalpy change of -96.0 kJ, and we need to find how many grams of MgO are produced. We'll use the stoichiometric ratio of heat and MgO, which is 1204 kJ: 2 mol MgO. First, we'll determine the amount of MgO in moles: \( \frac{-96.0 \, \text{kJ}}{1204 \, \text{kJ/mol}} = 0.08 \, \text{mol} \) of MgO. Now, we'll convert the moles of MgO into grams, using its molar mass (40.3 g/mol): \( 0.08 \, \text{mol} × 40.3 \, \text{g/mol} = 3.2 \, \text{g} \) 3.2 g of MgO is produced when the enthalpy change is -96.0 kJ.

(d) Calculate the heat absorbed when 7.5 g of MgO is decomposed

We are given 7.5 g of MgO, and we need to calculate the heat absorbed during its decomposition at constant pressure. First, we'll convert the mass of MgO into moles. The molar mass of MgO is 40.3 g/mol: \( \frac{7.5 \, \text{g}}{40.3 \, \text{g/mol}} = 0.186 \, \text{mol} \) of MgO. Since the reaction is exothermic in the forward direction, it will be endothermic in the reverse direction. The stoichiometric ratio between MgO and the heat released is 2 mol MgO: 1204 kJ. We'll use this ratio to calculate the heat absorbed: Heat absorbed = \( \frac{0.186 \, \text{mol}}{2 \, \text{mol}} × 1204 \, \text{kJ} = 112.4 \, \text{kJ} \) The heat absorbed when 7.5 g of MgO is decomposed into Mg(s) and O₂(g) at constant pressure is 112.4 kJ.

Key concepts

Enthalpy Change

Enthalpy change, denoted as ΔH, refers to the amount of heat energy released or absorbed during a chemical reaction occurring at constant pressure. It's a key concept in thermochemistry. The enthalpy change provides insight into whether a reaction is exothermic or endothermic, based on the sign of ΔH.
If ΔH is negative, it indicates that energy is released to the surroundings, making the reaction exothermic. Conversely, if ΔH is positive, the reaction absorbs energy from its surroundings, categorizing it as endothermic. In our example, the reaction of magnesium (Mg) with oxygen (O₂) has ΔH = -1204 kJ, indicating an exothermic reaction.
Understanding whether a reaction releases or absorbs heat is crucial when predicting reaction behavior and calculating energy changes involved in chemical processes.

Exothermic Reaction

An exothermic reaction is a type of chemical reaction that releases energy, usually in the form of heat. This release occurs when bonds form in the products releasing more energy than is consumed during the breaking of bonds in the reactants.
In the context of the reaction between magnesium and oxygen to form magnesium oxide (MgO), the negative enthalpy change of -1204 kJ signifies that it is exothermic. This means the reaction releases a significant amount of heat as the chemical bonds in MgO are stronger and more stable than those in the reactants.
Exothermic reactions are not only important in chemical manufacturing and energy production but are also a source of heat in everyday occurrences like combustion and metabolism.

Heat Transfer

Heat transfer in the realm of thermochemistry refers to the movement of thermal energy from one substance to another. It occurs due to the temperature difference and is a critical concept in understanding enthalpy changes in chemical reactions.
In our exercise, calculating the heat transfer involved converting the mass of magnesium into moles, and then using stoichiometric ratios to determine the heat released. For example, with 2.4 g of Mg reacting, the heat transferred was calculated to be 60.2 kJ using the stoichiometric relationship from the reaction and its enthalpy change.
This practical calculation illustrates how energy transfers in chemical reactions are quantifiable and predictable through stoichiometry and mole conversions.

Molar Mass Calculations

Molar mass calculations are crucial for converting between grams of a substance and moles, which are the bridge to understanding chemical equations and reaction stoichiometry. The molar mass of an element or compound, expressed in g/mol, is equivalent to the atomic or molecular weight found on the periodic table.
For magnesium and magnesium oxide in the exercise, the molar masses used were approximately 24.3 g/mol and 40.3 g/mol respectively. These calculations allowed for converting grams into moles, and subsequently, for determining the amount of heat transferred in the reactions.
For instance, converting 2.4 g of Mg into moles using its molar mass enabled further energy calculations. Similarly, converting the number of moles of MgO to grams allowed us to find out how much product formed under specific enthalpy changes.