Calculate the rate for the SN 2 reaction of 0.1-M C2 H5 I with 0.1-M CN^-if the reaction rate fo

step 1 in this problem as mole per liter of n205 reacted is equal to 2 multiplication 0 .1 which is equ

Calculate the rate for the SN 2 reaction of 0.1-M C2 H5 I...

Calculate the rate for the $\mathrm{S}_{\mathrm{N}} 2$ reaction of 0.1-M $\mathrm{C}_2 \mathrm{H}_5 \mathrm{I}$ with 0.1-M $\mathrm{CN}^{-}$if the reaction rate for $0.01 \mathrm{M}$ concentration is $5.44 \times 10^{-9} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}$. The rates are proportional to the products of the concentrations, $$ \begin{aligned} \frac{\text { Rate }}{5.44 \times 10^{-9} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}} & =\frac{[0.1][0.1]}{[0.01][0.01]} \\ \text { Rate } & =100 \times 5.44 \times 10^{-9} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}=5.44 \times 10^{-7} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s} \end{aligned} $$

Calculate the rate for the $\mathrm{S}_{\mathrm{N}} 2$ reaction of 0.1-M $\mathrm{C}_2 \mathrm{H}_5 \mathrm{I}$ with 0.1-M $\mathrm{CN}^{-}$if the reaction rate for $0.01 \mathrm{M}$ concentration is $5.44 \times 10^{-9} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}$.
The rates are proportional to the products of the concentrations,
$$
\begin{aligned}
\frac{\text { Rate }}{5.44 \times 10^{-9} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}} & =\frac{[0.1][0.1]}{[0.01][0.01]} \\
\text { Rate } & =100 \times 5.44 \times 10^{-9} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}=5.44 \times 10^{-7} \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s}
\end{aligned}
$$

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Key Concepts

S_N2 Reaction Mechanism

The S_N2 (bimolecular nucleophilic substitution) reaction is a one-step process where a nucleophile attacks an electrophilic carbon, resulting in the simultaneous displacement of the leaving group. This mechanism is characterized by its concerted nature, meaning that the bond formation and bond breaking occur in a single transition state, leading to an inversion of configuration at the carbon center.

Bimolecular Rate Law

In a bimolecular reaction such as S_N2, the rate law is typically given as rate = k[substrate][nucleophile]. This equation shows that the reaction rate depends on the concentrations of both the electrophilic substrate and the nucleophile, making the reaction second order overall. The rate constant k embodies the intrinsic kinetics of the reaction under specific conditions.

Concentration Dependence

The reaction rate’s dependency on the product of the reactants’ concentrations underscores how changes in concentration can linearly affect the rate. For instance, if the concentrations of both reacting species increase by a factor, the reaction rate increases by the square of that factor. This concept is key in predicting and comparing the kinetics of similar reactions when the reactant concentrations are altered.

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