Comparing rates of substitution reactions

The following question was asked in an exam I gave recently

Compare the overall rates of the following substitution reactions $$\ce{CH3Cl ->[OH-][Weak P.A.S] CH3OH}$$

$$\ce{CH3CH2Cl ->[OH-][ Weak P.A.S] CH3CH2OH}$$ $$\ce{(CH3)2CHCl ->[OH-][ Weak P.A.S] (CH3)2CHOH}$$ $$\ce{(CH3)3CCl ->[OH-][ Weak P.A.S] (CH3)3COH}$$ (P.A.S means polar aprotic solvent). I know that $$\ce{CH3Cl , CH3CH2Cl}$$ react mainly via $$S_{N^2}$$ mechanism, $$\ce{(CH3)2CHCl}$$ react via both $$S_{N^2} , S_{N^1}$$ mechanisms considerably and $$\ce{(CH3)3CCl}$$ via $$S_{N^1}$$ mechanism.

The rates of the reactions can be given by the following rate equations

$$r_1 = k_1[\ce{CH3Cl}][\ce{OH-}] + k_1^☆[\ce{CH3Cl}]$$,

$$k_1^☆$$ being negligible

$$r_2 = k_2[\ce{CH3CH2Cl}][\ce{OH-}] + k_2^☆[\ce{CH3CH2Cl}]$$

,$$k_2^☆$$ being negligible

$$r_3 = k_3[\ce{(CH3)2CHCl}][\ce{OH-}] + k_3^☆[\ce{(CH3)2CHCl}]$$

can't neglect anything here,

$$r_4 = k_4[\ce{(CH3)3CCl}][\ce{OH-}] + k_4^☆[\ce{(CH3)3CCl}]$$ $$k_4$$ can be neglected here.

So, I would assume the reaction-3 occurs at least rate as $${k_3}$$ and $${k_3^☆}$$ are both low, but I don't know how to compare between $$k_1 , k_2 , k_4^☆$$.

Is there any theoretical way to compare them? If yes, then how?

• What is P.A.S? Also it should be $\ce{S_N2}$ and $\ce{S_N1}$ and not $\ce{S_{N^2}}$ and $\ce{S_{N^1}}$. Jul 18 at 18:15
• By "exam I gave recently" you mean that you are the author of this question? Or do you mean that you wrote this exam? I think it should depend on whether the solvent is protic or aprotic, but in neither case I see why this order is correct Jul 18 at 19:18
• @Azamat No, I am not the author of the question. I've recently written a mock test for JEE conducted by a local institute. Jul 18 at 21:33
• $S_n2$ in general is faster reaction than $S_n1$ and rate of $S_n2$ directly depends on stability of transition state (here bulky transition states are less stable). Also you can neglect $S_n2$ here because polar aprotic solvents favor $S_n2$ (since as transition state proceeds charge density reduces which is better stabilized by aprotic solvents). I would think (theoretically) the order is $S_n2$ based unless relevant data is provided. Jul 20 at 13:00
• How do you measure the rate of substitution based on RCl concentration when elimination is appreciable in the secondary and tertiary halides? Isn't the appearance of alcohol more relevant? Sep 3 at 18:16

Actually one can't always find answers through logical formulations to these JEE problems on organic chemistry , but we can understand and compare logical constraints. I remember this question was asked in two different ways in my examinations - one considering only $$\mathrm{S_N2}$$ among the reactions and the other one is same as yours.

$$\ce{CH3Cl ->[OH-][Weak P.A.S] CH3OH}$$

$$\ce{CH3CH2Cl ->[OH-][ Weak P.A.S] CH3CH2OH}$$ $$\ce{(CH3)2CHCl ->[OH-][ Weak P.A.S] (CH3)2CHOH}$$ $$\ce{(CH3)3CCl ->[OH-][ Weak P.A.S] (CH3)3COH}$$

If we only consider $$\mathrm{S_N2}$$ among these reactions order will be $$\mathrm{1>2>3>4}$$.

But we have to consider how large the other atoms or functional groups bonded to the carbon are, compared to $$\ce{OH^-}$$ also known as steric inheritance or steric crowding, then

For this question we are considering a substitution reaction..

You said the answer yourself - $$\ce{CH3Cl, CH3CH2Cl}$$ react mainly via $$\mathrm{S_N2}$$ mechanism, $$\ce{(CH3)2CHCl}$$ react mainly via both $$\mathrm{S_N2, S_N1}$$ mechanisms considerably and $$\ce{(CH3)3CCl}$$ via $$\mathrm{S_N1}$$ mechanism.

Now you have to consider steric hindrance in $$\ce{(CH3)3CCl}$$ where the three $$\ce{CH3}$$ groups makes $$\mathrm{S_N1}$$ more favourable. Also the tert-butyl carbocation $$\ce{(CH3)3C^+}$$ is more stable beacause of 9 alpha hydrogens which involve in hyperconjugation. In most cases when steric factors and hyperconjugation both favour carbocation formation then $$\mathrm{S_N1}$$ is the major pathway preferred over $$\mathrm{S_N2}$$.

So for $$\mathrm{4}$$, strongly favoured $$\mathrm{S_N1}$$ pathway increases rate of reaction. For the other 3, $$\mathrm{S_N2}$$ is dominant which follows the order $$\mathrm{1>2>3}$$. Hence overall order is $$\mathrm{4>1>2>3}$$.

• But can you say that $\ce{S_N1}$ is always faster than $\ce{S_N2}$? I don't understand what "Weak P. A. S." means but the rates of the two mechanisms and what mechanism is dominant depend on the solvent. Or am I missing something? Jul 20 at 6:09
• @Azamat No we can't say $S_N1$ is faster than $S_N2$ vice versa. without knowing the solvent .this may help you know about solvents also about "Weak P. A. S." [link]quora.com/… Jul 20 at 12:47