Problem 24 - Chemistry: The Central Science

Question

A buffer is prepared by adding \(7.00 \mathrm{~g}\) of ammonia \(\left(\mathrm{NH}_{3}\right)\) and \(20.0 \mathrm{~g}\) of ammonium chloride \(\left(\mathrm{NH}_{4} \mathrm{Cl}\right)\) to enough water to form \(2.50 \mathrm{~L}\) of solution. (a) What is the \(\mathrm{pH}\) of this buffer? (b) Write the complete ionic equation for the reaction that occurs when a few drops of nitric acid are added to the buffer. (c) Write the complete ionic equation for the reaction that occurs when a few drops of potassium hydroxide solution are added to the buffer.

Step-by-Step Solution

Answer

The pH of the buffer solution is approximately 9.34. The complete ionic equation for the reaction with nitric acid is: \( NH_3 (aq) + H^+(aq) + NO_3^-(aq) \rightarrow NH_4^+(aq) + NO_3^-(aq) \). The complete ionic equation for the reaction with potassium hydroxide is: \( NH_4^+(aq) + K^+(aq) + OH^-(aq) \rightarrow NH_3(aq) + K^+(aq) + H_2O(l) \).

Step 1: Calculate the moles and concentrations of NH3 and NH4+ in the buffer solution

We know the mass and volume of the chemicals added to the solution so we can calculate their respective moles: For NH3, Moles of NH3 = (Mass of NH3) / (Molar mass of NH3) Moles of NH3 = \( \frac{7.00 \thinspace g}{17.03 \thinspace g/mol} = 0.411 \thinspace moles \) For NH4Cl, Moles of NH4Cl = (Mass of NH4Cl) / (Molar mass of NH4Cl) Moles of NH4Cl = \( \frac{20.0 \thinspace g}{53.50 \thinspace g/mol} = 0.374 \thinspace moles \) Now we can calculate the concentrations: Concentration of NH3 = Moles of NH3 / Volume of solution Concentration of NH3 = \( \frac{0.411 \thinspace moles}{2.50 \thinspace L} = 0.164 \thinspace M \) Concentration of NH4+ = Moles of NH4Cl / Volume of solution Concentration of NH4+ = \( \frac{0.374 \thinspace moles}{2.50 \thinspace L} = 0.150 \thinspace M \)

Step 2: Calculate pH using the Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation can be used to find the pH of the buffer. First, we need to know the pKa value of the NH3/NH4+ system. It can be found using the Ka value of NH3: \( Ka = 5.56 \times 10^{-10} \) pKa = -log(Ka) = 9.25 Now we can plug the values into the Henderson-Hasselbalch equation: pH = pKa + log (\( \frac{[A-]}{[HA]} \)) pH = 9.25 + log (\( \frac{0.164}{0.150} \)) pH ≈ 9.34 Therefore, the pH of the buffer solution is approximately 9.34.

Step 3: Write the complete ionic equation for the reaction with nitric acid

When nitric acid (HNO3) is added to the buffer, it donates a proton (H+) to the NH3 molecule in the buffer, forming NH4+ and NO3- ions. \( NH_3 + HNO_3 \rightarrow NH_4^+ + NO_3^- \) Thus, the complete ionic equation for the reaction with nitric acid is as follows: \( NH_3 (aq) + H^+(aq) + NO_3^-(aq) \rightarrow NH_4^+(aq) + NO_3^-(aq) \)

Step 4: Write the complete ionic equation for the reaction with potassium hydroxide

When potassium hydroxide (KOH) is added to the buffer, it donates a hydroxide ion (OH-) to the NH4+ in the buffer, forming NH3 and water (H2O) \( NH_4^+ + KOH \rightarrow NH_3 + K^+ + H_2O \) Thus, the complete ionic equation for the reaction with potassium hydroxide is as follows: \( NH_4^+(aq) + K^+(aq) + OH^-(aq) \rightarrow NH_3(aq) + K^+(aq) + H_2O(l) \)

