Question

When sodium hydroxide, $\mathrm{NaOH}$, is added dropwise to a buffered solution, the component of the buffer consumes the added hydroxide ion.

Short answer

When sodium hydroxide (NaOH) is added to a buffer solution, it contributes hydroxide ions (${\mathrm{OH}}^{-}$) that react with the acidic component of the buffer ($\mathrm{HA}$), as follows: ${\mathrm{OH}}^{-}+\mathrm{HA}\to {\mathrm{H}}_2\mathrm{O}+{\mathrm{A}}^{-}$. This reaction consumes the hydroxide ions, which helps in maintaining the equilibrium in the solution. The buffer capacity, which determines the ability of the buffer to resist changes in pH, depends on the concentrations of the buffer components and the acid dissociation constant ($K_a$).

Step-by-step solution

1. Identify the components of the buffer solution

A buffer solution usually consists of a weak acid and its conjugate base, or a weak base and its conjugate acid. The pH of the solution is maintained by the equilibrium between the acid and base pair in the buffer. Let's represent the weak acid as $\mathrm{HA}$ and its conjugate base as ${\mathrm{A}}^{-}$.

2. Write the equilibrium expression for the buffer components

The equilibrium reaction for the buffer components can be expressed as follows: $$\mathrm{HA}\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{A}}^{-}$$ The equilibrium constant for this reaction, also known as the acid dissociation constant, is given by: $$K_a=\frac{[{\mathrm{H}}^{+}][{\mathrm{A}}^{-}]}{[\mathrm{HA}]}$$

3. Understand the role of sodium hydroxide in the buffer solution

When sodium hydroxide (NaOH) is added to the buffer solution, it donates hydroxide ions (${\mathrm{OH}}^{-}$) to the solution. These hydroxide ions react with the acidic component, $\mathrm{HA}$, of the buffered solution, consuming the OH- ions as follows: $${\mathrm{OH}}^{-}+\mathrm{HA}\to {\mathrm{H}}_2\mathrm{O}+{\mathrm{A}}^{-}$$

4. Explain how the buffer resists changes in pH

The reaction between the hydroxide ions and the acidic component of the buffer consumes the hydroxide ions, which helps in maintaining the equilibrium in the solution. The consumed $\mathrm{HA}$ is replenished by the dissociation of $\mathrm{HA}$ in the reverse direction, and the concentration of ${\mathrm{A}}^{-}$ increases due to the reaction with OH-. Consequently, the concentrations of the buffer components change to accommodate the added hydroxide ions, and the pH remains relatively constant.

5. Determine the buffer capacity

The buffer capacity depends on the concentrations of the buffer components and the value of the acid dissociation constant ($K_a$). The higher the concentrations of the components, the higher the buffer capacity, which means a greater ability to resist changes in pH upon addition of a strong acid or base. The buffer capacity can be estimated using the following formula: $$\beta =\frac{2.303(C_{\mathrm{HA}}+C_{{\mathrm{A}}^{-}})}{1+\frac{K_a}{[{\mathrm{H}}^{+}]}+\frac{[{\mathrm{H}}^{+}]}{K_a}}$$ Where $\beta$ is the buffer capacity, $C_{\mathrm{HA}}$ and $C_{{\mathrm{A}}^{-}}$ are the concentrations of the acidic and basic components respectively, and $K_a$ is the acid dissociation constant.

Key concepts

Acid-Base Equilibrium

In the world of chemistry, acid-base equilibrium refers to the balance of acidic (proton donor) and basic (proton acceptor) species in a solution. A buffer solution comprises either a weak acid and its conjugate base or a weak base and its conjugate acid. This setup helps maintain a balance between acidic and basic components. Let’s use the weak acid as an example, symbolized by $\mathrm{HA}$, which can dissociate into ${\mathrm{H}}^{+}$ ions and ${\mathrm{A}}^{-}$, its conjugate base:

$\mathrm{HA}\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{A}}^{-}$

The above equation represents an equilibrium, where both the forward dissociation of the acid and the reverse protonation of the base occur simultaneously. The state of equilibrium is crucial as it dictates how the buffer behaves upon the addition of external agents, like $\mathrm{NaOH}$ in this discussion.
To quantify the degree of dissociation, we use the acid dissociation constant, $K_a$, which is calculated as:

$$K_a=\frac{[{\mathrm{H}}^{+}][{\mathrm{A}}^{-}]}{[\mathrm{HA}]}$$

This constant helps us understand the strength of the acid and the buffer's ability to maintain equilibrium. The balance of species in buffer solutions allows them to mitigate drastic changes in pH when acids or bases are introduced.

pH Maintenance

Buffer solutions play a crucial role in maintaining a stable pH level within certain limits. When an acid or base is introduced into the solution, a properly prepared buffer will effectively "neutralize" it by converting the additional protons or hydroxides into their buffered form. Here’s how it works:
- Upon adding $\mathrm{NaOH}$ to a buffer, ${\mathrm{OH}}^{-}$ ions are introduced.- These hydroxide ions primarily react with the free protons ${\mathrm{H}}^{+}$ from the weak acid, $\mathrm{HA}$, forming water:

${\mathrm{OH}}^{-}+\mathrm{HA}\to {\mathrm{H}}_2\mathrm{O}+{\mathrm{A}}^{-}$

This reaction prevents a significant increase in pH by absorbing the extra ${\mathrm{OH}}^{-}$ ions through conversion to water.
Meanwhile, the buffer's equilibrium will adjust, replenishing consumed $\mathrm{HA}$ by dissociation and increasing ${\mathrm{A}}^{-}$ concentration. Thanks to this dynamic adjustment, the overall pH of the solution remains more constant than a non-buffered solution would after an addition of a base or acid. In biological systems, such pH maintenance is vital for processes such as enzyme activity, which is sensitive to changes in pH.

Buffer Capacity

Buffer capacity is a measure of a buffer solution's ability to resist pH changes upon the addition of an acid or a base. It is directly related to the concentration of the buffer components and the acid dissociation constant, $K_a$. The more concentrated the buffer components, $\mathrm{HA}$ and ${\mathrm{A}}^{-}$, the more capable the solution is of maintaining its pH.
The buffer capacity $\beta$ can be calculated using the formula:

$$\beta =\frac{2.303(C_{\mathrm{HA}}+C_{{\mathrm{A}}^{-}})}{1+\frac{K_a}{[{\mathrm{H}}^{+}]}+\frac{[{\mathrm{H}}^{+}]}{K_a}}$$

Where:
- $C_{\mathrm{HA}}$ is the concentration of the acidic component.- $C_{{\mathrm{A}}^{-}}$ is the concentration of the basic component.- $K_a$ is the acid dissociation constant.
Higher buffer capacity means the solution can absorb more ${\mathrm{H}}^{+}$ or ${\mathrm{OH}}^{-}$ ions with minimal changes in pH. It’s important in environments where steady pH is required despite potential disturbances, such as in biochemical assays or pharmaceutical formulations. Understanding buffer capacity allows chemists to tailor the solution to specific needs, ensuring effective pH control in diverse chemical and biological contexts.