Problem 147 - General Chemistry

Question

You have the following solutions at your disposal to prepare a buffer solution with a pH greater than 7.0 : $$ \begin{array}{ll} 50.0 \mathrm{~mL} \text { of } 0.10 \mathrm{M} \mathrm{NH}_{3} & 20.0 \mathrm{~mL} \text { of } 0.10 \mathrm{M} \mathrm{NaCl} \end{array} $$ \(55.0 \mathrm{~mL}\) of \(0.10 \mathrm{M} \mathrm{NaOH}\) $$ 20.0 \mathrm{~mL} \text { of } 0.10 \mathrm{M} \mathrm{HNO}_{3} $$ \(50.0 \mathrm{~mL}\) of \(0.10 \mathrm{M} \mathrm{HCl}\) \(20.0 \mathrm{~mL}\) of \(0.10 \mathrm{M} \mathrm{KOH}\) a. Assuming that you are going to mix the entire quantity of the listed solutions to prepare the buffer, which two solutions would you use? b. Calculate the \(\mathrm{pH}\) of the buffer solution that you prepared in part a.

Step-by-Step Solution

Answer

Mix \( \mathrm{NH}_3 \) and \( \mathrm{HCl} \); the buffer solution's pH will be approximately 9.25.

Step 1: Identify Basic and Acidic Components

To create a buffer solution with a pH greater than 7.0, we need to combine a weak base with a strong acid or a weak acid with a strong base. Here, ammonia \( \mathrm{NH}_3 \) is a weak base, and hydrochloric acid \( \mathrm{HCl} \) and nitric acid \( \mathrm{HNO}_3 \) are strong acids. Other compounds like \( \mathrm{NaOH} \) and \( \mathrm{KOH} \) are strong bases, and \( \mathrm{NaCl} \) will not aid in forming a buffer.

Step 2: Choose Appropriate Solutions for Buffer

Since \( \mathrm{NH}_3 \) is a weak base, pair it with \( \mathrm{HCl} \), a strong acid, to form an ammonium chloride buffer. This combination will allow control over the pH to be slightly above 7, appropriate for an ammonium buffer.

Step 3: Calculate Amount of Each Component

Calculate the moles of \( \mathrm{NH}_3 \) and \( \mathrm{HCl} \):- \[ \text{Moles of } \mathrm{NH}_3 = 0.10 \, \text{M} \times 0.050 \, \text{L} = 0.005 \, \text{moles} \]- \[ \text{Moles of } \mathrm{HCl} = 0.10 \, \text{M} \times 0.050 \, \text{L} = 0.005 \, \text{moles} \]The moles are equal, leading to the formation of \( \mathrm{NH}_4^+ \), without excess \( \mathrm{NH}_3 \) or \( \mathrm{H^+} \).

Step 4: Calculate pH of Buffer Solution

The pH of the buffer solution formed by \( \mathrm{NH}_3 \) and \( \mathrm{HCl} \) can be found using the formula:\[ \text{pH} = \text{pK}_\text{a} + \log \left( \frac{[\mathrm{NH}_4^+]}{[\mathrm{NH}_3]} \right) \]Since after the reaction you have ammonium ions \( \mathrm{NH}_4^+ \) and ammonia left in equilibrium, assume that \( \mathrm{NH}_3 \) partially remains unreacted forming equilibrium:\[ \text{pK}_\text{a of } \mathrm{NH}_4^+ = 9.25 \]- Because \([\mathrm{NH}_3] = [\mathrm{NH}_4^+]\), then:\[ \text{pH} \approx \text{pK}_a = 9.25 \]

Step 5: Finalize the Buffer Solution's pH

Given equal concentrations of \( \mathrm{NH}_3 \) and \( \mathrm{HCl} \), the exact pH is the pKa of the ammonium ion which is approximately 9.25, forming a buffer solution with \( \mathrm{NH}_4^+ \) and \( \mathrm{NH}_3 \).

Key Concepts

pH calculation

Calculating the pH of a buffer solution is crucial to understanding its ability to resist changes in pH when acids or bases are added. For solutions involving ammonia (\( \mathrm{NH}_3 \)), a weak base, paired with hydrochloric acid (\( \mathrm{HCl} \)), a strong acid, we leverage an established formula to determine pH:\[\text{pH} = \text{pK}_{\text{a}} + \log \left( \frac{[\mathrm{NH}_4^+]}{[\mathrm{NH}_3]} \right)\] enables us to find the relative acidity or alkalinity of the buffer. It's important to note that the ratio of ammonium ions (\( \mathrm{NH}_4^+ \)) to ammonia dictates the pH.
Efficient pH calculation ensures that the buffer can maintain stability against outside acidic or basic influences, which is critical in both laboratory and practical chemical applications.

weak acid-strong base buffer

A weak acid-strong base buffer system helps maintain the pH of a solution by neutralizing added acids or bases.When \( \mathrm{NH}_3 \) (ammonia) is combined with a strong acid like \( \mathrm{HCl} \), it forms a buffer system.This pairing takes advantage of the ammonia's ability to react with protons (\( \mathrm{H}^{+} \)) released by acids, reducing their impact on the solution's pH.- \( \mathrm{NH}_3 \) is a weak base, allowing it to partially dissociate. It can react with \( \mathrm{HCl} \) to form \( \mathrm{NH}_4^+ \) (ammonium ions).- This reaction is central to the buffer's function, as it helps to consume excess \( \mathrm{H}^{+} \) ions, stabilizing the pH.The weak base-strong acid nature of this buffer makes it ideal for maintaining a pH slightly greater than 7, suitable for many biological and chemical processes.

ammonium chloride buffer

An ammonium chloride buffer is easily formed by mixing ammonia (\( \mathrm{NH}_3 \)) and hydrochloric acid (\( \mathrm{HCl} \)).This buffer type is especially effective for solutions where a neutral or slightly alkaline pH is desired.When ammonia reacts with \( \mathrm{HCl} \), ammonium chloride (\( \mathrm{NH}_4Cl \)) is produced.
This results in a buffer solution with ammonium ions (\( \mathrm{NH}_4^+ \)) and free ammonia still in solution.

• The immediate product of ammonium chloride helps absorb additional \( \mathrm{H}^+ \) ions, preventing drastic pH changes.
• Ammonium chloride buffers are often used in biochemical applications and industrial settings where pH stability is paramount.

The presence of both ammonia and ammonium ions in the solution allows the system to efficiently handle small additions of strong acids or bases.

buffer capacity

Buffer capacity refers to a buffer's ability to resist pH changes upon the addition of acid or base.It's an essential feature of any buffer system, defined by the concentration ratios in the solution.
An effective buffer must have sufficient concentrations of both its conjugate acid (e.g., \( \mathrm{NH}_4^+ \)) and base (e.g., \( \mathrm{NH}_3 \)).

• High buffer capacity implies the solution can absorb a large amount of added acid or base before significant pH change.
• This capacity is maximized when the pH of the buffer is close to the \( \text{pK}_{\text{a}} \) of the buffer system.

For an ammonium chloride buffer, having equal moles of ammonia and \( \mathrm{HCl} \) means it can effectively resist pH changes within a moderate range of alkaline conditions.