Key Concepts

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a formula used to estimate the pH of a buffer solution. This equation links the pH of a solution to the concentration of an acid and its conjugate base. It's especially handy when dealing with weak acids and bases like ammonia (NH_3) and ammonium chloride (NH_4 ext{Cl})

• The equation is structured as: \[\text{pH} = \text{pKa} + \log \left(\frac{[\text{A}^-]}{[\text{HA}]\right)\]
• Here, \([\text{A}^-]\) stands for the conjugate base concentration and \([\text{HA}]\) is the acid concentration.
• By understanding the pKa (which is the negative log of the Ka) of the system, we can plug values in to calculate the buffer's pH.

This equation simplifies understanding of how the pH of buffer solutions remains relatively stable, even when small amounts of acid or base are added.

pH Calculation

Calculating the pH of a buffer solution involves using the values obtained from moles and concentrations of the components involved. This solution had 0.411 moles of ammonia and 0.374 moles of ammonium chloride. First, the concentration values are computed as follows:

• Concentration of NH_3: \( \text{Concentration} = \frac{0.411\,\text{moles}}{2.50\,\text{L}} = 0.164\,M\)
• Concentration of NH_4^+: \( \text{Concentration} = \frac{0.374\,\text{moles}}{2.50\,\text{L}} = 0.150\,M\)

The next step is to use the Henderson-Hasselbalch equation. Given a Ka of 5.56 \times 10^{-10}, the calculated pKa comes out to 9.25. The pH calculation thus results in:\[pH = 9.25 + \log \left(\frac{0.164}{0.150}\right) \approx 9.34\]Therefore, the buffer solution's pH is approximately 9.34.

Ionic Equations

Ionic equations represent reactions in an informative manner, especially useful in describing buffer reactions. They break down the compounds involved into ions, depicting what actually occurs in a solution when a reaction takes place. This focus is essential when predicting outcomes of reactions in chemical solutions like buffers.

• When nitric acid (HNO_3) is added to our buffer, it reacts with ammonia (NH_3). The complete ionic equation for this reaction is:\[NH_3 (aq) + H^+(aq) + NO_3^-(aq) \rightarrow NH_4^+(aq) + NO_3^-(aq)\]
• Similarly, if potassium hydroxide (KOH) is added to the buffer, the reaction targets ammonium ions (NH_4^+), forming water and ammonia. This reaction is shown as:\[NH_4^+(aq) + OH^-(aq) \rightarrow NH_3(aq) + H_2O(l)\]

These equations ensure we visualize the transformations more clearly, aiding in understanding the buffer system's effectiveness.

Ammonia Buffer

Ammonia buffers are ideal examples of basic buffer solutions. They comprise ammonia ( NH_3 ), a weak base, and its conjugate acid, ammonium ion ( NH_4^+ ). These buffers tend to resist changes in pH when small amounts of acid or base are added due to the equilibrium established within the solution.

• Ammonia acts as the base part of the buffer, accepting protons to form NH_4^+ .
• NH_4^+ acts as the conjugate acid, releasing a proton to revert to NH_3 when bases are added.

Such buffers are crucial in many chemical and biological systems where maintaining a stable pH is essential. By adding ammonia and ammonium chloride, we create a solution that stabilizes around a pH of 9.34, as seen in the calculation.

Acid-Base Reactions

Acid-base reactions in buffer systems depict how buffers counteract changes in pH despite additions of acidic or basic solutions. A critical aspect of buffer solutions lies in their ability to adjust and neutralize such changes through reaction intermediates.

• Adding an acid like nitric acid slowly increases H^+ in the buffer, which is neutralized by NH_3 , creating more NH_4^+ .
• Conversely, adding a base like potassium hydroxide introduces OH^- , which reacts with NH_4^+ to produce more NH_3 and water, mitigating the base effect.

This process is central to understanding how buffers maintain their function, promoting pH stability through specific ionic reactions.