Question

Consider \(1.0 \mathrm{L}\) of a solution that is \(0.85 \mathrm{M} \mathrm{HOC}_{6} \mathrm{H}_{5}\) and \(0.80 M \mathrm{NaOC}_{6} \mathrm{H}_{5} .\left(K_{\mathrm{a}} \text { for } \mathrm{HOC}_{6} \mathrm{H}_{5}=1.6 \times 10^{-10} .\right)\) a. Calculate the \(\mathrm{pH}\) of this solution. b. Calculate the \(\mathrm{pH}\) after 0.10 mole of HCl has been added to the original solution. Assume no volume change on addition of HCl. c. Calculate the \(\mathrm{pH}\) after 0.20 mole of \(\mathrm{NaOH}\) has been added to the original buffer solution. Assume no volume change on addition of NaOH.

Short answer

a) The initial pH of the solution is 9.77. b) The pH after the addition of 0.10 moles of HCl is 9.65. c) The pH after the addition of 0.20 moles of NaOH to the initial buffer solution is 10.03.

Step-by-step solution

Identify the initial concentrations of the species in the solution

The initial concentrations are: [HOC6H5] = 0.85 M, [NaOC6H5] = 0.80 M, and Ka = 1.6 x 10^(-10).

Calculate the initial pH of the solution using the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation for a weak acid and its conjugate base is: pH = pKa + log([Conjugate Base] / [Weak Acid]) First, we need to find pKa. We are given Ka = 1.6 x 10^(-10), so pKa = -log(Ka) = 9.80. Now, plug the initial concentrations into the equation: pH = 9.80 + log(0.80 / 0.85) = 9.80 - 0.027 = 9.77. The initial pH of the solution is 9.77.

Calculate the pH after the addition of 0.10 moles of HCl

When HCl is added, it will react with the conjugate base present in the solution, decreasing the [Conjugate Base] and increasing the [Weak Acid]. The new concentrations will be: [NaOC6H5] = 0.80 - 0.10 = 0.70 M [HOC6H5] = 0.85 + 0.10 = 0.95 M Now, use the updated concentrations in the Henderson-Hasselbalch equation: pH = 9.80 + log(0.70 / 0.95) = 9.80 - 0.145 = 9.65. The pH after the addition of 0.10 moles of HCl is 9.65.

Calculate the pH after the addition of 0.20 moles of NaOH to the initial buffer solution

When NaOH is added, it will react with the weak acid present in the solution, decreasing the [Weak Acid] and increasing the [Conjugate Base]. The new concentrations will be: [HOC6H5] = 0.85 - 0.20 = 0.65 M [NaOC6H5] = 0.80 + 0.20 = 1.00 M Now, use the updated concentrations in the Henderson-Hasselbalch equation: pH = 9.80 + log(1.00 / 0.65) = 9.80 + 0.225 = 10.03. The pH after the addition of 0.20 moles of NaOH to the initial buffer solution is 10.03. So, the pHs for the different conditions are: a) initial pH: 9.77 b) after 0.10 moles of HCl added: 9.65 c) after 0.20 moles of NaOH added: 10.03.

Key concepts

Buffer Solutions

Buffer solutions are a mixture of a weak acid and its conjugate base, or a weak base and its conjugate acid, that resists changes in pH upon the addition of small amounts of acid or base. They work by neutralizing added acids (H⁺ ions) or bases (OH^- ions), thus maintaining an equilibrium.

For example, in the given exercise, the buffer is composed of phenol (weak acid, HOC₆H₅) and sodium phenoxide (conjugate base, NaOC₆H₅). When HCl is added, it’s the sodium phenoxide that reacts with the H⁺, preventing a significant change in pH. Conversely, when NaOH is added, phenol reacts with the OH^-, again preventing a drastic change in pH. Buffers are essential in biological systems and chemical processes where maintaining a stable pH is crucial.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation provides a quantitative relationship between the pH of a buffer solution and the concentrations of a weak acid and its conjugate base. It is expressed as:

pH = pKa + log([Conjugate Base] / [Weak Acid])

Here, pKa is the negative logarithm of the acid dissociation constant (Ka), which measures the strength of the weak acid. This equation simplifies the pH calculation for buffer solutions as logarithms of ratios reflect concentration changes. In the exercise, we use this equation to find the pH of the buffer solution before and after the addition of strong acids (HCl) and bases (NaOH). It underscores the concept of buffer capacity, i.e., the ability of a buffer to resist pH changes, which depends on the absolute concentrations of the weak acid and its conjugate base.

Acid-Base Equilibrium

Acid-base equilibrium refers to the state of balance between the concentrations of acids and bases in a solution. It's governed by the principle of Le Châtelier, which dictates that an equilibrium will shift to counteract the effect of a disturbance.

When an acid (proton donor) or base (proton acceptor) is added to a system in equilibrium, the concentrations of the components of the acid-base pair will adjust to minimize the impact on pH. This process is elegantly captured by the acid dissociation constant (Ka) for acids, which signifies the partial dissociation of the acid into its ions in water and helps predict the direction of the reaction.

Understanding acid-base equilibrium is vital for interpreting titration curves and the buffering action in various chemical and biological contexts. The adjustments in concentrations after adding HCl or NaOH, which were calculated in the step-by-step solution, exemplify the dynamic nature of acid-base equilibrium.