PROBLEM 7.23 - Organic Chemistry

Question

Question: What happens to the rate of an S_N1  reaction under each of the following conditions?

a. [RX] is tripled, and $\left[:{\mathrm{Nu}}^{-}\right]$stays the same.

b. Both [RX] and $\left[:{\mathrm{Nu}}^{-}\right]$are tripled.  

c. [RX] is halved, and $\left[:{\mathrm{Nu}}^{-}\right]$ stays the same.

d. [RX] is halved, and$\left[:{\mathrm{Nu}}^{-}\right]$ is doubled.

Step-by-Step Solution

Answer

Answer

a. The reaction rate increases thrice when the concentration of [RX] is tripled and $\left[:{\mathrm{Nu}}^{-}\right]$ stays the same.

 

b. The reaction rate increases thrice when the concentration of [RX] and $\left[:{\mathrm{Nu}}^{-}\right]$  is tripled. 

 

c. The reaction rate decreases by half when the concentration of [RX] is halved and$\left[:{\mathrm{Nu}}^{-}\right]$  stays the same. 

 

d. The reaction rate decreases by half when the concentration of [RX] is halved $\left[:{\mathrm{Nu}}^{-}\right]$ is doubled.

 

S N 1 reaction

The reaction rate is influenced only by the reactant concentration and not by the nucleophile concentration in an reaction. A carbocation intermediate is created in this particular reaction.  

Equation concerning S N 1 reaction

The equation that is utilized to denote S_N1  reaction can be given as:

$\mathrm{Rate} =\mathrm{k}\left[\mathrm{RX}\right]$

Here, [RX] represents the reactant concentration.

Rate of S N 1 reaction under various conditions

a. The S_N1  reaction rate depends on the concentration of the reactant [RX]. The nucleophile concentration does not have an impact on the S_N1  reaction. 

 The  S_N1  reaction rate can be given as:

$\mathrm{Rate} =\mathrm{k}\left[\mathrm{RX}\right]$

 When the concentration is tripled, the rate can be found as:

$$\begin{gathered} \mathrm{Rate} =\mathrm{k}\left[3\mathrm{RX}\right] \\ =3\left(\mathrm{k}\left[\mathrm{RX}\right]\right) \end{gathered}$$

Hence, the reaction rate increases thrice when the concentration is tripled.

b. The reaction rate of S_N1  reaction depends only on the reactant concentration. The concentration of nucleophiles does not have any effect. The reaction rate can be found as follows:

$$\begin{gathered} \mathrm{Rate} =\mathrm{k}\left[3\mathrm{RX}\right] \\ =3\left(\mathrm{k}\left[\mathrm{RX}\right]\right) \end{gathered}$$

 

Hence, the reaction rate increases thrice when the reactant and nucleophile concentration is tripled.

c. The reaction rate when [RX] is halved and$\left[:{\mathrm{Nu}}^{-}\right]$remains the same can be given as:

$$\begin{gathered} \mathrm{Rate}=\mathrm{k}\left[\frac{1}{2}\times \mathrm{RX}\right] \\ =\frac{1}{2}\left(\mathrm{k}\left[\mathrm{RX}\right]\right) \end{gathered}$$

 Hence, the reaction rate becomes halved when the reactant concentration is halved and  stays the same.

d. The rate of reaction when [RX] is halved and $\left[:{\mathrm{Nu}}^{-}\right]$is doubled can be given as follows:

$$\begin{gathered} \mathrm{Rate}=\mathrm{k}\left[\frac{1}{2}\times \mathrm{RX}\right] \\ =\frac{1}{2}\left(\mathrm{k}\left[\mathrm{RX}\right]\right) \end{gathered}$$

 Hence, the reaction rate remains halved when [RX] is halved and$\left[:{\mathrm{Nu}}^{-}\right]$ is doubled.