Indicate whether each of the following statements is true or false. If the statement is false, restate it to make it true. (a) The formate ion (CHO \(\left._{2}^{-}\right)\) concentration in \(0.10 \mathrm{M} \mathrm{HCHO}_{2}\) is the same as in \(0.10 \mathrm{M} \mathrm{NaCHO}_{2}\). (b) A buffer can be destroyed by adding too much strong acid. (c) A buffer can be made up by any combination of weak acid and weak base. (d) Because \(K_{\mathrm{a}}\) for \(\mathrm{HCO}_{3}^{-}\) is \(4.7 \times 10^{-11}, K_{\mathrm{b}}\) for \(\mathrm{HCO}_{3}^{-}\) is \(2.1 \times 10^{-4}\).

Understanding formate ion concentration is crucial in the context of buffer solutions and acid-base chemistry. The formate ion, denoted as CHO₂⁻, is derived from formic acid (HCHO₂). In a water solution, the acid partially ionizes to produce formate ions and hydrogen ions. When sodium formate (NaCHO₂) is introduced in water, it completely dissociates, releasing formate ions and sodium ions into the solution.

In a scenario with equal molarity, the concentration of formate ions sourced from sodium formate will be higher than that from formic acid because the latter does not fully dissociate. While sodium formate is a salt and dissolves to produce its constituent ions completely, formic acid being a weak acid only partially ionizes. Therefore, the solution of 0.10 M NaCHO₂ will have a higher concentration of formate ions compared to the solution of 0.10 M HCHO₂. This understanding is vital when preparing buffer solutions or performing titration experiments where ion concentration plays a significant role.

Buffer capacity refers to the amount of acid or base a buffer solution can absorb without a significant change in pH. It is primarily determined by the concentration of the acid-base conjugate pair that constitutes the buffer.

A buffer functions by utilizing the weak acid to neutralize added bases and the conjugate base to neutralize added acids. However, if an excessive amount of a strong acid or base is introduced, the buffer's weak acid or base becomes depleted, and the solution can no longer maintain its pH. This is known as 'buffer breakdown.' The truth that adding too much strong acid can destroy a buffer reveals the finite buffer capacity and underscores the importance of concentration ratios and total molarity when designing buffers for various applications, such as biochemical assays or industrial processes.

Acid-base conjugate pairs are a foundational concept in buffer chemistry. They consist of a weak acid and its corresponding conjugate base or a weak base and its conjugate acid. These pairs are related by the loss or gain of a proton (H⁺).

In a functional buffer solution, the conjugate pairs work synergistically to neutralize small amounts of added acids or bases, thereby stabilizing the pH of the solution. It's important to note that not any combination of weak acid and weak base will form a buffer. Only when the substances are conjugate pairs will they be effective in buffering, because their presence in significant and comparable amounts ensures the necessary equilibrium for pH stability. This highlights why effective buffer systems rely on correct pairings, such as acetic acid with its conjugate base, acetate, or ammonia with its conjugate acid, ammonium.

The relationship between the acid dissociation constant (Ka) and the base dissociation constant (Kb) is fundamental in understanding acid-base equilibrium. Ka and Kb are indicators of the strength of an acid and a base, respectively. For a given acid-base conjugate pair, these values are inversely related to each other through the ion product of water (\(K_w\)), which at 25°C is always equal to 1 x 10⁻¹⁴.

The relationship is captured by the formula:
\(K_a \times K_b = K_w\).
Therefore, knowing either the Ka or Kb for a substance allows you to determine the other constant for the conjugate acid or base. This relationship is pivotal when assessing equilibrium in aqueous solutions and in predicting the direction of acid-base reactions. Understanding this interdependence helps in various calculations, including those involved in designing buffer solutions and determining pKa or pKb values, key components in acid-base chemistry.