Problem 38 - Chemistry Matter and Change

Question

Explain what is meant by Hess’s law and how it is used to determine \(\Delta H_{{ran}}^{0}\)

Step-by-Step Solution

Answer

Hess's law states that the total enthalpy change in a reaction is the same, whether the reaction occurs in one step or several steps, as enthalpy is a state function. To determine \(\Delta H_{\text{ran}}^{0}\) using Hess's law, find the known standard enthalpies of formation (\(\Delta H_{\text{f}}^{0}\)) for related reactions and use the equation \(\Delta H_{\text{ran}}^{0} = \sum{n_{p} \Delta H_{\text{f}}^{0}(\text{products})} - \sum{n_{r} \Delta H_{\text{f}}^{0}(\text{reactants})}\), where \(n_{p}\) and \(n_{r}\) represent the stoichiometric coefficients of products and reactants, respectively.

Step 1: Define Hess's Law

Hess's law states that the total enthalpy change in a reaction is the same, whether the reaction occurs in one step or several steps. In other words, the enthalpy change of a chemical process is independent of the path taken, as long as the initial and final states are the same.

Step 2: Identify Known Enthalpy Changes for Related Reactions

In order to use Hess's law to determine \(\Delta H_{\text{ran}}^{0}\) for a reaction, you need to find previously known enthalpy changes for reactions that are related to the reaction of interest. These known values are called standard enthalpies of formation, denoted by \(\Delta H_{\text{f}}^{0}\), and are the enthalpy changes associated with the formation of one mole of a compound from its constituent elements in their standard states.

Step 3: Write the Reaction Equation and Corresponding Enthalpy Change

Write down the balanced chemical equation for the reaction of interest, along with its corresponding enthalpy change. This enthalpy change will be the sum of the products' enthalpy changes minus the sum of the reactants' enthalpy changes, as shown in the equation: \[\Delta H_{\text{ran}}^{0} = \sum{n_{p} \Delta H_{\text{f}}^{0}(\text{products})} - \sum{n_{r} \Delta H_{\text{f}}^{0}(\text{reactants})}\] Here, \(n_{p}\) and \(n_{r}\) represent the stoichiometric coefficients of the products and reactants, respectively.

Step 4: Calculate \(\Delta H_{\text{ran}}^{0}\) Using Known Standard Enthalpies of Formation and Hess's Law

With all the required information in hand, proceed to calculate the enthalpy change of the reaction using Hess's law. Substitute the known standard enthalpies of formation for the reactants and products (multiplied by their respective stoichiometric coefficients) into the equation, and then calculate \(\Delta H_{\text{ran}}^{0}\). Following these steps, you will be able to explain Hess's law and use it to determine the standard enthalpy change of a reaction, \(\Delta H_{\text{ran}}^{0}\).

Key Concepts

Enthalpy Change

Enthalpy change (\( \Delta H \)) represents the heat absorbed or released during a chemical reaction at constant pressure. It is a fundamental concept in thermochemistry because it helps predict whether a reaction will be endothermic or exothermic.

- **Endothermic Reactions**: These absorb heat from the surroundings, resulting in a positive enthalpy change. Examples include photosynthesis and melting of ice.- **Exothermic Reactions**: These release heat into the surroundings, leading to a negative enthalpy change. Common exothermic reactions are combustion and freezing of water.

Enthalpy is a state function, meaning that the change in enthalpy depends only on the initial and final states of a reaction, not on the pathway taken. This property is crucial for applying Hess's Law, which allows us to calculate unknown enthalpy changes by using known values from stepwise reactions or cycles.

Standard Enthalpies of Formation

Standard enthalpies of formation (\( \Delta H_{\text{f}}^{0} \)) refer to the enthalpy change when one mole of a compound is formed from its elements in their most stable forms at 1 atm and 298 K. This provides a baseline to compare thermodynamic data.

- **Reference State**: The elements must be in their standard states, such as hydrogen gas (\( \text{H}_{2} (g) \)) or graphite for carbon.- **Values and Use**: A standard enthalpy of formation value for any element in its standard state is zero. It is used to calculate enthalpy changes for various processes by piecing together reactions that lead to the formation of a compound.

Using these values in Hess's Law allows easy computation of the total enthalpy change in reactions where direct measurement is not feasible. By summing the standard enthalpies of formation for the respective products and subtracting those of the reactants, we find the overall enthalpy change for a reaction.

Chemical Equations

Chemical equations depict the substances involved in a chemical reaction, showing reactants on the left and products on the right. A balanced chemical equation is essential to accurately represent the conservation of mass.

- **Balanced Equations**: Ensure the number of atoms for each element is the same on both sides of the equation. For example, the combustion of methane is balanced as:\[ \text{CH}_{4} + 2\text{O}_{2} \rightarrow \text{CO}_{2} + 2\text{H}_{2}\text{O} \]- **Stoichiometry**: Involves using the coefficients of the balanced equation to convert between moles of reactants and products. These coefficients are crucial when calculating enthalpy changes as they determine the proportionate effect on enthalpy based on the reaction scale.

Accurate chemical equations are crucial in applying Hess's Law to determine enthalpy changes. They allow the precise calculation of the overall enthalpy change by summing contributions of the individual steps or related reactions. This approach underscores the efficiency and elegance of Hess's Law in deriving thermodynamic insights.