Question

Consider the generic reaction: $$\mathrm{A}+2 \mathrm{~B} \longrightarrow \mathrm{C}+3 \mathrm{D} \quad \Delta H=155 \mathrm{~kJ}$$ Determine the value of \(\Delta H\) for each related reaction. a. \(3 \mathrm{~A}+6 \mathrm{~B} \longrightarrow 3 \mathrm{C}+9 \mathrm{D}\) b. \(C+3 D \longrightarrow A+2 B\) c. \(1 / 2 \mathrm{C}+{ }^{3} /{ }_{2} \mathrm{D} \longrightarrow{ }^{1} /{ }_{2} \mathrm{~A}+\mathrm{B}\)

Short answer

\(\textbackslash Delta H\) for reactions a, b, and c are 465 \textbackslash mathrm{kJ}, -155 \textbackslash mathrm{kJ}, and 77.5 \textbackslash mathrm{kJ}, respectively.

Step-by-step solution

- Analyze the Related Reactions

Examine how each related reaction compares to the original reaction in terms of the stoichiometry of reactants and products. Determine if the stoichiometric coefficients of the related reaction are multiplied or divided relative to the original reaction.

- Determine \(\textbackslash Delta H\) for Reaction (a)

Reaction (a) has stoichiometric coefficients that are exactly three times the original reaction. This means that the enthalpy change will also be three times the original enthalpy change \((\textbackslash Delta H = 3 \times 155 \, \textbackslash mathrm{kJ})\).

- Determine \(\textbackslash Delta H\) for Reaction (b)

Reaction (b) is the reverse of the original reaction. The enthalpy change for the reverse reaction will be the negative of the original reaction \((\textbackslash Delta H = -155 \, \textbackslash mathrm{kJ})\), since reversing a reaction changes the sign of \(\textbackslash Delta H\).

- Determine \(\textbackslash Delta H\) for Reaction (c)

Reaction (c) has stoichiometric coefficients that are one half of the original reaction. Therefore, the enthalpy change will be one half of the original enthalpy change \((\textbackslash Delta H = 0.5 \times 155 \, \textbackslash mathrm{kJ})\).

Key concepts

Chemical Reaction Stoichiometry

Chemical reaction stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It's the backbone of chemical equation balancing and helps to predict the quantities of substances consumed and produced.

In the given exercise, stoichiometry plays a crucial role in understanding how the amounts of reactants and products relate to each other. For instance, if the coefficients of the reactants double in a balanced equation, the amount of products formed will also double. It's vital to notice that the stoichiometric relationship is based on the mole concept, which states that one mole of any substance contains the same number of entities as there are atoms in exactly 12 g of carbon-12.

To understand stoichiometry:

• Identify the substances involved and their chemical formulas.
• Write down the balanced equation for the reaction.
• Determine the molar ratios of reactants and products from the equation.
• Use these ratios to calculate the necessary amounts of reactants or products.

By employing stoichiometry, you establish a foundation for solving part (a) of the exercise by recognizing that tripling the coefficients correlates with tripling the enthalpy change.

Enthalpy Change of Reaction

The enthalpy change of reaction, often denoted as \(\Delta H\), is the heat absorbed or released during a chemical reaction at constant pressure. It is a crucial concept in thermochemistry as it helps us understand how much energy is involved in breaking and forming chemical bonds.

Enthalpy changes are determined by the type and number of chemical bonds affected in a reaction. Since energy is required to break bonds and is released when bonds form, the overall enthalpy change depends on the balance between these two processes.

There are a few key points to remember:

• An exothermic reaction releases heat (\(\Delta H < 0\)), whereas an endothermic reaction absorbs heat (\(\Delta H > 0\)).
• Enthalpy is a state function, meaning it depends only on the initial and final states of the system, not on the path taken.
• The stoichiometry of the reaction can determine the scale of the enthalpy change; for instance, doubling the reaction will double the enthalpy change, as seen in solving part (c) of the exercise.

This concept helps us solve part (b) of the exercise by recognizing that the negative sign indicates a reversal of the reaction, which changes the direction of heat flow.

Hess's Law

Hess's Law is a principle in chemistry that states the overall enthalpy change for a chemical reaction is the same, regardless of the number of steps or its path, as long as the initial and final conditions are the same. This law allows us to calculate enthalpy changes for reactions that are difficult to perform directly.

To use Hess's Law effectively:

• Break down complex reactions into simpler steps for which enthalpy changes are known.
• Add up the enthalpy changes of these steps to determine the overall enthalpy change.
• Consider the stoichiometry of the individual steps to ensure that they sum correctly to give the overall reaction.

In practice, Hess's Law reaffirms that reversing the reaction, as seen in part (b), changes the sign but not the magnitude of the enthalpy change. Moreover, if the reaction is scaled up or down, as in parts (a) and (c), the enthalpy change must be multiplied or divided accordingly, maintaining the principle that the state's function quality of enthalpy holds true.