Calculate the pH of an aqueous solution at 25^∘ C that is...

Calculate the $\mathrm{pH}$ of an aqueous solution at $25^{\circ} \mathrm{C}$ that is $0.095 \mathrm{M}$ in hydrocyanic acid (HCN). $\left(K_{\mathrm{a}} \text { for hydrocyanic acid }=\right.$ $\left.4.9 \times 10^{-10} .\right)$

Key Concepts

Weak Acid Equilibrium

In the case of weak acids, the dissociation into ions is partial and reaches an equilibrium state between the undissociated acid and its ions. Understanding this equilibrium is essential for calculating the hydrogen ion concentration and, consequently, the pH, since the acid does not completely ionize.

Equilibrium Calculations and Approximations

Equilibrium calculations involve setting up an expression that relates the concentrations of the acid, its conjugate base, and the hydrogen ion, based on the known Ka value. Often, the approximation is made that the change in concentration due to ionization is negligible compared to the initial concentration, which simplifies the calculation while remaining accurate for weak acids.

pH is a logarithmic measure of the hydrogen ion concentration in a solution. It provides a scale to quantify the acidity or basicity of a solution, where lower values indicate higher acidity. Calculating pH involves understanding the relationship between hydrogen ion concentration and the acid–base properties of the solution.

Acid Dissociation Constant (Ka)

The acid dissociation constant (Ka) quantifies the strength of an acid by expressing the equilibrium constant for its dissociation into hydrogen ions and its conjugate base. It is a crucial parameter for weak acids, as it helps in predicting the extent to which the acid ionizes in solution.

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