Problem 21 - Chemistry and Chemical Reactivity

Question

A buffer solution is prepared by adding 0.125 mol of ammonium chloride to \(5.00 \times 10^{2} \mathrm{mL}\) of \(0.500 \mathrm{M}\) solution of ammonia. (a) What is the pH of the buffer? (b) If 0.0100 mol of \(\mathrm{HCl}\) gas is bubbled into \(5.00 \times 10^{2}\) mL of the buffer, what is the new \(\mathrm{pH}\) of the solution?

Step-by-Step Solution

Answer

The initial pH is 9.55 and the pH after adding HCl is 9.50.

Step 1: Determine initial buffer concentrations

The initial concentration of ammonia (\(\text{NH}_3\)) is given by the formula: \[\text{Concentration of NH}_3 = \frac{0.500 \text{ moles/L} \times 0.500 \text{ L}}{0.500 \text{ L}} = 0.500 \text{ M}\]The concentration of ammonium chloride (\(\text{NH}_4\text{Cl}\)) can be calculated using:\[\text{Concentration of NH}_4^+ = \frac{0.125 \text{ mol}}{0.500 \text{ L}} = 0.250 \text{ M}\]We now know the concentrations of the base and the conjugate acid.

Step 2: Calculate buffer pH using Henderson-Hasselbalch Equation

The pH of the buffer can be calculated using the Henderson-Hasselbalch equation:\[\text{pH} = \text{pKa} + \log\left(\frac{[\text{Base}]}{[\text{Acid}]\right)\]For ammonia, the pKa is known to be 9.25. Plugging in the values:\[\text{pH} = 9.25 + \log\left(\frac{0.500}{0.250}\right) = 9.25 + \log(2)\]\[\text{pH} = 9.25 + 0.3010 \approx 9.55\]

Step 3: Account for added HCl

The addition of 0.0100 mol of HCl will react with the ammonia buffer. We can use stoichiometry to adjust the concentrations:\(\text{New } [\text{NH}_3] = 0.500 \text{ M} - \frac{0.0100 \text{ mol}}{0.500 \text{ L}} = 0.480 \text{ M}\)\(\text{New } [\text{NH}_4^+] = 0.250 \text{ M} + \frac{0.0100 \text{ mol}}{0.500 \text{ L}} = 0.270 \text{ M}\)

Step 4: Recalculate pH with new concentrations

Using the updated concentrations in the Henderson-Hasselbalch equation:\[\text{pH} = 9.25 + \log\left(\frac{0.480}{0.270}\right)\]\[\text{pH} = 9.25 + \log(1.778)\]\[\text{pH} = 9.25 + 0.2504 \approx 9.50\]

Key Concepts

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a handy tool in chemistry for calculating the pH of buffer solutions. A buffer solution is a system that can maintain its pH within a narrow range, even when small amounts of acid or base are added. This equation connects the pH of a solution to the pKa, which is the acid dissociation constant, and the concentrations of the acid and its conjugate base. The equation is given by:\[ \text{pH} = \text{pKa} + \log\left(\frac{[\text{Base}]}{[\text{Acid}]}\right) \]This formula is particularly useful because it allows for a straightforward calculation of pH when the concentrations of the components of the buffer are known.

Common uses of the Henderson-Hasselbalch equation:

• Predicting the pH of a buffer solution
• Designing buffer systems with a specific pH
• Determining the effect of adding acids or bases on the pH

Using this equation requires knowing both the pKa value of the acid as well as the concentrations of the acid and the conjugate base in the buffer solution. This is why it is crucial to understand how to calculate and adjust these concentrations in practical scenarios.

Acid-Base Chemistry

Acid-base chemistry is an essential part of studying how substances interact in solutions, particularly in terms of their hydrogen ion concentrations. Acids are substances that can donate protons (H⁺ ions) in aqueous solutions, while bases can accept these protons. This proton transfer plays a fundamental role in the behavior of many chemical reactions. There are a few key concepts within acid-base chemistry to be aware of:

• Strong vs. Weak Acids and Bases: Strong acids/bases completely disassociate in water, while weak ones only partially dissociate. This distinction is important when considering how solutions like buffers work.
• Conjugate Acid-Base Pairs: When an acid donates a proton, what remains is its conjugate base. Similarly, when a base accepts a proton, its conjugate acid is formed.
• The Role of Water: Water can act as both an acid and a base (amphoteric), which is vital in understanding acidity and basicity in solutions.

Understanding these principles allows scientists to manipulate and predict the outcomes of adding various acids and bases to a solution, as we see in the buffer systems. Buffers utilize weak acids and their conjugate bases to stabilize pH effectively.

pH Calculation

Calculating the pH of a solution, particularly buffer solutions, is a central task in analyzing acidity or basicity in a chemical context. The pH scale measures how acidic or basic a solution is, ranging from 0 to 14. In the context of buffer solutions, the calculation involves not just the simple concentration of H⁺ ions, but also the response of the buffer components to any added acids or bases. To calculate the pH of a buffer:

1. Identify the concentrations of the weak acid and its conjugate base within the solution.
2. Use the Henderson-Hasselbalch equation to determine the pH based on these concentrations.
3. Consider any changes to the concentrations due to reactions, such as the addition of strong acids or bases.

For example, when an acid like HCl is added to a buffer, it changes the concentrations of the components, and thus the equation must be updated to reflect this interaction. The resulting pH calculation reflects how the buffer accommodates the added acid by adjusting the balance between the acid and base present. From understanding how to perform these calculations, chemists are able to design buffer systems that maintain a desired pH even in changing conditions, which is vital in many laboratory and industrial processes.