Question

The rate law for the reaction \(\mathrm{RCl}+\mathrm{NaOH}\) (aq) \(\longrightarrow \mathrm{ROH}+\mathrm{NaCl}\) is given by Rate \(=k[\mathrm{RCl}]\). The rate of the reaction will be (a) doubled on doubling the concentration of sodium hydroxide (b) halved on reducing the concentration of alkyl halide to one half (c) decreased on increasing the temperature of reaction (d) unaffected by increasing the temperature of the reaction.

Short answer

Option (b) is correct: the rate is halved when the concentration of RCl is halved.

Step-by-step solution

Understand the Rate Law

The given rate law is Rate \( = k[\mathrm{RCl}]\), which implies that the rate of reaction depends linearly on the concentration of \(\mathrm{RCl}\) only and is independent of the concentration of \(\mathrm{NaOH}\). The rate constant \(k\) may change with temperature but not with concentration.

Analyze Option (a)

The option states that the rate is doubled on doubling the concentration of \(\mathrm{NaOH}\). Since \(\mathrm{NaOH}\) does not appear in the rate law expression, altering its concentration will have no effect on the rate of reaction. Thus, this option is incorrect.

Analyze Option (b)

This option suggests that the rate is halved if the concentration of \(\mathrm{RCl}\) is reduced by half. Since the rate depends directly on \([\mathrm{RCl}]\), if \([\mathrm{RCl}]\) is halved, the rate of reaction will also be halved, making this option correct.

Analyze Option (c)

Option (c) proposes that increasing the temperature decreases the rate of reaction. Typically, increasing temperature increases the reaction rate due to the Arrhenius equation effect, making this option incorrect.

Analyze Option (d)

Option (d) claims that the rate is unaffected by temperature changes. For most reactions, rate increases with temperature, due to increased kinetic energy and more effective collisions, hence this statement is incorrect.

Key concepts

Rate Law

The rate law is an important concept in chemical kinetics. It is a mathematical expression that describes the rate of a chemical reaction in terms of the concentration of reactants. In the given reaction, the rate law is expressed as \( \text{Rate} = k[\text{RCl}] \). This indicates that the rate of this reaction is directly proportional to the concentration of RCl (alkyl halide). It is important to note that in this particular case, the rate of reaction does not depend on the concentration of sodium hydroxide (NaOH).

The rate constant \( k \) in the rate law equation is a proportionality factor that links the rate of reaction to the concentration of the reactants. While \( k \) itself is unaffected by the concentration of reactants like NaOH, it can be influenced by other factors, like temperature.

In summary, the rate law provides a clear depiction of how reactant concentrations influence the speed of a reaction. If a reactant's concentration is in the rate law equation, altering its amount will affect the reaction rate. If it's absent, as in the case of NaOH here, changing its concentration won't influence the rate.

Reaction Rate

The reaction rate is a measure of how quickly a chemical reaction occurs. It can be thought of as the speed at which reactants are converted to products. In the context of the reaction \( \text{RCl} + \text{NaOH} \rightarrow \text{ROH} + \text{NaCl} \), only the concentration of RCl influences the rate. Therefore, any change in the concentration of RCl will have a direct impact on the reaction rate.

Consider these scenarios:

• If the concentration of RCl is reduced by half, as in option (b) from the exercise, the rate of reaction also decreases by half. This is because the reaction rate is directly proportional to the concentration of RCl.
• Conversely, if the concentration of RCl is increased, the reaction rate will increase proportionally. This reflects the linear relationship between the reactant concentration and the reaction rate as indicated by the rate law.

Understanding the reaction rate is crucial for controlling and optimizing chemical reactions, especially in industrial settings.

Temperature Effect on Reaction Rate

Temperature is a key factor that significantly affects the rate of chemical reactions. According to the Arrhenius equation, the rate constant \( k \), and hence the reaction rate, generally increases with temperature. This happens because higher temperatures provide reactant molecules with greater kinetic energy, leading to more frequent and energetic collisions.

In the exercise, options (c) and (d) mistakenly suggest that the reaction rate decreases or remains unaffected by an increase in temperature, which is typically not the case. Higher temperatures usually result in faster reactions. Here's why:

• With increased thermal energy, more molecules surpass the activation energy barrier needed for the reaction to occur.
• This results in a higher probability of effective collisions that lead to the formation of products.

By understanding the effect of temperature on reaction rates, chemists can better predict how changing conditions will influence chemical processes.