Saccharin, a sugar substitute, is a weak acid with p Ka=2.32 at 25^∘ C. It ionizes in aqueous so

step 1 In this question, P .K. of saccharine, which is a weak acid, given as 2 .32. Also, initial conce

Saccharin, a sugar substitute, is a weak acid with p Ka=2.32...

Saccharin, a sugar substitute, is a weak acid with $\mathrm{p} K_{a}=2.32$ at $25^{\circ} \mathrm{C}$. It ionizes in aqueous solution as follows: $$ \mathrm{HNC}_{7} \mathrm{H}_{4} \mathrm{SO}_{3}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{NC}_{7} \mathrm{H}_{4} \mathrm{SO}_{3}^{-}(a q) $$ What is the pH of a $0.25 \mathrm{M}$ solution of this substance?

Saccharin, a sugar substitute, is a weak acid with $\mathrm{p} K_{a}=2.32$ at $25^{\circ} \mathrm{C}$. It ionizes in aqueous solution as follows:
$$ \mathrm{HNC}_{7} \mathrm{H}_{4} \mathrm{SO}_{3}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{NC}_{7} \mathrm{H}_{4} \mathrm{SO}_{3}^{-}(a q) $$
What is the pH of a $0.25 \mathrm{M}$ solution of this substance?

Key Concepts

pH Calculation

pH is a measure of the acidity of a solution, defined as the negative logarithm of the hydrogen ion concentration. In problems involving weak acids, calculating pH requires determining the equilibrium concentration of hydrogen ions generated by the acid’s partial ionization. Understanding how to compute pH from the equilibrium concentrations is fundamental in acid-base chemistry.

Equilibrium Calculations and Approximations

When dealing with weak acids, it is often appropriate to use approximations—such as assuming that the change in concentration due to ionization is small compared to the initial concentration—to simplify equilibrium calculations. This often involves setting up an ICE table and, if justified, neglecting small quantities relative to larger initial amounts. These techniques streamline the process of solving the equilibrium expression to find hydrogen ion concentration.

Acid Dissociation Constant (Ka) and pKa

The acid dissociation constant, Ka, quantitatively expresses the strength of an acid in solution by indicating the extent of its ionization. pKa is the negative logarithm of Ka and provides a more convenient scale for comparing acid strengths. Recognizing how to relate Ka to pKa is crucial for calculating the concentrations of species in an equilibrium system and for further deriving the pH of a solution.

Weak Acid Equilibrium

This concept refers to the reversible process by which a weak acid partially dissociates into its constituent ions in solution. In acid-base chemistry, the equilibrium between the undissociated acid and its dissociated form (the hydrogen ion and the conjugate base) is described by an equilibrium constant. This understanding allows the prediction of the degree of dissociation and is essential for determining solution pH.

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