Question

Consider the following balanced thermochemical equation for the decomposition of the mineral magnesite: $$\mathrm{MgCO}_{3}(s) \longrightarrow \mathrm{MgO}(s)+\mathrm{CO}_{2}(g) \quad \Delta H=117.3 \mathrm{~kJ}$$ (a) Is heat absorbed or released in the reaction? (b) What is \(\Delta H\) for the reverse reaction? (c) What is \(\Delta H\) when \(5.35 \mathrm{~mol}\) of \(\mathrm{CO}_{2}\) reacts with excess \(\mathrm{MgO} ?\) (d) What is \(\Delta H\) when \(35.5 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) reacts with excess \(\mathrm{MgO} ?\)

Short answer

Heat is absorbed. \( \text{ΔH}_{\text{reverse}} = -117.3 \text{ kJ}\). \( \text{ΔH} = 627.555 \text{ kJ} \) for 5.35 mol and \( \text{ΔH} = 94.63 \text{ kJ} \) for 35.5 g of \(\text{CO}_{2}\).

Step-by-step solution

Understand the given information

The balanced thermochemical equation for the decomposition of the mineral magnesite is provided: \(\text{MgCO}_{3}(s) \rightarrow \text{MgO}(s) + \text{CO}_{2}(g) \) with \(\text{ΔH} = 117.3 \text{ kJ}\). This indicates the enthalpy change for the reaction.

Determine if heat is absorbed or released

Since \(\text{ΔH}\) is positive (\(117.3 \text{ kJ}\)), the reaction is endothermic and heat is absorbed.

Calculate \( \text{ΔH} \) for the reverse reaction

For the reverse reaction \(\text{MgO}(s) + \text{CO}_{2}(g) \rightarrow \text{MgCO}_{3}(s)\), the enthalpy change is the negative of the given \(\text{ΔH}\). Therefore, \(\text{ΔH}_{\text{reverse}} = -117.3 \text{ kJ}\).

Calculate \( \text{ΔH} \) for 5.35 mol of \( \text{CO}_{2}\bar}

The given \(\text{ΔH}\) is for 1 mol of \(\text{CO}_{2}\). For 5.35 mol of \(\text{CO}_{2}\): \( \text{ΔH} = 5.35 \text{ mol} \times 117.3 \text{ kJ/mol} = 627.555 \text{ kJ} \).

Calculate \( \text{ΔH} \) for 35.5 g of \( \text{CO}_{2}\bar}

First, convert grams to moles: Molar mass of \(\text{CO}_{2}\) is \(44 \text{ g/mol}\). Moles of \(\text{CO}_{2} = \frac{35.5 \text{ g}}{44 \text{ g/mol}} = 0.807 \text{ mol}\). Then, use this to find \(\text{ΔH}\): \( \text{ΔH} = 0.807 \text{ mol} \times 117.3 \text{ kJ/mol} = 94.63 \text{ kJ} \).

Key concepts

endothermic reaction

In this exercise, the decomposition of magnesite is represented by the reaction: \(\text{MgCO}_{3}(s) \rightarrow \text{MgO}(s) + \text{CO}_{2}(g) \quad \Delta H=117.3 \text{ kJ}\). The positive \(\Delta H\) value, 117.3 kJ, indicates that the reaction absorbs heat from its surroundings. This type of reaction is called an endothermic reaction. In simple terms, an endothermic reaction requires energy input, making it feel cold to the touch because it takes heat away from its environment.
For example, in the given exercise, when magnesite decomposes, it absorbs heat, making the surrounding area cooler. In contrast, an exothermic reaction would release heat, making the surroundings warmer. Understanding whether a reaction is endothermic or exothermic is crucial, especially in environmental and industrial applications, where energy management is a key factor.

thermochemical equations

Thermochemical equations provide essential information about the energy changes accompanying chemical reactions. In the decomposition of magnesite \(\text{MgCO}_{3}(s) \rightarrow \text{MgO}(s) + \text{CO}_{2}(g) \quad \Delta H=117.3 \text{ kJ}\), the equation not only shows the reactants and products but also includes the enthalpy change (\(\Delta H\)).
This enthalpy change tells us whether the reaction absorbs or releases heat and how much. The \(\Delta H\) can be positive or negative. For instance, in this exercise, a positive \(\Delta H\) of 117.3 kJ tells us the reaction is endothermic (absorbs heat). If the \(\Delta H\) were negative, it would indicate an exothermic reaction (releases heat).
Thermochemical equations are vital for predicting energy requirements or yields in chemical processes. They help chemists and engineers design processes to be efficient and safe, taking into account how much energy will be absorbed or released. For instance, knowing \(\Delta H\) for reactions can influence decisions in industrial manufacturing to optimize energy consumption.

reaction enthalpy

The reaction enthalpy (\(\Delta H\)) is a measure of heat change during a reaction at constant pressure. In the exercise, we see the decomposition of magnesite with \(\Delta H = 117.3 \text{ kJ}\). This tells us how much energy is absorbed for the reaction to proceed.
Reaction enthalpy is crucial for understanding the energy dynamics of a reaction. It can be calculated for different amounts of reactants. For example, if 5.35 mol of \(\text{CO}_{2}\) is produced, the \(\Delta H\) is 5.35 mol times 117.3 kJ/mol, resulting in a total enthalpy change of 627.555 kJ. For another scenario, calculating \(\Delta H\) for 35.5 g of \(\text{CO}_{2}\), we first convert grams to moles (\(\frac{35.5 \text{ g}}{44 \text{ g/mol}} = 0.807 \text{ mol}\)), then multiply by 117.3 kJ/mol to get 94.63 kJ.
Reaction enthalpy also allows us to determine the heat change for reverse reactions. For the reverse of our given reaction, \(\text{MgO}(s) + \text{CO}_{2}(g) \rightarrow \text{MgCO}_{3}(s) \), the \(\Delta H\) would be negative, -117.3 kJ, indicating heat is released. Understanding these concepts helps in controlling and optimizing chemical processes.