Question

For the reaction \(\mathrm{HgO}(s) \rightarrow \mathrm{Hg}(l)+\frac{1}{2} \mathrm{O}_{2}(g), \Delta H=+90.7 \mathrm{~kJ}:\) a. What quantity of heat is required to produce \(1 \mathrm{~mol}\) of mercury by this reaction? b. What quantity of heat is required to produce \(1 \mathrm{~mol}\) of oxygen gas by this reaction? c. What quantity of heat would be released in the following reaction as written? $$ 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{HgO}(s) $$

Short answer

Answer: a) +90.7 kJ is required to produce 1 mol of Hg. b) +181.4 kJ is required to produce 1 mol of O₂. c) -181.4 kJ of heat would be released in the reverse reaction as written.

Step-by-step solution

Given information

We have the balanced equation: HgO(s) → Hg(l) + 0.5 O₂(g) with ΔH = +90.7 kJ.

Calculate heat for 1 mol Hg

In this reaction, 1 mol of HgO decomposes to produce 1 mol of Hg. Thus, the heat required to produce 1 mol Hg is directly given by the value of ΔH, which is +90.7 kJ. Answer (a): +90.7 kJ is required to produce 1 mol of Hg. #b. Calculating heat for 1 mol O₂ production#

Determine stoichiometric relationships

From the balanced equation: HgO(s) → Hg(l) + 0.5 O₂(g), we can see that 2 mol of HgO are needed to produce 1 mol of O₂.

Calculate heat for 1 mol O₂

Since ΔH is +90.7 kJ for 1 mol HgO producing 0.5 mol O₂, in order to produce 1 mol O₂, we need to double this value. Therefore, the heat required to produce 1 mol O₂ is: \(2 \times 90.7 \text{ kJ} = 181.4 \text{ kJ}\) Answer (b): +181.4 kJ is required to produce 1 mol of O₂. #c. Calculating heat released in the reverse reaction#

Reverse reaction

The reverse reaction is: $$ 2 \mathrm{Hg}(l)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{HgO}(s) $$

Calculate heat released in the reverse reaction

Since the reaction is reversed and we are dealing with the inverse stoichiometry, the heat change will also have an opposite sign. (Note that the forward reaction ΔH = +90.7 kJ for 1 mol HgO) Thus, for 2 mol HgO produced in the reverse reaction, the heat change would be: $$ \Delta H_{\text{reverse}} = -1 \times (2 \times 90.7 \text{ kJ}) = -181.4 \text{ kJ} $$ Answer (c): -181.4 kJ of heat would be released in the reverse reaction as written.

Key concepts

Understanding Enthalpy Change

Thermochemistry revolves around the study of heat exchange in chemical reactions, and a fundamental concept here is the enthalpy change, denoted as \( \Delta H \). It tells us how much heat is absorbed or released during a reaction at constant pressure.
For example, in the given exercise, the reaction involved is the decomposition of mercury oxide (\(\mathrm{HgO}\)) into mercury (\(\mathrm{Hg}\)) and oxygen (\(\mathrm{O}_2\)). The positive \( \Delta H \) value of +90.7 kJ indicates that the reaction absorbs heat; hence, it is endothermic.
Enthalpy change is used to understand various aspects of reactions:

• Heat Absorption/Release: A positive \( \Delta H \) means heat absorption (endothermic), while a negative value indicates heat release (exothermic).
• Reaction Direction: Sign change in \( \Delta H \) is crucial when considering reverse reactions.
• Quantitative Measures: It provides a numerical way to measure the energy change associated with reactions.

The enthalpy change is always related to the stoichiometry of the reaction, which remains a critical consideration in thermochemical calculations.

The Role of Stoichiometry

Stoichiometry is a term you will often encounter in chemistry, specifically in calculating the amounts of reactants and products in a chemical reaction. It comes from the Greek words 'stoikheion' meaning element, and 'metron' meaning measure.
In the context of our exercise, stoichiometry helps us determine how much heat is needed or released during chemical changes based on the balanced equation:

• For the decomposition of 1 mol of \( \mathrm{HgO} \), 0.5 mol of \( \mathrm{O}_2 \) is produced. Hence, to produce 1 mol of \( \mathrm{O}_2 \), stoichiometry shows that 2 mol of \( \mathrm{HgO} \) are required, influencing the calculation of energy change.
• Understanding stoichiometry also allows us to calculate the heat change for the reverse reaction, requiring adjustments in chemical amounts and energy values.

Knowing the stoichiometry is essential for correctly scaling up reactions or estimating the energy change when the amount of substances varies, embodying its importance in chemicals and energy balance calculations.

Exploring Endothermic Reactions

Endothermic reactions are those that absorb heat from their surroundings. This characteristic is evident when the enthalpy change \( \Delta H \) is positive, indicating energy intake.
Take the decomposition of \( \mathrm{HgO} \) as an example, where \( \Delta H = +90.7 \text{ kJ} \). This shows that the reaction requires heat to proceed, completing the breaking of bonds in \( \mathrm{HgO} \) to form \( \mathrm{Hg} \) and \( \mathrm{O}_2 \).
Key features of endothermic reactions include:

• Energy Demand: They need external energy sources to take place.
• Temperature Drop: They often result in a cooler reaction environment due to heat absorption.
• Product Formation: They often make products that are higher in energy than reactants.

Understanding endothermic reactions is crucial in contexts like thermal decomposition reactions or processes like photosynthesis where energy input is a key part of the reaction mechanism. Their study helps in designing experiments, energy systems, and industrial processes involving heat exchange.