Problem 9 - General Chemistry: Principles and Modern Applications

Question

Calculate \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) for each solution:(a) \(0.00165 \mathrm{M} \mathrm{HNO}_{3} ;\) (b) \(0.0087 \mathrm{M} \mathrm{KOH} ;\) (c) \(0.00213 \mathrm{M}\) \(\operatorname{Sr}(\mathrm{OH})_{2} ;(\mathrm{d}) 5.8 \times 10^{-4} \mathrm{M} \mathrm{HI}\)

Step-by-Step Solution

Answer

\(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) concentrations for each soultion are: (a) \(0.00165 M\) and \(6.06 \times 10^{-12} M\); (b) \(6.06 \times 10^{-12} M\) and \(0.0087 M\); (c) \(2.35 \times 10^{-12} M\) and \(0.00426 M\); (d) \(5.8 \times 10^{-4} M\) and \(1.72 \times 10^{-11} M\).

Step 1: Solve for (a): 0.00165 M HNO3

This is a strong acid. For every mole of HNO3, one mole of \(\mathrm{H}_{3} \mathrm{O}^{+}\) is produced. So, the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions is \(0.00165 M\). Knowing that \(KW=[\mathrm{H}_{3}\mathrm{O}^{+}][\mathrm{OH}^{-}]=1.0 \times 10^{-14} M^{2} \), we can find the concentration of \(\mathrm{OH}^{-}\) ions to be \( \frac{1.0 \times 10^{-14} M^2}{0.00165M} = 6.06 \times 10^{-12} M\).

Step 2: Solve for (b): 0.0087 M KOH

KOH is a strong base. One mole of KOH results in one mole of \(\mathrm{OH}^{-}\) ions. So, the concentration of \(\mathrm{OH}^{-}\) is \(0.0087M\). Using the water ion product, we get the \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration to be \( \frac{1.0 \times 10^{-14} M^2}{0.0087M} = 1.15 \times 10^{-12} M \).

Step 3: Solve for (c): 0.00213 M Sr(OH)2

This is a strong base with two hydroxyl ions for each formula unit. This means we have \(0.00213 M \times 2 = 0.00426 M\) of \(\mathrm{OH}^{-} \). The \(\mathrm{H}_{3} \mathrm{O}^{+}\) concentration is thus \( \frac{1.0 \times 10^{-14} M^2}{0.00426M} = 2.35 \times 10^{-12} M \).

Step 4: Solve for (d): 5.8 x 10^{-4} M HI

HI is a strong acid. For each mole of HI, one mole of \(\mathrm{H}_{3} \mathrm{O}^{+}\) ions is produced. This makes the concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) to be \( 5.8 \times 10^{-4} M \). Now, compute for the \(\mathrm{OH}^{-}\) concentration giving \( \frac{1.0 \times 10^{-14} M^2}{5.8 \times 10^{-4}M} = 1.72 \times 10^{-11} M \).

Key Concepts

Hydronium Ion Concentration

Hydronium ion concentration reflects the acidic nature of a solution. In aqueous solutions, an acid donates protons (H⁺), which then bond with water molecules (H₂O) to form hydronium ions (H₃O⁺).
This process increases the hydronium concentration in the solution, indicating stronger acidity.

For strong acids, this relationship is straightforward. Each molecule of a strong acid like nitric acid (HNO₃) or hydroiodic acid (HI) dissociates completely in water. This means that the concentration of the acid equals the concentration of hydronium ions in the solution.

Let's consider nitric acid (HNO₃) at a concentration of 0.00165 M:

• Because it is a strong acid, it fully dissociates, creating 0.00165 M hydronium ions.

Under these conditions, the solution is quite acidic, and its interplay with the hydrogen ion concentration delineates how it drives the equilibrium.

Hydroxide Ion Concentration

The hydroxide ion concentration in a solution signifies the basic nature of the solution. When a base dissolves in water, it usually generates hydroxide ions (OH⁻).
Strong bases like potassium hydroxide (KOH) or strontium hydroxide \((\text{Sr(OH)}_2\)) release hydroxide ions in a similar way strong acids release hydronium ions. This means each unit of these bases will dissociate completely to release hydroxide ions.

For KOH with a concentration of 0.0087 M:

• Since KOH is a strong base, it fully dissociates, resulting in 0.0087 M of hydroxide ions.

Similarly, \(\text{Sr(OH)}_2\) is unique because each molecule provides two moles of hydroxide, doubling the effective concentration of hydroxide ions at 0.00213 M to 0.00426 M.
The presence of these ions dictates the basicity of the solutions and influences acid-base equilibria.

Strong Acids and Bases

Strong acids and bases are substances that completely dissociate into their constituent ions in a solution. Because of this complete dissociation, the concentration of ions generated equals the initial concentration of the acid or base, simplifying the calculation of ion concentrations.

Strong acids, exemplified by HI and HNO₃, dissociate to form hydronium ions. This increase in hydronium ions results in a lower pH (more acidic). For example, a 5.8 x 10⁻⁴ M solution of HI, a strong acid, directly corresponds to a hydronium ion concentration of 5.8 x 10⁻⁴ M.

Similarly, strong bases like KOH and \(\text{Sr(OH)}_2\) dissociate to produce hydroxide ions.

• In the case of 0.0087 M KOH, this leads to 0.0087 M hydroxide ions.
• For \(\text{Sr(OH)}_2\), since each molecule provides double the hydroxide ions, a concentration of 0.00213 M produces 0.00426 M of hydroxide ions.

Understanding these principles allows us to predict the behavior of solutions involving these strong acids and bases effortlessly.