Question

For the reaction having \(\Delta / /\) and \(\Delta S\) both positive, the rate of reaction (1) incrcases with the increasc in temperaturc (2) decreascs with the increase in tempcrature (3) has no effect on temperature (4) decreascs with the increase in pressure

Short answer

The correct option is (1): increases with the increase in temperature.

Step-by-step solution

Understand the Reaction Parameters

Here \(\text{Δ} H\) and \(\text{Δ} S\) are positive. \( \text{Δ} H \) represents the change in enthalpy and \( \text{Δ} S \) represents the change in entropy.

Recall the Gibbs Free Energy Equation

The equation for Gibbs Free Energy is \[ \text{Δ} G = \text{Δ} H - T \text{Δ}S \].

Analyze Temperature Influence

Since both \( \text{Δ} H \) and \( \text{Δ} S \) are positive, an increase in temperature \( T \) would make the term \( T \text{Δ}S \) larger, thus reducing \( \text{Δ} G \) and making the reaction more spontaneous.

Conclude on Reaction Rate with Temperature

As the reaction becomes more spontaneous with increasing temperature, the rate of reaction typically increases.

Evaluate Other Options

Check other options: (2) decreasing reaction rate with temperature is incorrect based on the analysis. (3) no effect on temperature is also incorrect. (4) reaction rate decreasing with pressure is not relevant to the given data.

Key concepts

Enthalpy

Enthalpy, represented as \( \text{Δ} H \), is a measure of the total energy of a thermodynamic system. It includes internal energy plus the product of pressure and volume. In chemical reactions, it's important to note whether a reaction is endothermic or exothermic:

• Endothermic Reactions: These reactions absorb heat from the surroundings and have a positive \( \text{Δ} H \).
• Exothermic Reactions: These reactions release heat and have a negative \( \text{Δ} H \).

In the given exercise, \( \text{Δ} H \) is positive, indicating the reaction is endothermic and absorbs heat. This is a key factor that influences the reaction's spontaneity and its sensitivity to temperature changes.

Entropy

Entropy, denoted as \( \text{Δ} S \), measures the disorder or randomness in a system. Higher entropy means more disorder. Chemical reactions can either increase or decrease the entropy of the system and the surroundings:

• Positive \( \text{Δ} S \): Indicates an increase in entropy or disorder.
• Negative \( \text{Δ} S \): Indicates a decrease in entropy or increased order.

In the presented exercise, \( \text{Δ} S \) is positive. This suggests that the products of the reaction are more disordered than the reactants. As temperature increases, the \( T \text{Δ} S \) term in the Gibbs Free Energy equation \( (\text{Δ} G = \text{Δ} H - T \text{Δ} S) \) becomes more significant, thereby reducing \( \text{Δ} G \) and making the reaction more spontaneous.

Reaction Rate

Reaction rate refers to how fast or slow a chemical reaction proceeds. It is influenced by several factors, including temperature, pressure, concentration, and the presence of catalysts:

• Temperature: Increasing the temperature generally increases the reaction rate by providing more energy to the reactants.
• Pressure: This mostly affects gases; increasing pressure can increase the reaction rate if it increases the concentration of reactants.
• Catalysts: These substances increase the reaction rate without being consumed in the reaction by lowering the activation energy.

In the given exercise, the rate of reaction increases with increasing temperature. Because the \( \text{Δ} H \) and \( \text{Δ} S \) are positive, a higher temperature reduces \( \text{Δ} G \), making the reaction more likely to proceed spontaneously and quickly.

Temperature Effect on Reactions

Temperature has a profound impact on the spontaneity and rate of chemical reactions. The main points to remember are:

• Increase in Temperature: Generally increases the reaction rate because molecules move faster and collide more frequently and energetically.
• Gibbs Free Energy Equation: \( \text{Δ} G = \text{Δ} H - T \text{Δ}S \) shows that as the temperature rises, the \( T \text{Δ} S \) term becomes more significant.
• Spontaneity: If both \( \text{Δ} H \) and \( \text{Δ} S \) are positive, increasing the temperature generally decreases \( \text{Δ} G \), making the reaction more spontaneous.

In the context of the given exercise, an increase in temperature increases the reaction rate. This is because both the enthalpy change (\text{Δ} H) and entropy change (\text{Δ} S) are positive, leading to a more negative \( \text{Δ} G \) as temperature increases.