PROBLEM 7.18 - Organic Chemistry

Question

Question: What happens to the rate of an S_N2  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 rate of the reaction increases thrice when the concentration of $\left[\mathrm{RX}\right]$ is tripled and   $\left[:{\mathrm{Nu}}^{-}\right]$  stays the same.

 

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

 

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

 

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

S N 2 reaction

The nucleophile strikes from the front side or the rear side in an  S_N2  reaction. The rate-determining step for this particular reaction is based on species like nucleophiles and the reactant. 

 

Equation concerning S N 2 reaction

The equation that is employed to represent  S_N2  reaction can be given as.

$\mathrm{Rate}=\mathrm{k}\left[\mathrm{RX}\right]\left[:{\mathrm{Nu}}^{-}\right]$

Here, [RX] indicates the reactant concentration and $\left[:{\mathrm{Nu}}^{-}\right]$indicates the nucleophilic concentration.

Rate of reaction under various conditions

a. The S_N2 rate of reaction depends on the concentration of the reactant, [RX], and the incoming nucleophile$\left[:{\mathrm{Nu}}^{-}\right]$ .

 

The rate of S_N2 reaction can be given as:

Rate = k$\left[\mathrm{RX}\right]\left[:{\mathrm{Nu}}^{-}\right]$

When the concentration is tripled, the rate can be given as follows:

Rate =k$\left[3\mathrm{RX}\right]\left[:{\mathrm{Nu}}^{-}\right]$

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

 

b. When the concentration of the reactant, [RX], and  the incoming nucleophile is$\left[:{\mathrm{Nu}}^{-}\right]$tripled, the reaction rate can be given as:

Rate = k$\left[3\mathrm{RX}\right]\left[3:{\mathrm{Nu}}^{-}\right]$

         =9$\left[\mathrm{kRX}\right]\left[:{\mathrm{Nu}}^{-}\right]$

 

Hence, the reaction rate increases by nine times when the concentration of the reactant and nucleophile is tripled.

 

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

$\mathrm{Rate} =\mathrm{k}\left[\frac{1}{2}\times \mathrm{RX}\right]\left[:{\mathrm{Nu}}^{-}\right]$

          =$\frac{1}{2}\times \left(\mathrm{k}\left[\mathrm{RX}\right]\right)\left[:{\mathrm{Nu}}^{-}\right]$

 

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

 

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

$$\begin{gathered} \mathrm{Rate} =\mathrm{k}\left[\frac{1}{2}\times \mathrm{RX}\right]\left[2\times :{\mathrm{Nu}}^{-}\right] \\ =\mathrm{k}\left[\mathrm{RX}\right]\left[:{\mathrm{Nu}}^{-}\right] \end{gathered}$$ 

 

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