Problem 67 - Chemistry: Principles and Reactions

Question

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 \(2.1 \times 10^{-4}\).

Step-by-Step Solution

Answer

If false, restate it to make it true. a) The formate ion (CHO\(_2^-\)) concentration in 0.10 M HCHO\(_2\) is equal to 0.10 M NaCHO\(_2\). Answer: False. Restated Statement: The formate ion (CHO\(_2^-\)) concentration in 0.10 M HCHO\(_2\) is less than in 0.10 M NaCHO\(_2\). b) A buffer can be destroyed by adding a large amount of strong acid. Answer: True. c) A buffer can be made by a combination of any weak acid and any weak base. Answer: False. Restated Statement: A buffer can be made up by a combination of a weak acid and its conjugate base or a weak base and its conjugate acid. d) The ion-product constant for the bicarbonate ion (HCO\(_3^-\)), Kb, is about 2.1 × 10\(^{-4}\). Answer: True.

Step 1: (a) Determine the truthfulness of the statement

The statement is comparing the concentration of formate ions in two different solutions: 0.10 M HCHO\(_2\) and 0.10 M NaCHO\(_2\). In the first solution, the formate ion (CHO\(_2^-\)) can be produced via the ionization of formic acid (HCHO\(_2\)). In the second solution, sodium formate (NaCHO\(_2\)) is a salt, and it will readily dissociate to produce formate ions and sodium ions. Now, in the first solution, not all HCHO\(_2\) is ionized to form CHO\(_2^-\), so the concentration of CHO\(_2^-\) will be less than 0.10 M. However, in the second solution with NaCHO\(_2\), the concentration of CHO\(_2^-\) will be equal to 0.10 M because it dissociated completely. So, the given statement is false.

Step 2: (a) Restate the statement to make it true

The formate ion (CHO\(_2^-\)) concentration in 0.10 M HCHO\(_2\) is less than in 0.10 M NaCHO\(_2\). #b) Statement about Destroying a Buffer#

Step 3: (b) Determine the truthfulness of the statement

A buffer can indeed be destroyed by adding too much strong acid. If large amounts of strong acid are added to a buffer, the buffer's capacity to maintain a narrow pH range can be overwhelmed, causing a significant pH change. The given statement is true. #c) Statement about Making a Buffer#

Step 4: (c) Determine the truthfulness of the statement

A buffer is a solution that resists significant changes in pH when small amounts of acid or base are added. To create a buffer, we need a weak acid and its conjugate base, or a weak base and its conjugate acid. A combination of any weak acid and weak base will not necessarily create a buffer solution since they might not be conjugate acid-base pairs. So, the given statement is false.

Step 5: (c) Restate the statement to make it true

A buffer can be made up by a combination of a weak acid and its conjugate base or a weak base and its conjugate acid. #d) Statement about Ka and Kb values#

Step 6: (d) Determine the truthfulness of the statement

For a given conjugate acid-base pair, \(K_\mathrm{a}\) and \(K_\mathrm{b}\) are related by the following equation: \(K_\mathrm{a} \cdot K_\mathrm{b} = K_\mathrm{w}\) where \(K_\mathrm{w}= 1 \times 10^{-14}\) at 25°C. Since the \(K_\mathrm{a}\) for HCO\(_3^-\) is \(4.7 \times 10^{-11}\), the \(K_\mathrm{b}\) for HCO\(_3^-\) can be calculated as: \(K_\mathrm{b} = \frac{K_\mathrm{w}}{K_\mathrm{a}}\) \(K_\mathrm{b} = \frac{1 \times 10^{-14}}{4.7 \times 10^{-11}} = 2.128 \times 10^{-4}\) The given statement states that \(K_\mathrm{b}\) for HCO\(_3^-\) is \(2.1 \times 10^{-4}\), which is approximately the same as the calculated value of \(2.128 \times 10^{-4}\). So, the given statement is true.

Key Concepts

Formate Ion Concentration

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

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

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.

Relationship Between Ka and Kb

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.