1\. Nitrous acid (HNO2) is a weak acid with a \(K_{\mathrm{a}}\) of \(4.3 \times 10^{-4}\). Estimate the hydronium ion concentration and the \(p \mathrm{H}\) for a \(0.50 \mathrm{M}\) solution of nitrous acid in distilled water. 2\. Acetic acid is a weak acid with \(K_{a}=1.8 \times 10^{-5}\). For a solution of acetic acid in water, the \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) is found to be \(4.2 \times\) \(10^{-3} \mathrm{M}\). What is the concentration of unionized acetic acid in this solution? $$ \mathrm{CH}_{3} \mathrm{COOH}(a q)+\mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightleftarrows \mathrm{CH}_{3} \mathrm{COO}^{-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q) $$ 3\. A solution is prepared in which acetic acid is \(0.700 \mathrm{M}\) and its conjugate base, acetate anion is \(0.600 \mathrm{M}\). As shown above, the \(K_{\mathrm{a}}\) of acetic acid is \(1.8 \times 10^{-5}\); what will the \(p \mathrm{H}\) of this solution be?

Step by step solution

01

Determine Hydronium Ion Concentration for HNO2

For a weak acid like HNO2, we can use the formula for dissociation: HNO2(aq) ⇌ H+(aq) + NO2−(aq). The equilibrium expression is: Ka = [H+][NO2−]/[HNO2]. For weak acids, we assume that the initial concentration of H+ is approximately equal to the change in concentration (x). We set up the equation 4.3 × 10−4 = x^2/0.50 and solve for x.

02

Calculate pH for HNO2 Solution

The pH of the solution is calculated by taking the negative logarithm (base 10) of the hydronium ion concentration: pH = -log[H+]. Use the value of x found from the previous step to determine pH.

03

Calculate Unionized Acetic Acid Concentration

The reaction for acetic acid in water is already given as at equilibrium. We’re given [H3O+], so we can find the concentration of CH3COO− (which equals [H3O+], since it's a 1:1 reaction). Then using the initial concentration of acetic acid and the dissociation equation, [CH3COOH] = [CH3COOH]initial - [CH3COO-]. Solving this provides the concentration of unionized acetic acid.

04

Determine pH for Acetic Acid and Acetate Anion Solution

For a solution with both the weak acid and its conjugate base present, we use the Henderson-Hasselbalch equation: pH = pKa + log([A−]/[HA]). We know [A−] is 0.600 M, [HA] is 0.700 M; pKa is -log(Ka). Calculate pKa using -log(1.8 × 10^-5), then calculate the pH.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Weak Acid

A weak acid is one that does not completely dissociate in water. This is fundamental to understanding acid-base chemistry in aqueous solutions. Unlike strong acids that completely ionize, weak acids only partially ionize in water, creating an equilibrium between the undissociated acid (HA) and the ions it forms (H+ and A-).

For instance, nitrous acid (HNO2) is a weak acid, and when it is dissolved in water, it reacts to form hydronium ions (H3O+) and nitrite ions (NO2−) but not completely. A small portion of the acid remains as HNO2. This incomplete dissociation is characterized by the acid dissociation constant, Ka, which provides a measure of the acid's strength; the smaller the Ka value, the weaker the acid.

pH Calculation

The pH of a solution is a logarithmic measure of the hydronium ion concentration. It indicates how acidic or basic a solution is. The pH scale usually runs from 0 to 14, with 7 being neutral. Acidic solutions have pH values less than 7 while basic solutions have pH values greater than 7.

To calculate pH from the hydronium ion concentration, one must take the negative log (base 10) of the hydronium ion concentration: pH = -log[H3O+]. For example, to find the pH of a 0.50 M solution of nitrous acid, you would first determine the hydronium ion concentration, and then use this formula to find the pH.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a crucial formula used in the calculation of the pH of a buffer solution, which is a mixture of a weak acid and its conjugate base. The equation is given by: pH = pKa + log([A−]/[HA]), where [A−] is the concentration of the conjugate base and [HA] is the concentration of the weak acid. pKa is the negative logarithm of the acid dissociation constant (Ka).

This equation simplifies pH calculations for buffer solutions by relating pH directly to the ratio of the concentrations of the conjugate base and the weak acid, as well as the strength of the weak acid itself.

Hydronium Ion Concentration

The hydronium ion concentration, [H3O+], is a direct measure of the acidity of a solution. For weak acids, it is less straightforward to determine [H3O+] due to the partial dissociation. In these cases, assuming that the change in concentration of H3O+ is equal to the concentration of the acid's conjugate base that is formed, an equilibrium calculation is used. One sets up an expression based on the acid dissociation constant (Ka), which leads to a quadratic equation that can be solved to find the hydronium ion concentration. Once [H3O+] is known, it can be used to calculate the pH of the solution.

Equilibrium Expression

The equilibrium expression is derived from the law of chemical equilibrium. It represents the ratio of the concentrations of the products of a reaction to the concentrations of the reactants, each raised to the power of their respective coefficients in the balanced chemical equation.

For the dissociation of a weak acid HA in water, the equilibrium expression is written as: Ka = [H+][A−]/[HA]. Here, Ka is the acid dissociation constant. Stronger acids have higher Ka values. In working out problems involving weak acids, the assumption is often made that the concentration of H+ or H3O+ is equal to the concentration of A−, leading to the expression Ka = [H+]^2/[HA]. This is valid when the acid dissociates slightly, making the change in the concentration of the undissociated acid negligible.