Question

In a buffer solution consisting of a weak acid and its salt, the ratio of concentration of salt to acid is increased 10 fold, then the \(\mathrm{pH}\) of the solution will (1) increase by one (2) increase by 10 fold (3) decrease by one (4) decrease by 10 fold

Short answer

The \( \text{pH} \) of the solution will increase by one unit.

Step-by-step solution

Understand the problem

We need to determine how the \(\text{pH} \) of a buffer solution changes when the ratio of salt to acid concentrations is increased 10 fold.

Use the Henderson-Hasselbalch equation

The \(\text{pH} \) of a buffer solution is given by the Henderson-Hasselbalch equation: \(\text{pH} = \text{pK}_a + \text{log} \left( \frac{[\text{salt}]}{[\text{acid}]} \right)\)

Identify the change in the ratio of salt to acid

According to the problem, the ratio of \[ \text{salt} \] to \[ \text{acid} \] is increased 10 fold. Initially, the ratio is \[ \frac{[\text{salt}_1]}{[\text{acid}_1]} \] but now becomes \[ \frac{[\text{salt}_2]}{[\text{acid}_2]} = 10 \times \frac{[\text{salt}_1]}{[\text{acid}_1]} \]

Apply the new ratio to the Henderson-Hasselbalch equation

Updating the Henderson-Hasselbalch equation with the new ratio: \(\text{pH}_{new} = \text{pK}_a + \text{log} \left( 10 \times \frac{[\text{salt}_1]}{[\text{acid}_1]} \right)\)

Simplify the equation

Simplify the log term: \(\text{pH}_{new} = \text{pH}_{initial} + \text{log}(10) = \text{pH}_{initial} + 1\)

Identify the correct answer

The \(\text{pH} \) of the solution will increase by 1 unit when the ratio of salt to acid is increased by 10 fold. So, the correct answer is option (1).

Key concepts

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a crucial formula in understanding buffer solutions. It relates the pH of a buffer solution to the pKa (acid dissociation constant) of the weak acid and the ratio of the concentrations of the conjugate base (salt) to the weak acid itself. The equation is: \[ \text{pH} = \text{pK}_a + \text{log} \frac{[\text{salt}]}{[\text{acid}]} \] This equation allows us to easily calculate the pH of a buffer solution by knowing the concentrations of the acid and its conjugate base. The pKa value is specific to each weak acid and is a measure of its strength — a lower pKa means a stronger acid. In this exercise, by increasing the ratio of salt to acid by 10 fold, we use the logarithmic property to see how this affects the pH.

Weak Acid and Salt Buffer

Buffer solutions are made from a weak acid and its salt (conjugate base). They are essential in maintaining stable pH levels in various chemical and biological systems. A weak acid only partially dissociates in water, which means it can both donate and accept protons (H+ ions). For instance, acetic acid (CH3COOH) and its salt, sodium acetate (CH3COONa), form a common buffer. In the solution, the weak acid and salt establish an equilibrium. When small amounts of strong acid or base are added to the solution, the buffer neutralizes them, keeping the pH relatively constant. This property is crucial for processes that require a stable pH, such as enzyme reactions in biological systems.

Ratio of Salt to Acid

The ratio of the concentration of salt to acid in a buffer solution is significant because it directly affects the solution's pH. According to the Henderson-Hasselbalch equation, changing this ratio will alter the pH. In this exercise, we saw that increasing the ratio of salt to acid by 10 fold causes the pH to increase by one unit. Here’s why: the logarithmic function in the equation is sensitive to changes in the ratio. When the ratio is scaled by a factor of 10, the log term increases by 1 (since \( \text{log}(10) = 1 \)). Therefore, any tenfold increase in the salt/acid ratio results in a pH increase of 1. This concept highlights the importance of careful balance in buffer systems to achieve desired pH levels.