A buffer contains \(0.10 \mathrm{~mol}\) of a weak acid and \(0.20 \mathrm{~mol}\) of its conjugate base in \(1.0 \mathrm{~L}\) of solution. Determine whether or not each addition exceeds the capacity of the buffer. a. adding \(0.020 \mathrm{~mol}\) of \(\mathrm{NaOH}\) b. adding \(0.020 \mathrm{~mol}\) of \(\mathrm{HCl}\) c. adding \(0.10 \mathrm{~mol}\) of \(\mathrm{NaOH}\) d. adding \(0.010 \mathrm{~mol}\) of \(\mathrm{HCl}\)

In the realm of buffer chemistry, the interplay between a weak acid (HA) and its conjugate base (A-) is foundational. When a weak acid donates a proton, it becomes its conjugate base, and this duo works in tandem to mitigate substantial pH changes in a buffer solution.

In our buffer example, reactions take place when either a strong acid or base is added. The weak acid reacts with hydroxide ions (OH-) from a strong base like NaOH, forming water (H2O) and increasing the amount of the conjugate base (A-). Conversely, the conjugate base can accept protons (H+) from a strong acid like HCl, converting back to the weak acid (HA).

This back-and-forth reaction between HA and A- maintains the pH level of the solution within a narrow range, which is the primary function of a buffer. Hence, understanding these reactions is crucial in predicting the response of a buffer system to the addition of external substances.

Buffers are designed to absorb the impact of added strong bases, like NaOH, but they have limits. When a strong base is introduced, it reacts with the weak acid component of the buffer, thereby converting it to its conjugate base. This is represented by the equation: \( \text{HA} + \text{OH}^- \rightarrow \text{A}^- + \text{H}_2\text{O} \).

What Determines Buffer Capacity?

The buffer capacity is essentially determined by the molar amounts of the weak acid and its conjugate base present within the solution. If more base is added than the buffer's weak acid can react with, the buffer's capacity is exceeded and its ability to maintain pH decreases significantly. Adding 0.020 mol of NaOH to our example buffer doesn't exceed its capacity, leaving it functional. However, when 0.10 mol is added, the buffer's weak acid is entirely consumed, and its capacity is surpassed, rendering it ineffective to counter additional strong base.

A buffer system also counters the addition of strong acids like HCl. In this case, the conjugate base component of the buffer neutralizes the added acid. The reaction looks like: \( \text{A}^- + \text{H}^+ \rightarrow \text{HA} \).

The ability of a buffer to manage the addition of strong acids also hinges on the ratio and amounts of HA and A- in the solution. Adding 0.020 mol of HCl is within the capability of our example buffer system; it can absorb the acid without exceeding its buffer capacity. The conjugate base is consumed and replenished as necessary to keep the pH stable. On the other hand, if an excessive amount of strong acid were added, just as in the case with a strong base, it would overwhelm the buffer's capacity and compromise its pH-stabilizing function.