Problem 19 - Chemistry: Principles and Reactions

Question

Use Table \(17.1\) to calculate \(\Delta S^{\circ}\) for each of the following reactions. (a) \(2 \mathrm{Cl}^{-}(a q)+\mathrm{I}_{2}(s) \longrightarrow \mathrm{Cl}_{2}(g)+2 \mathrm{I}^{-}(a q)\) (b) \(\mathrm{SO}_{4}{\underline{\phantom{xx}}}^{2-}(a q)+4 \mathrm{H}^{+}(a q)+\mathrm{Cd}(s) \longrightarrow\) \(\mathrm{Cd}^{2+}(a q)+\mathrm{SO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\) (c) \(2 \mathrm{Br}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Br}_{2}(l)+\mathrm{H}_{2}(g)+2 \mathrm{OH}^{-}(a q)\)

Step-by-Step Solution

Answer

Question: Calculate the standard entropy change for the following reactions using the data provided in Table 17.1: (a) 2Cl⁻(aq) + I₂(s) → Cl₂(g) + 2I⁻(aq) (b) SO₄²⁻(aq) + 4H⁺(aq) + Cd(s) → Cd²⁺(aq) + SO₂(g) + 2H₂O(l) (c) 2Br⁻(aq) + 2H₂O(l) → Br₂(l) + H₂(g) + 2OH⁻(aq)

Step 1: (a) Calculate the entropy for the reactants and products

First, we will find the entropy for the reactants and products using the values from Table \(17.1\). For the reactants: \(2\mathrm{Cl}^{-}(a q)\) and \(\mathrm{I}_{2}(s)\), For the products: \(\mathrm{Cl}_{2}(g)\) and \(2\mathrm{I}^{-}(a q)\). Note: Remember to multiply the individual entropy values by the stoichiometric coefficients before calculating the entropy change.

Step 2: (a) Calculate the standard entropy change, \(\Delta S^{\circ}\)

Now that we have the entropies for the reactants and products, we can calculate the standard entropy change for the reaction using the following formula: \(\Delta S^{\circ} = S_{\text{products}} - S_{\text{reactants}}\)

Step 3: (b) Calculate the entropy for the reactants and products

For the reactants: \(\mathrm{SO}_{4}^{2-}(a q)\), \(4\mathrm{H}^{+}(a q)\), and \(\mathrm{Cd}(s)\), For the products: \(\mathrm{Cd}^{2+}(a q)\), \(\mathrm{SO}_{2}(g)\), and \(2\mathrm{H}_{2}\mathrm{O}(l)\). Proceed similarly as in part (a).

Step 4: (b) Calculate the standard entropy change, \(\Delta S^{\circ}\)

Use the same formula as in part (a) to calculate the standard entropy change for the second reaction.

Step 5: (c) Calculate the entropy for the reactants and products

For the reactants: \(2\mathrm{Br}^{-}(a q)\) and \(2\mathrm{H}_{2}\mathrm{O}(l)\), For the products: \(\mathrm{Br}_{2}(l)\), \(\mathrm{H}_{2}(g)\), and \(2\mathrm{OH}^{-}(a q)\). Proceed similarly as in part (a).

Step 6: (c) Calculate the standard entropy change, \(\Delta S^{\circ}\)

Use the same formula as in part (a) to calculate the standard entropy change for the third reaction.

Key Concepts

Standard Entropy

Standard entropy, often denoted as \( S^{\circ} \), is a fundamental concept in chemical thermodynamics that measures the absolute disorder or randomness of substances at standard conditions. Essentially, it quantifies the degree of distribution of microscopic states among energy levels at a standard state. Standard conditions typically refer to a pressure of 1 bar and a specified temperature, usually 298 K (25°C).

The value of entropy can help predict the spontaneity of a reaction. A positive change in entropy indicates an increase in disorder, while a negative change implies more order in the system. It's crucial to note that gases generally have higher entropies than liquids, which in turn have higher entropies than solids. This hierarchy is because gas particles move freely and occupy more space compared to liquids and solids.

When calculating changes in standard entropy for a chemical reaction, scientists use tabulated entropy values. They apply the formula:

• \( \Delta S^{\circ} = \sum S^{\circ}_{\text{products}} - \sum S^{\circ}_{\text{reactants}} \)

This formula accounts for the sum of the standard entropies of the products minus the sum for the reactants, also taking into account their respective stoichiometric coefficients. This step is fundamental in determining whether a reaction leads to an increase in system disorder.

Stoichiometry

Stoichiometry is the study of the quantitative relationships between the reactants and products in a chemical reaction. It plays a critical role in ensuring that chemical equations are balanced, allowing chemists to appropriately calculate how much of each substance is involved in a reaction.

For instance, in the problem, each reaction involves calculating the entropy change based on stoichiometric coefficients. These coefficients indicate the proportions of reactants and products involved, which directly influence the resulting entropy change. When coefficients are present in balanced chemical equations, they help to determine the total number of each substance contributing to the overall entropy change.

Using stoichiometry, we adjust the molar entropy values by their corresponding coefficients to calculate the total entropy contribution from each reactant and product. This step is vital as it ensures the calculations reflect the actual quantities of substances undergoing reaction, providing accurate results essential for predicting chemical behavior.

Chemical Thermodynamics

Chemical thermodynamics is the field of chemistry that examines the energy changes associated with chemical reactions. It focuses on the concepts of enthalpy, entropy, and free energy. Understanding these elements helps predict whether reactions are spontaneous under certain conditions.

Entropy, as part of chemical thermodynamics, is used in combination with enthalpy to determine spontaneity through the Gibbs free energy equation:

• \( \Delta G^{\circ} = \Delta H^{\circ} - T\Delta S^{\circ} \)

Here, \( \Delta G^{\circ} \) represents the change in Gibbs free energy, \( \Delta H^{\circ} \) is the change in enthalpy, and \( T \) is the temperature in Kelvin. A negative \( \Delta G^{\circ} \) indicates a spontaneous process.

Even though the calculation of \( \Delta S^{\circ} \) itself, as in this solution, focuses on measuring disorder, it is a vital component of understanding the driving forces of reactions. It aids in determining not merely if a reaction is possible, but how it can proceed effectively given the energetic landscape dictated by temperature and system entropy.