Problem 157 - General Chemistry

Question

Weak base \(\mathrm{B}\) has a \(\mathrm{p} K_{b}\) of 6.78 and weak acid \(\mathrm{HA}\) has a p \(K_{a}\) of 5.12 . a. Which is the stronger base, \(\mathrm{B}\) or \(\mathrm{A}^{-} ?\) b. Which is the stronger acid, HA or \(\mathrm{BH}^{+} ?\) c. Consider the following reaction: \(\mathrm{B}(a q)+\mathrm{HA}(a q) \rightleftharpoons \mathrm{BH}^{+}(a q)+\mathrm{A}^{-}(a q)\) Based on the information about the acid/base strengths for the species in this reaction, is this reaction favored to proceed more to the right or more to the left? Why? d. An aqueous solution is made in which the concentration of weak base \(\mathrm{B}\) is one half the concentration of its acidic salt, \(\mathrm{BHCl}\), where \(\mathrm{BH}^{+}\) is the conjugate weak acid of B. Calculate the \(\mathrm{pH}\) of the solution. e. An aqueous solution is made in which the concentration of weak acid HA is twice the concentration of the sodium salt of the weak acid, NaA. Calculate the \(\mathrm{pH}\) of the solution. f. Assume the conjugate pairs \(\mathrm{B} / \mathrm{BH}^{+}\) and \(\mathrm{HA} / \mathrm{A}^{-}\) are capable of being used as color-based end point indicators in acid-base titrations, where \(\mathrm{B}\) is the base form indicator and \(\mathrm{BH}^{+}\) is the acid form indicator, and HA is the acid form indicator and \(\mathrm{A}^{-}\) is the base form indicator. Select the indicator pair that would be best to use in each of the following titrations: (1) Titration of a strong acid with a strong base. (i) \(\mathrm{B} / \mathrm{B} \mathrm{H}^{+}\) (ii) \(\mathrm{HA} / \mathrm{A}^{-}\) (2) Titration of a weak base with a strong acid. (i) \(\mathrm{B} / \mathrm{B} \mathrm{H}^{+}\) (ii) \(\mathrm{HA} / \mathrm{A}^{-}\)

Step-by-Step Solution

Answer

a. B is stronger. b. HA is stronger. c. Reaction favors right. d. pH = 6.92. e. pH = 4.82. f. Use HA/A- for weak base-strong acid titration.

Step 1: Determine Stronger Base

To determine which is the stronger base, compare the given p\(K_b\) and p\(K_a\) values. Since p\(K_a\) + p\(K_b\) = 14 for a conjugate pair, calculate p\(K_b\) for \(A^-\) which is derived from the given p\(K_a\) of \(HA\). If p\(K_b\) is smaller, the base is stronger. Here, \( pK_b(A^-) = 14 - 5.12 = 8.88 \). Since \( pK_b(B) = 6.78 \), \( B \) is the stronger base since \( B \)'s p\(K_b\) is smaller.

Step 2: Determine Stronger Acid

Compare \(HA\) with \(BH^+\). \(HA\) is given with a p\(K_a\) of 5.12. The p\(K_b\) of \(B\) is 6.78, which gives \( pK_a(BH^+) = 14 - 6.78 = 7.22 \). Since \(HA's\) p\(K_a\) is smaller, \(HA\) is the stronger acid.

Step 3: Reaction Direction Analysis

Species on the left (\(B\) and \(HA\)) are stronger; \(B\) is a stronger base than \(A^-\), and \(HA\) is a stronger acid than \(BH^+\). The equilibrium favors the formation of the weaker acids and bases (on the right side), thus the equilibrium lies to the right.

Step 4: Calculate pH of Solution with B and BHCl

Using the Henderson-Hasselbalch equation for a buffer: \(pH = pK_a + \log(\frac{[Base]}{[Acid]})\). Since \([B] = \frac{1}{2}[BH^+]\), \(pH = 14 - pK_b - \log(2) = 14 - 6.78 - 0.301 = 6.92\).

Step 5: Calculate pH of Solution with HA and NaA

Using the Henderson-Hasselbalch equation for a weak acid solution: \(pH = pK_a + \log(\frac{[A^-]}{[HA]})\). Given \([HA] = 2[NaA]\), \(pH = 5.12 + \log(\frac{1}{2}) = 5.12 - 0.301 = 4.82\).

Step 6: Select Indicators for Titrations

1. For a strong acid-strong base titration, use a neutral pH range indicator: suitable pairs are not provided in the options for this specific range. 2. For a weak base-strong acid titration, the pH at equivalence is acidic; use the \(HA/A^-\) indicator due to its transition in an acidic range.

Key Concepts

pKa and pKb values

Understanding the concept of pKa and pKb values is crucial for analyzing the strength of acids and bases in chemical reactions. These values allow us to compare which acid or base is stronger and predict the direction of equilibrium. The pKa value measures the strength of an acid; the lower the pKa, the stronger the acid. Meanwhile, the pKb value measures the strength of a base; the lower the pKb, the stronger the base. The relationship between these values can be represented by the equation: \[ pK_a + pK_b = 14 \] This equation shows that for a conjugate acid-base pair, the sum of the pKa and pKb values equals 14, which is a crucial point during calculations.

Buffer Solution pH Calculation

Calculating the pH of a buffer solution involves understanding how a buffer system works. A buffer solution contains a weak acid and its conjugate base, or a weak base and its conjugate acid, which resist changes in pH when small amounts of acids or bases are added. The Henderson-Hasselbalch equation simplifies these calculations by providing an easy way to determine the pH of such solutions. For a buffer made from a weak acid (HA) and its salt (A⁻), the equation is:\[ pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right) \] When solving problems, substitute the given concentrations of the acid and conjugate base into this formula to find the pH of the solution. This calculation assumes that the concentrations of acid and base do not deviate significantly from the initial values provided.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch Equation serves as a key tool in calculating the pH of a buffer solution. This equation relates the pH of a solution, the pKa of the weak acid or base, and the ratio of the concentrations of dissociated and undissociated species. This equation is beneficial because it allows us to estimate the pH of a buffer system without needing to calculate the full chemical equilibrium. Mathematically, the equation is represented as:\[ pH = pK_a + \log\left(\frac{[Base]}{[Acid]}\right) \] This form is particularly useful for determining how the pH changes when the relative concentrations of acid and base change, offering a practical approach to buffer system analysis.

Chemical Equilibrium Analysis

Chemical equilibrium analysis involves determining the position of equilibrium in a reaction, such as whether a reaction favors the formation of products or reactants. Equilibrium is reached when the rate of the forward reaction equals the rate of the reverse reaction, leading to a constant concentration of both reactants and products. In the given exercise, the equilibrium position is influenced by the relative strengths of the acid and base involved. - A stronger acid or base tends to drive the reaction toward the side of the weaker species. - The relative pKa and pKb values provide insight into which species are stronger. By comparing these values, one can determine which direction the reaction is favored, thereby predicting the equilibrium state.

Acid-Base Titration Indicators

Acid-base titration indicators are crucial in determining the endpoint of a titration. These indicators change color at a particular pH, allowing us to visually recognize when the titration is complete. Choosing the correct indicator depends on the type of titration being conducted: - For a strong acid-strong base titration, use an indicator that changes around pH 7, reflecting the sharp pH change at the equivalence point. - For a weak acid-strong base or weak base-strong acid titration, opt for indicators that transition at the pH range of the solution at the equivalence point, which usually skews more towards the acidic or basic side depending on the weakness of the acid or base. By selecting an appropriate indicator, the equivalence point can be accurately determined, ensuring precise measurements and successful titration outcomes.