Question

Define buffering capacity. How do the following buffers differ in buffering capacity? How do they differ in pH? Buffer a: \(0.01 \mathrm{M} \mathrm{Na}_{2} \mathrm{HPO}_{4}\) and \(0.01 \mathrm{MNaH}_{2} \mathrm{PO}_{4}\) Buffer b: \(0.10 \mathrm{M} \mathrm{Na}_{2} \mathrm{HPO}_{4}\) and \(0.10 \mathrm{MNaH}_{2} \mathrm{PO}_{4}\) Buffer \(c: 1.0 M \mathrm{Na}_{2} \mathrm{HPO}_{4}\) and \(1.0 \mathrm{MNaH}_{2} \mathrm{PO}_{4}\)

Short answer

Higher molarity buffers have higher buffering capacities. All buffers have the same pH since their molar ratios are identical.

Step-by-step solution

Define Buffering Capacity

Buffering capacity is a measure of the ability of a buffer solution to resist changes in pH when an acid or base is added. A higher buffering capacity indicates that the buffer can neutralize more added acid or base without significantly changing its pH.

Distinguish Buffering Capacities

To compare the buffering capacities of Buffers a, b, and c, examine their molar concentrations:Buffer a: 0.01 M NaH2PO4 and 0.01 M Na2HPO4Buffer b: 0.10 M NaH2PO4 and 0.10 M Na2HPO4Buffer c: 1.0 M NaH2PO4 and 1.0 M Na2HPO4The buffering capacity increases with the concentration of the buffer components. Therefore, Buffer c has the highest buffering capacity, followed by Buffer b and then Buffer a.

Compare pH Values

The pH of a buffer solution is determined by the ratio of the concentration of the weak acid (NaH2PO4) to its conjugate base (Na2HPO4). Since all buffers (a, b, c) have the same 1:1 molar ratio of NaH2PO4 to Na2HPO4, they will have the same pH, regardless of their concentrations.

Key concepts

Buffer Solution

A buffer solution is a special type of solution that helps maintain a stable pH when small amounts of acids or bases are added to it. This is possible because a buffer usually contains a weak acid and its conjugate base or a weak base and its conjugate acid. They work together to neutralize any added acid or base, keeping the pH relatively constant.

Acid-Base Equilibrium

The concept of acid-base equilibrium involves the balance that occurs between acids and bases in a solution. When an acid (such as NaH2PO4) dissociates in water, it releases hydrogen ions (H+), while a base (such as Na2HPO4) can accept these hydrogen ions. The equilibrium is maintained by the constant interplay between these acidic and basic species. In a buffer solution, this equilibrium ensures that the concentration of hydrogen ions remains relatively stable, hence maintaining a consistent pH. This equilibrium is described by the Henderson-Hasselbalch equation, which relates the pH of the buffer to the concentration of the acid and its conjugate base.

pH

The pH of a solution is a measure of its hydrogen ion concentration. It quantifies how acidic or basic a solution is on a scale from 0 to 14. pH = -log[H+]. In the case of our buffer solutions, the pH is influenced by the ratio of the weak acid (NaH2PO4) to its conjugate base (Na2HPO4). Because all of the buffer solutions in the exercise have the same 1:1 ratio, their pH remains the same regardless of the overall concentration of the buffering components. This demonstrates that while buffering capacity might differ, the pH itself can remain unchanged due to the consistent ratio.

Molar Concentration

Molar concentration, also known as molarity, is a way of expressing how much of a substance (solute) is present in a given volume of solution. It is expressed in moles per liter (M). In the exercise, three different buffers are compared: Buffer a (0.01 M), Buffer b (0.10 M), and Buffer c (1.0 M). All three have equal amounts of NaH2PO4 and Na2HPO4, but their differing molarities indicate varying buffering capacities. Higher molarity means more molecules are available to neutralize added acids or bases, thus a higher buffering capacity.