Calculate the pH and the pOH of each of the following solutions at 25^∘ C for which the substanc

step 1 Here, the HCL is a strong asset which completely dissociates in water to produce hydrogen ions a

Calculate the pH and the pOH of each of the following...

Calculate the pH and the pOH of each of the following solutions at $25^{\circ} \mathrm{C}$ for which the substances ionize completely: $$ \begin{array}{l}{\text { (a) } 0.200 \mathrm{M} \mathrm{Cl}} \\ {\text { (b) } 0.0143 \mathrm{M} \mathrm{NaOH}} \\ {\text { (c) } 3.0 \mathrm{M} \mathrm{HNO}_{3}} \\ {\text { (d) } 0.0031 \mathrm{M} \mathrm{Ca}(\mathrm{OH})_{2}}\end{array} $$

Calculate the pH and the pOH of each of the following solutions at $25^{\circ} \mathrm{C}$ for which the substances ionize completely:
$$
\begin{array}{l}{\text { (a) } 0.200 \mathrm{M} \mathrm{Cl}} \\ {\text { (b) } 0.0143 \mathrm{M} \mathrm{NaOH}} \\ {\text { (c) } 3.0 \mathrm{M} \mathrm{HNO}_{3}} \\ {\text { (d) } 0.0031 \mathrm{M} \mathrm{Ca}(\mathrm{OH})_{2}}\end{array}
$$

Key Concepts

Logarithmic Calculations

The computation of pH and pOH relies on the logarithmic function, which transforms the wide range of ion concentrations into a more manageable scale. Mastery of logarithmic calculations is essential, as the negative logarithm is used to convert hydrogen or hydroxide ion concentrations to the pH or pOH values, thereby providing a practical measure of a solution's acidity or basicity.

Stoichiometry of Ionization

In reactions where a substance dissociates into more than one ion per formula unit, stoichiometry plays a critical role. For example, bases like Ca(OH)? produce two hydroxide ions per molecule. This stoichiometric relationship must be considered when determining the concentration of H? or OH? ions to accurately calculate pH or pOH.

pH and pOH Concepts

pH is a measure of the hydrogen ion concentration in a solution and is defined as the negative logarithm of the H? concentration (-log[H?]). Similarly, pOH measures the hydroxide ion concentration as -log[OH?]. At 25°C, the sum of pH and pOH is 14, a relationship that is derived from the autoionization constant of water (K?w? = 1.0×10?¹?). Understanding this relationship is essential for interconverting between pH and pOH in aqueous solutions.

Strong Electrolyte Behavior

Strong acids and bases are characterized by their complete ionization in water. This means that when they dissolve, they dissociate entirely into their constituent ions. The complete ionization property simplifies the calculation of ion concentrations, as the concentration of the generated ions is equal to the initial concentration of the solute (after accounting for the stoichiometry of the dissociation reaction).

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