Problem 130 - General Chemistry

Question

Given the following (hypothetical) thermochemical equations: $$ \begin{aligned} &\mathrm{A}+\mathrm{B} \longrightarrow 2 \mathrm{C} ; \Delta H=-447 \mathrm{~kJ} \\ &\mathrm{~A}+3 \mathrm{D} \longrightarrow 2 \mathrm{E} ; \Delta H=-484 \mathrm{~kJ} \\ &2 \mathrm{D}+\mathrm{B} \longrightarrow 2 \mathrm{~F} ; \Delta H=-429 \mathrm{~kJ} \end{aligned} $$ Calculate \(\Delta H\), in \(\mathrm{kJ}\), for the equation $$ 4 \mathrm{E}+5 \mathrm{~B} \longrightarrow 4 \mathrm{C}+6 \mathrm{~F} $$

Step-by-Step Solution

Answer

\(\Delta H = -1213\) kJ.

Step 1: Reverse and Scale the Second Equation

The desired equation involves 4 \( \mathrm{E} \), so we start by reversing the second given equation and scaling it by a factor of 2. The reversed equation becomes: \( 4 \mathrm{E} \rightarrow 2 \mathrm{~A} + 6 \mathrm{D} \). Because the reaction is reversed, we change the sign of \( \Delta H \), and multiplying the original \( \Delta H = -484 \) kJ by 2, we get: \( \Delta H = 2 \times 484 = 968 \) kJ.

Step 2: Scale the First Equation

To match the presence of \( 4 \mathrm{C} \) in the target equation, scale the first given equation by a factor of 2: \( 2 \mathrm{A} + 2 \mathrm{B} \rightarrow 4 \mathrm{C} \). Multiply the original \( \Delta H = -447 \) kJ by 2, resulting in \( \Delta H = 2 \times (-447) = -894 \) kJ.

Step 3: Scale the Third Equation

To match \( 6 \mathrm{F} \) in the target equation, scale the third given equation by a factor of 3: \( 6 \mathrm{D} + 3 \mathrm{B} \rightarrow 6 \mathrm{F} \). Multiply the original \( \Delta H = -429 \) kJ by 3 to get \( \Delta H = 3 \times (-429) = -1287 \) kJ.

Step 4: Combine and Calculate Total \( \Delta H \)

Combine the scaled equations from Steps 1, 2, and 3, ensuring the terms on both sides cancel appropriately: \( 4 \mathrm{E} + 5 \mathrm{B} \rightarrow 4 \mathrm{C} + 6 \mathrm{F} \). The total \( \Delta H \) is the sum of \( 968 \), \( -894 \), and \( -1287 \) kJ, which equals \( -1213 \) kJ.

Key Concepts

Understanding Thermochemical Equations

Thermochemical equations are a type of chemical equation that show not only the reactants and products but also the enthalpy change (ΔH) of the reaction. These equations are essential in chemistry because they help us understand the energy changes that occur during a chemical reaction.
In a thermochemical equation, you will typically see the following elements:

• The reactants and products involved in the chemical reaction.
• The states of matter of each substance (solid, liquid, gas, or aqueous).
• The enthalpy change, ΔH, which is usually given in kilojoules (kJ).

Thermochemical equations allow us to visualize how energy is absorbed or released when bonds are broken or formed. Understanding the enthalpy values provided in such equations can help predict the heat flow associated with reactions, making them particularly useful in fields like thermodynamics and engineering.

Grasping the Concept of Enthalpy Change

Enthalpy change, denoted as ΔH, is a key concept in thermochemistry that quantifies the heat absorbed or released during a chemical reaction. It is typically measured at constant pressure.
Enthalpy change is important because it helps determine whether a reaction is exothermic or endothermic:

• Exothermic Reaction: If ΔH is negative, the reaction releases energy to the surroundings, usually in the form of heat.
• Endothermic Reaction: If ΔH is positive, the reaction absorbs energy from the surroundings.

Enthalpy change is used in Hess's Law, a fundamental principle in chemistry that states the total enthalpy change for a chemical reaction is the same, regardless of the pathway taken. This is particularly useful in calculating unknown enthalpy changes by using known thermochemical equations combined in different ways. For students calculating enthalpy changes, it’s crucial to keep track of the sign and magnitude of ΔH values.

Understanding Chemical Reactions

Chemical reactions involve the rearrangement of atoms to form new substances, and they are fundamental to understanding how materials interact and change. In the context of thermochemistry, chemical reactions are closely tied to energy changes.
Here are some important factors about chemical reactions you should know:

• Reactions involve breaking bonds in reactant molecules and forming new bonds in product molecules.
• The energy required to break bonds and the energy released during the formation of new bonds are vital factors in the enthalpy change.
• Balancing chemical equations ensures the conservation of mass and correct stoichiometry, which is essential for accurate enthalpy calculations.

Understanding these elements of chemical reactions helps in applying Hess's Law efficiently, making it possible to determine the total enthalpy of a process even when direct measurement is challenging. Alway approach equations methodically by balancing, scaling, and adjusting them as required for thermochemical calculations.