Consider the following three reactions: (i) Ti(s) + 2 Cl₂(g) → TiCl₄(1g) (ii) C₂H₆(g) + 7 Cl₂(g) → 2 CCl₄(g) + 6 HCl(g) (iii) BaO(s) + CO₂(g) → BaCO₃(s) (c) For each of the reactions, predict the manner in which the change in free energy varies with an increase in temperature.

Verified step by step guidance

1. Step 1: Understand the concept of Gibbs free energy change (ΔG) and its relation to temperature. The equation ΔG = ΔH - TΔS helps us predict how free energy changes with temperature, where ΔH is the change in enthalpy, T is the temperature, and ΔS is the change in entropy.
2. Step 2: Analyze reaction (i) Ti(s) + 2 Cl_2(g) → TiCl_4(l). Consider the states of matter: solid and gas to liquid. Generally, this reaction involves a decrease in entropy (ΔS < 0) because gases are converted to a liquid. If ΔH is negative (exothermic), increasing temperature will make ΔG less negative or more positive.
3. Step 3: Analyze reaction (ii) C_2H_6(g) + 7 Cl_2(g) → 2 CCl_4(g) + 6 HCl(g). This reaction involves gases on both sides, but the number of gas molecules decreases, suggesting a decrease in entropy (ΔS < 0). If ΔH is negative, increasing temperature will make ΔG less negative or more positive.
4. Step 4: Analyze reaction (iii) BaO(s) + CO_2(g) → BaCO_3(s). This reaction involves a gas being converted to a solid, indicating a decrease in entropy (ΔS < 0). If ΔH is negative, increasing temperature will make ΔG less negative or more positive.
5. Step 5: Conclude that for all three reactions, if they are exothermic (ΔH < 0), an increase in temperature will generally make ΔG less negative or more positive due to the negative ΔS, potentially making the reactions less spontaneous at higher temperatures.

Key Concepts

Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is defined as G = H - TS, where H is enthalpy, T is temperature, and S is entropy. The change in Gibbs Free Energy (ΔG) indicates the spontaneity of a reaction: if ΔG is negative, the reaction is spontaneous; if positive, it is non-spontaneous.

Temperature Dependence of Free Energy

The temperature dependence of Gibbs Free Energy is significant because it affects both enthalpy and entropy. As temperature increases, the TΔS term becomes more influential. For reactions where entropy increases (ΔS > 0), higher temperatures can favor spontaneity, while for reactions with negative entropy changes (ΔS < 0), higher temperatures may hinder spontaneity, leading to a positive ΔG.

Reaction Types and Their Characteristics

The reactions presented include synthesis and decomposition reactions, each with distinct characteristics. Synthesis reactions, like Ti + Cl2 → TiCl4, typically release energy and may have negative ΔG at lower temperatures. In contrast, reactions involving gaseous reactants and products, such as C2H6 + Cl2 → CCl4 + HCl, can have varying ΔS values, influencing how ΔG changes with temperature. Understanding these characteristics is crucial for predicting the behavior of free energy with temperature.