Question

From the enthalpies of reaction \(\begin{aligned} 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) & \Delta H &=-483.6 \mathrm{~kJ} \\ 3 \mathrm{O}_{2}(g) & \cdots &-\cdots & 2 \mathrm{O}_{3}(g) & \Delta H &=+284.6 \mathrm{~kJ} \end{aligned}\) calculate the heat of the reaction $$ 3 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{3}(\mathrm{~g}) \longrightarrow 3 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$

Short answer

The heat of the reaction for \(3 \mathrm{H}_{2}(g)+\mathrm{O}_{3}(g) \longrightarrow 3\mathrm{H}_{2}\mathrm{O}(g)\) is \(-583.1 \mathrm{kJ}\).

Step-by-step solution

Write the target reaction

The target reaction we need to calculate the heat of is: $$ 3 \mathrm{H}_{2}(g)+\mathrm{O}_{3}(g) \longrightarrow 3\mathrm{H}_{2}\mathrm{O}(g) $$

Analyze the given reactions

We are given two reactions with their enthalpy changes: $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2\mathrm{H}_{2}\mathrm{O}(g) \qquad \Delta H_1=-483.6 \mathrm{kj} $$ $$ 3\mathrm{O}_{2}(g) \longrightarrow 2\mathrm{O}_{3}(g) \qquad \Delta H_2=+284.6 \mathrm{kJ} $$

Manipulate the given reactions to match the target reaction

In order to apply Hess's Law, we must manipulate the given reactions so that they sum to the target reaction: 1. Multiply the first reaction by 3/2 to get 3 moles of water on the product side: $$ 3 \mathrm{H}_{2}(g) + \frac{3}{2}\mathrm{O}_{2}(g) \longrightarrow 3\mathrm{H}_{2}\mathrm{O}(g) \qquad \Delta H_1'= 3/2(-483.6) \mathrm{kJ} $$ 2. Divide the second reaction by 2 to obtain 1 mole of ozone in the reactant side: $$ \frac{3}{2}\mathrm{O}_{2}(g) \longrightarrow \mathrm{O}_{3}(g) \qquad \Delta H_2'= 1/2(+284.6) \mathrm{kJ} $$

Apply Hess's Law

Now that the reactions have been manipulated, we can sum them up to get the target reaction: $$ 3 \mathrm{H}_{2}(g)+\mathrm{O}_{3}(g) \longrightarrow 3\mathrm{H}_{2}\mathrm{O}(g) $$ Applying Hess's Law, we add the enthalpy changes of the manipulated reactions to find the enthalpy change of the target reaction: $$ \Delta H_{target} = \Delta H_1' + \Delta H_2' = 3/2(-483.6 \mathrm{kJ}) + 1/2(+284.6 \mathrm{kJ}) $$

Calculate the enthalpy of the target reaction

Finally, we calculate the enthalpy change of the target reaction: $$ \Delta H_{target} =-725.4 \mathrm{kJ} + 142.3 \mathrm{kJ} = -583.1\mathrm{kJ} $$ The heat of the reaction is -583.1 kJ.

Key concepts

Enthalpy Change

Enthalpy change, represented with the symbol \( \Delta H \), is a measure of heat energy released or absorbed when a chemical reaction takes place at constant pressure. Understanding this concept is fundamental to grasping chemical reactions, as it indicates whether a process is endothermic (heat absorbed, \( \Delta H > 0 \) or exothermic (heat released, \( \Delta H < 0 \).

In the given exercise, the enthalpy change of a reaction transforming hydrogen gas and ozone into water vapor is calculated using given enthalpy values for related reactions. The key aspect to discern here is that the enthalpy is a state function, meaning its value depends only on the initial and final states of a system, not on the path taken.

By understanding and working with enthalpy changes, students can predict the heat released or absorbed during reactions, which is critical in both academic studies and real-world applications like energy production and material synthesis.

Chemical Thermodynamics

Chemical thermodynamics is the branch of chemistry that deals with the energy changes accompanying chemical reactions and physical processes. It provides tools to predict whether processes are feasible under given conditions and to understand how systems reach equilibrium.

Hess's Law, an application of the first law of thermodynamics, is instrumental in chemical thermodynamics. It states that the total enthalpy change for a chemical reaction is the same, regardless of the number of stages in which the reaction is carried out. As seen in our exercise, we utilized Hess's Law to find the enthalpy change of a complex reaction by combining simpler reactions whose enthalpy changes are known.

For students, mastering chemical thermodynamics means getting comfortable with concepts such as enthalpy, entropy, and Gibbs free energy, which together describe the energy changes and spontaneity of reactions.

Enthalpies of Reaction

Enthalpies of reaction refer to the amount of heat absorbed or released by a system during a chemical reaction at constant pressure. Each chemical equation has an associated enthalpy change, which can be either positive or negative depending on whether the reaction is endothermic or exothermic.

The balancing of equations in a manner that reflects the conservation of mass and the use of stoichiometry are important when working with enthalpies of reaction, as seen in the exercise. Manipulating the given reactions properly to have the correct stoichiometry, thus allowing the application of Hess's Law, was critical. Each adjusted reaction represented steps contributing to the overall reaction, and their individual enthalpies were combined accurately to give the enthalpy of the desired reaction.

This understanding aids in many practical applications, such as calculating energy requirements for industrial chemical processes and designing reactions for new materials.