Cyanohydrin formation needs the cyanide ion as nucleophile. The pKa of HCN is 9.2 and the total cyanide concentration (HCN plus CN-) is fixed. When the pH of the medium is lowered from 9.2 to 6.2, the concentration of CN- falls by a factor of about

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Cyanohydrin formation needs the cyanide ion as nucleophile. The pKa of $HCN$ is 9.2 and the total cyanide concentration (HCN plus $CN X^{-}$ ) is fixed. When the pH of the medium is lowered from 9.2 to 6.2, the concentration of $CN X^{-}$ falls by a factor of about

The fraction as

CN X^{-}

1/ (1 + 1 0^{p K_{a} - p H})

. At pH 9.2 it is 0.500; at pH 6.2 it is

1/ (1 + 1 0^{3}) = 0.00100

. The ratio is 500.5, about 500. Using

1 0^{3}

directly (ignoring the half ionisation at pH 9.2) would wrongly give 1000, so a mildly basic medium accelerates the addition.