Question

Which of the following would form a buffer if added to \(250.0 \mathrm{~mL}\) of \(0.150 \mathrm{M} \mathrm{SnF}_{2} ?\) (a) \(0.100 \mathrm{~mol}\) of \(\mathrm{HCl}\) (b) \(0.060 \mathrm{~mol}\) of \(\mathrm{HCl}\) (c) \(0.040 \mathrm{~mol}\) of \(\mathrm{HCl}\) (d) \(0.040 \mathrm{~mol}\) of \(\mathrm{NaOH}\) (e) \(0.040 \mathrm{~mol}\) of \(\mathrm{HF}\)

Short answer

Based on the given information and calculations, the correct option to form a buffer solution is option (d) - adding 0.040 mol NaOH to the 0.150 M SnF2 solution. This maintains the necessary molar ratio range of 0.1 to 10 for a functioning acidic and basic components, resulting in a buffer solution that can maintain its pH when small amounts of acids or bases are added.

Step-by-step solution

Determine the initial number of moles of SnF2

Given that we have \(250.0 \mathrm{~mL}\) of \(0.150 \mathrm{M} \mathrm{SnF_2}\), we can calculate the initial number of moles of \(\mathrm{SnF_2}\) in the solution by multiplying the volume and concentration: \(\text{moles of SnF2} = (250.0 \times 10^{-3}\mathrm{L}) \times 0.150\mathrm{M} = 0.0375\mathrm{mol}\)

Identify the nature of the compounds in the reaction

\(\mathrm{SnF_2}\) is a weak base since it is the salt of a weak acid, \(\mathrm{HF}\). In solution, \(\mathrm{SnF_2}\) will undergo hydrolysis to form \(\mathrm{F^-}\) ions and weakly acidic \(\mathrm{HF}\). The presence of \(\mathrm{F^-}\) ions in the solution would allow the solution to act as a base while the presence of the weak acid, \(\mathrm{HF}\), would allow the solution to act as an acid. Buffer solutions require a weak acid and its conjugate base (or a weak base and its conjugate acid) to be mixed.

Understand the impact of each added component on SnF2

Now, let's see the impact of the following added components: (a) \(\mathrm{HCl}\) - This is a strong acid. If added in adequate amounts, it will consume \(\mathrm{F^-}\) ions, generating more \(\mathrm{HF}\). (b) \(\mathrm{HCl}\) - Same as (a) but in a different amount. (c) \(\mathrm{HCl}\) - Same as (a) and (b) but in a different amount. (d) \(\mathrm{NaOH}\) - This is a strong base. If added in adequate amounts, it will consume \(\mathrm{HF}\) (since it is a weak acid), generating more \(\mathrm{F^-}\) ions. (e) \(\mathrm{HF}\) - This is a weak acid. When added to the mixture, it will increase the acid component of the buffer system without changing the base component.

Determine the required molar ratios for a buffer

A functioning buffer contains a weak acid and its conjugate base (or a weak base and its conjugate acid). To maintain a buffering capacity, the molar ratio of weak acid to conjugate base should be within the range of 0.1 to 10 (i.e., one component of the buffer should not exceed 10 times the other component).

Calculate the molar ratios of each option

We will now calculate the molar ratios for each option and check if they fulfill the buffering capacity requirements. (a) 0.100 mol HCl consumes 0.100 mol F- from the SnF2 solution, converting 0.100 mol SnF2 to 0.100 mol HF. New moles of SnF2 = 0.0375 - 0.100 = -0.0625 (negative moles indicate that it does not form a buffer). (b) 0.060 mol HCl consumes 0.060 mol F- from the SnF2 solution, converting 0.060 mol SnF2 to 0.060 mol HF. New moles of SnF2 = 0.0375 - 0.060 = -0.0225 (negative moles again). (c) 0.040 mol HCl consumes 0.040 mol F- from the SnF2 solution, converting 0.040 mol SnF2 to 0.040 mol HF. New moles of SnF2 = 0.0375 - 0.040 = -0.0025 (still negative). (d) 0.040 mol NaOH consumes 0.040 mol HF and generates 0.040 mol F-. The new molar ratio = 0.0775 / 0.040 = 1.9375, which is within the range of 0.1 to 10, so this option does form a buffer. (e) 0.040 mol HF is a weak acid, so it will enhance the already present weak acid nature of the solution, but it will not form a buffer.

Identify the correct option

Based on the molar ratio calculations and the buffer capacity requirements, the only option that forms a functioning buffer is option (d) - adding 0.040 mol NaOH to the 0.150 M SnF2 solution.

Key concepts

Chemical Equilibrium

Understanding the concept of chemical equilibrium is crucial when studying buffer solutions in chemistry. At the most basic level, chemical equilibrium refers to a state in which the rate of the forward reaction equals the rate of the reverse reaction, resulting in no net change in the concentrations of reactants and products over time.

This balance is not static but dynamic, meaning the reactions are still occurring, but each at a rate that maintains stable concentrations. This is beautifully represented in buffer solutions, where a weak acid and its conjugate base, or vice versa, resist changes in pH by neutralizing added acids or bases. In fact, the equilibrium between these components ensures that the pH of the solution remains relatively constant, even when small amounts of other chemicals are introduced.

For instance, when a strong acid like HCl is added to a buffer solution, it reacts with the conjugate base present in the buffer to form the weak acid and water, barely affecting the pH. The dynamic equilibrium adjusts to absorb the added HCl without a significant change in pH. Thus, chemical equilibrium is an essential concept to grasp for understanding how buffers work and maintain a stable environment in various biological and chemical systems.

Acid-Base Reaction

An acid-base reaction is a chemical reaction that occurs between an acid and a base, which can be a fundamental part of buffer solution chemistry. Typically, these reactions involve the transfer of a proton (H+) from an acid to a base. These reactions are pivotal in the formation of buffer solutions, which rely on the presence of weak acids and bases to perform their function effectively.

In the context of the given exercise, when a strong acid (like HCl) is added to the buffer solution consisting of a base (like \(SnF_2\)), the strong acid reacts with the base, producing a weak acid and altering the composition of the buffer. However, the unique property of a buffer solution is its ability to withstand this change by utilizing its components, which act in an acid-base reaction, to return to a state of equilibrium, therefore stabilizing the pH. This demonstrates the practical utility of acid-base reactions in maintaining environments like biological fluids, where pH needs to be precisely managed.

Conjugate Acid-Base Pairs

Conjugate acid-base pairs are a central concept in buffer solution chemistry. They consist of two species that transform into each other by the gain or loss of a proton (H+). The acid of the pair is the species that donates the proton, while the base is the species that accepts it. In a buffer solution, the conjugate acid-base pair work in tandem to neutralize any added acid or base.

Let's take the buffer components from our exercise for example: \(SnF_2\), a weak base, and its conjugate acid \(HF\). When \(HCl\) is added to a solution containing this pair, it donates a proton to the \(F^-\) from the salt \(SnF_2\), forming more \(HF\). Conversely, when a strong base like \(NaOH\) is added, it reacts with \(HF\) to generate \(F^-\) and water. The existence of both the weak acid (\(HF\)) and its conjugate base (\(F^-\)) in adequate proportions is the key to the buffer's capacity to moderate pH changes and maintain equilibrium. This concept of conjugate acid-base pairs is fundamental in the mechanism of buffer action, enabling buffers to respond to pH changes efficiently and is pivotal in countless biological and chemical systems.