Question

Which of the following solutions is a buffer? (a) A solution made by mixing \(50 \mathrm{~mL}\) of \(0.200 \mathrm{M}\) formic acid \((\mathrm{HCOOH})\) and \(250 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{KOH},(\mathbf{b})\) A solution made by mixing \(50 \mathrm{~mL}\) of \(0.200 \mathrm{M}\) formic acid \((\mathrm{HCOOH})\) and \(25 \mathrm{~mL}\) of \(0.200 M\) nitric acid \(\left(\mathrm{HNO}_{3}\right),(\mathbf{c})\) A solution made by mixing \(50 \mathrm{~mL}\) of \(0.200 \mathrm{M}\) potassium formate \((\mathrm{HCOOK})\) and \(25 \mathrm{~mL}\) of \(0.200 \mathrm{MKNO}_{3},(\mathbf{d})\) A solution made by mixing \(50 \mathrm{~mL}\) of \(0.200 M\) formic acid \((\mathrm{HCOOH})\), and \(25 \mathrm{~mL}\) of \(0.200 \mathrm{MKOH}\).

Short answer

The buffer solutions are (c) a solution made by mixing 50 mL of 0.200 M potassium formate (HCOOK) and 25 mL of 0.200 M KNO3, and (d) a solution made by mixing 50 mL of 0.200 M formic acid (HCOOH) and 25 mL of 0.200 M KOH.

Step-by-step solution

Identify the species present in each solution

: For each solution, we will identify the species present and determine whether they are weak acids, weak bases, and their conjugate counterparts. a) HCOOH is a weak acid, and KOH is a strong base. In this solution, the base will neutralize the acid, producing water and its conjugate base, the formate ion (HCOO-). b) HCOOH is a weak acid again, and HNO3 is a strong acid. There is no base in this solution to create a conjugate counterpart. c) HCOOK is a salt that dissociates into the formate anion (HCOO-) and K+. The formate ion is the conjugate base of the weak acid formic acid (HCOOH). KNO3 is a salt of a strong base (KOH) and a strong acid (HNO3) and doesn't affect the pH of the solution. d) HCOOH is a weak acid, and KOH is a strong base, but the amount of each is different from solution (a). Now we will calculate the amount of weak acid and its conjugate base in each solution to determine if any meet the requirements for being a buffer.

Calculate the moles of each species in solution (a)

: Let's find the moles of weak acid and strong base in solution (a). Moles of HCOOH = Volume × Concentration = 50 mL × 0.200 M = 10 mmol Moles of KOH = Volume × Concentration = 250 mL × 0.200 M = 50 mmol Given that KOH is a strong base, it will react completely with formic acid: HCOOH + OH- → H2O + HCOO- 10 mmol of HCOOH will react with 10 mmol of OH- from KOH, forming 10 mmol of HCOO-. The excess 40 mmol of OH- will not form a buffer as the pH will be more alkaline than that required for a buffer.

Calculate the moles of each species in solution (b)

: Let's find the moles of weak acid and strong acid in solution (b): Moles of HCOOH = Volume × Concentration = 50 mL × 0.200 M = 10 mmol Moles of HNO3 = Volume × Concentration = 25 mL × 0.200 M = 5 mmol There is no base in this solution, so it cannot act as a buffer.

Calculate the moles of each species in solution (c)

: Let's find the moles of the salt HCOOK and KNO3 in solution (c): Moles of HCOOK = Volume × Concentration = 50 mL × 0.200 M = 10 mmol Moles of KNO3 = Volume × Concentration = 25 mL × 0.200 M = 5 mmol In solution (c), there are 10 mmol of formate ion (HCOO-), which is the conjugate base of formic acid (HCOOH). As KNO3 is the salt of a strong acid and a strong base and does not affect the pH, we can say that this solution is a buffer.

Calculate the moles of each species in solution (d)

: Let's find the moles of weak acid and strong base in solution (d): Moles of HCOOH = Volume × Concentration = 50 mL × 0.200 M = 10 mmol Moles of KOH = Volume × Concentration = 25 mL × 0.200 M = 5 mmol For this solution, the reaction will proceed as follows: HCOOH + OH- → H2O + HCOO- 5 mmol of HCOOH will react with 5 mmol of OH- from KOH, forming 5 mmol of HCOO-. The remaining 5 mmol of HCOOH will not fully react, making this solution a buffer with both formic acid and its conjugate base formate ion.

Determine which solutions are buffers

: Based on the analysis above, we can conclude that the following solutions are buffers: c) A solution made by mixing 50 mL of 0.200 M potassium formate (HCOOK) and 25 mL of 0.200 M KNO3. d) A solution made by mixing 50 mL of 0.200 M formic acid (HCOOH) and 25 mL of 0.200 M KOH.

Key concepts

Formic Acid

Formic acid, with the chemical formula \( \text{HCOOH} \), is the simplest carboxylic acid. It is naturally found in the venom of ant stings and is used in various industrial applications.
As a member of the weak acids family, formic acid only partially ionizes in a solution, meaning it doesn't fully dissociate into its ions like strong acids do.
This partial ionization is essential in chemical buffers, where a weak acid is paired with its conjugate base to resist changes in pH. When mixed with a base like potassium hydroxide (KOH), formic acid donates a proton to the base, forming water and a formate ion (\( \text{HCOO}^- \)).
This reaction is crucial for establishing buffer solutions, as it provides a mixture of both the weak acid and its conjugate base. Formic acid is integral in forming buffers when combined properly, such as in solutions (c) and (d) from the exercise.

Weak Acids

Weak acids are substances that do not fully dissociate in solution. This means that only a small fraction of the acid molecules release hydrogen ions \( \text{H}^+ \).
This partial ionization is quantitatively described using an equilibrium constant known as the acid dissociation constant \( K_a \). For weak acids like formic acid, \( K_a \) is significantly smaller than for strong acids. In buffer chemistry, weak acids are crucial because they provide a stable pH by releasing or absorbing \( \text{H}^+ \) ions as needed.

• When an excess of \( \text{H}^+ \) ions are added, the weak acid's conjugate base captures them, minimizing the change in pH.
• Conversely, if the pH rises, more of the weak acid will dissociate to release \( \text{H}^+ \), maintaining pH equilibrium.

Understanding weak acids is vital in recognizing how solutions like (d) evolve into buffers by balancing formic acid and its conjugate base.

Conjugate Base Chemistry

In chemistry, the term 'conjugate base' refers to what becomes of an acid once it has donated a proton. For formic acid, \( \text{HCOOH} \), the conjugate base is the formate ion \( \text{HCOO}^- \).
Conjugate bases play a pivotal role in buffer systems. They are responsible for capturing excess \( \text{H}^+ \) ions in the solution, thereby resisting changes in pH.
When an acid loses a proton to become a conjugate base, the system remains in dynamic equilibrium. This means the concentration of the acid and its conjugate base remains constant, given typical buffer amounts. Buffers, such as those produced in exercise solutions (c) and (d), rely on the presence of both the weak acid and its conjugate base.

• By having both components, buffers maintain a consistent pH even when external acids or bases are introduced.
• This equilibrium makes conjugate base chemistry fascinating and crucial, especially for applications requiring stable pH conditions, like biochemical reactions.

Understanding the concept of conjugate bases helps clarify the mechanisms behind buffering solutions and their practical utility.