Comprehensive Guide to Sodium Cyanide Hydrolysis
Sodium cyanide ($\text{NaCN}$) is a water-soluble ionic salt formed from a strong base ($\text{NaOH}$) and a weak acid ($\text{HCN}$). When dissolved in an aqueous environment, it completely dissociates into sodium cations ($\text{Na}^+$) and cyanide anions ($\text{CN}^-$). Because the cyanide ion is the conjugate base of the weak acid hydrocyanic acid, it undergoes significant base hydrolysis. This reaction generates hydroxide ions ($\text{OH}^-$), creating an alkaline solution profile.
Formula Used and Mathematical Model
The core chemical equilibrium governing the system is expressed as follows:
$\text{CN}^- + \text{H}_2\text{O} \rightleftharpoons \text{HCN} + \text{OH}^-$
The base dissociation constant ($K_b$) for the cyanide ion relates directly to the acid dissociation constant ($K_a$) of hydrocyanic acid via the autoionization constant of water ($K_w$):
$K_b = \frac{K_w}{K_a} = \frac{[\text{HCN}][\text{OH}^-]}{[\text{CN}^-]}
By solving the quadratic expression derived from mass action laws and charge balance, the exact concentration of hydroxide ions is computed. From $[\text{OH}^-]$, the solution finds the $\text{pOH}$ and subsequently determines the final $\text{pH}$ value through standard logarithmic conversion.
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