Mechanism of reaction between triphenylmethanol and acetyl chloride
I find it unlikely that the substitution proceeds via the hydroxyl group directly leaving. If there is any evidence that this reaction proceeds via direct $\mathrm{S_N1}$ of $\ce{OH-}$ by $\ce{Cl-}$, I would be very interested to see it. When an alcohol and an acyl chloride are mixed, I think it is much more probable that they will initially form the ester via nucleophilic acyl substitution:

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Presumably, this ester is rather unstable because of steric repulsions between the three phenyl groups and the ester group. So now, the $\ce{-OAc}$ group ($\ce{Ac} = \ce{COCH3}$) can leave as a relatively stable carboxylate ion to give the resonance-stabilised carbocation:

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The carbocation is then intercepted by chloride ions that were formed earlier to give the product you want. So, the second part of the reaction is a $\mathrm{S_N1}$ substitution of $\ce{OAc-}$ by $\ce{Cl-}$.

$\ce{OAc-}$ ($\mathrm{p}K_\mathrm{aH} = 4.76$) is a much better leaving group than $\ce{OH-}$ ($\mathrm{p}K_\mathrm{aH} = 15.7$).



There is another pathway possible, since $\ce{HCl}$ is formed from the initial reaction of the alcohol with the acyl chloride. If $\ce{HCl}$ is present in appreciable quantities, it can protonate the original alcohol and you could perhaps have a direct $\mathrm{S_N1}$ of $\ce{H2O}$ by $\ce{Cl-}$.

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