Question

The rate law for the reaction \(\mathrm{RCl}+\mathrm{NaOH} \rightarrow \mathrm{ROH}+\mathrm{NaCl}\) is given by Rate \(=\mathrm{k}(\mathrm{RCl})\). The rate of the reaction is a. Halved by reducing the concentration of \(\mathrm{RCl}\) by one half. b. Increased by increasing the temperature of the reaction. c. Remains same by change in temperature. d. Doubled by doubling the concentration of \(\mathrm{NaOH}\).

Short answer

The rate is halved when [RCl] is halved and increased by raising the temperature.

Step-by-step solution

Understand the Rate Law

The rate law for the reaction is given as \( \text{Rate} = k [\text{RCl}] \). This implies that the rate of reaction depends only on the concentration of \( \text{RCl} \) and is independent of the concentration of \( \text{NaOH} \).

Analyze Effect of Changing [RCl]

According to the rate law \( \text{Rate} = k [\text{RCl}] \), if the concentration of \( \text{RCl} \) is halved, the rate of the reaction will also be halved. Hence, option (a) is correct.

Analyze Effect of Temperature Change

Changing the temperature can affect the rate constant \( k \). Increasing the temperature usually increases the rate of reaction because the rate constant \( k \) generally increases with temperature. Therefore, option (b) is correct. Option (c) is incorrect because the rate remains the same only if there is no change in temperature.

Analyze Effect of Changing [NaOH]

From the rate law \( \text{Rate} = k [\text{RCl}] \), the rate is independent of the concentration of \( \text{NaOH} \). Thus, doubling \( [\text{NaOH}] \) will not affect the rate of the reaction, making option (d) incorrect.

Key concepts

reaction rate

The rate of a chemical reaction is a measure of how quickly reactants are converted into products over time. In simple terms, it tells us how fast a reaction is happening. The rate can be expressed as the change in concentration of a reactant or product per unit time. For the reaction \(\text{RCl} + \text{NaOH} \rightarrow \text{ROH} + \text{NaCl}\)\, the rate is determined only by the concentration of \(\text{RCl}\). This is because the provided rate law is \(\text{Rate} = k [\text{RCl}]\). Here, \(k\) is the rate constant, and \([\text{RCl}]\) represents the concentration of \(\text{RCl}\). The reaction rate is directly proportional to \([\text{RCl}]\). So if you increase the amount of \(\text{RCl}\), the reaction rate will also increase, and vice versa for decrease.

• **Rate Constant (\(k\))**: A unique value for each reaction at a specific temperature that shows the relationship between concentration and rate.
• **Reaction Rate**: Depends on \([\text{RCl}]\). Doubling \([\text{RCl}]\) doubles the reaction rate, and halving \([\text{RCl}]\) halves it.

temperature effect

The temperature plays a crucial role in influencing the rate of a chemical reaction. Increasing the temperature generally increases the reaction rate. This is because a higher temperature provides reactant molecules with more energy, which leads to more effective collisions between them.In the context of reaction kinetics, as temperature rises, the rate constant \(k\) also increases, thus increasing the reaction rate. However, this temperature effect is typically not part of the rate law and must be considered as a separate factor.

• **More Energy at Higher Temperatures**: Molecules move faster and collide more effectively.
• **Changes in \(k\)**: With increased temperature, \(k\) tends to increase, thereby boosting the reaction rate.

concentration effect

The concentration of reactants can significantly impact the speed at which a reaction proceeds. According to the rate law \(\text{Rate} = k [\text{RCl}]\), the reaction rate is directly proportional to the concentration of \(\text{RCl}\). However, changes in \([\text{NaOH}]\) have no impact on the reaction rate, as it doesn't appear in the rate law.When the concentration of \(\text{RCl}\) is halved, the reaction rate is halved too, making this a linear relationship between concentration and rate.

• **Direct Proportionality**: Halve \([\text{RCl}]\), halve the rate; double \([\text{RCl}]\), double the rate.
• **Irrelevance of \([\text{NaOH}]\)**: No effect on the rate due to absence in the rate law.

reaction kinetics

Reaction kinetics is the study of the rates of chemical processes and the factors affecting them. Understanding reaction kinetics helps predict how changes in conditions like concentration and temperature affect the reaction rate. The kinetic study involves exploring the relationship between the rate and the concentrations of reactants as depicted by the rate law. It also takes into account the molecular mechanism of the reaction.

• **Determining Rate Laws**: Identify which concentrations affect the rate.
• **Molecular Motion and Collision**: More collisions often mean faster reactions and are influenced by both concentration and temperature.
• **Applications**: Useful in designing chemical processes and optimizing conditions for desired reaction rates.