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?
Answer given:
The answer is 4>1>2>3