Calculate the pH at 25^∘ C of a 0.25 M aqueous solution of...

Calculate the $\mathrm{pH}$ at $25^{\circ} \mathrm{C}$ of a $0.25 \mathrm{M}$ aqueous solution of phosphoric acid $\left(\mathrm{H}_{3} \mathrm{PO}_{4}\right) .\left(K_{\mathrm{a}}, K_{\mathrm{a}_{2}}, \text { and } K_{\mathrm{a}_{3}}$ for phosphoric acid \right. are $\left.7.5 \times 10^{-3}, 6.25 \times 10^{-8}, \text {and } 4.8 \times 10^{-13}, \text {respectively. }\right)$

Calculate the $\mathrm{pH}$ at $25^{\circ} \mathrm{C}$ of a $0.25 \mathrm{M}$ aqueous solution of phosphoric acid $\left(\mathrm{H}_{3} \mathrm{PO}_{4}\right) .\left(K_{\mathrm{a}}, K_{\mathrm{a}_{2}}, \text { and } K_{\mathrm{a}_{3}}$ for phosphoric acid \right.
are $\left.7.5 \times 10^{-3}, 6.25 \times 10^{-8}, \text {and } 4.8 \times 10^{-13}, \text {respectively. }\right)$

Key Concepts

pH Calculation

pH calculation involves determining the hydrogen ion concentration in a solution, followed by taking the negative logarithm of that concentration. This fundamental concept in chemistry helps quantify the acidity or basicity of a solution, which is crucial for understanding chemical reactivity and biological systems.

Acid Dissociation Constant (Ka)

The acid dissociation constant, Ka, is a quantitative measure of the strength of an acid in solution. It represents the equilibrium between the undissociated acid and the ions produced in the dissociation process. A larger Ka value indicates a stronger acid, which dissociates more completely in water.

Polyprotic Acids

Polyprotic acids are acids that can donate more than one proton (H+) per molecule. They undergo multiple dissociation steps, each with its own dissociation constant. Understanding polyprotic acids is key, as the sequential proton losses often occur to different extents, influencing the overall pH of the solution.

Stepwise Dissociation

Stepwise dissociation refers to the sequential loss of protons from polyprotic acids. Each dissociation step is characterized by its own equilibrium constant (Ka1, Ka2, etc.), with the first dissociation generally being the most significant. This concept is important because, in many cases, the first dissociation step largely determines the hydrogen ion concentration and thus the pH.

Equilibrium Expressions

Equilibrium expressions are used to relate the concentrations of reactants and products in a chemical reaction at equilibrium. For acid dissociation, the equilibrium expression provides a mathematical relationship involving the acid concentration, the hydrogen ion concentration, and the concentration of the conjugate base, which is critical for calculating pH in weak acid solutions.

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