Question

Calculate the pH after 0.010 mole of gaseous HCl is added to 250.0 $\mathrm{mL}$ of each of the following buffered solutions. $$\begin{array}{l}\text{ a. }0.050M{\mathrm{NH}}_3/0.15{\mathrm{MNH}}_4\mathrm{Cl}\\ \text{ b. }0.50\mathrm{M}{\mathrm{NH}}_3/1.50\mathrm{M}{\mathrm{NH}}_4\mathrm{Cl}\end{array}$$ Do the two original buffered solutions differ in their pH or their capacity? What advantage is there in having a buffer with a greater capacity?

Short answer

The pH values of the two buffered solutions after adding 0.010 moles of HCl are calculated to be 6.47 for solution (a) and 8.00 for solution (b). The two buffers differ in their pH values, with solution (b) having a higher buffer capacity due to the higher concentrations of NH3 and NH4+. A greater buffer capacity is advantageous because it can resist changes in pH more effectively, thus maintaining pH stability when acidic or basic substances are added.

Step-by-step solution

Problem Overview

We are given two buffered solutions and must calculate the new pH of each solution after the addition of 0.010 moles of gaseous HCl. To accomplish this task, we will use the Henderson-Hasselbalch equation and follow these steps: 1. Calculate moles of NH3 and NH4+ in each solution before reaction. 2. Determine the moles of NH3 and NH4Cl after the reaction by accounting for the added HCl. 3. Use the Henderson-Hasselbalch equation to calculate the new pH values for both solutions. 4. Calculate the buffer capacity of each solution and discuss the advantages of having a buffer with a greater capacity. We will now execute these steps separately for the two buffered solutions (a) and (b).

Solution (a) - Calculate moles before reaction

To calculate the moles of NH3 and NH4+ in solution (a), we will use the molarity and volume of the solution. Moles of NH3 = 0.050 moles/L * 0.250 L = 0.0125 moles Moles of NH4+ = 0.15 moles/L * 0.250 L = 0.0375 moles

Solution (a) - Determine moles after reaction

Upon addition of 0.010 moles of HCl, 0.010 moles of NH3 will react to produce 0.010 moles of NH4+. New moles of NH3 = 0.0125 - 0.010 = 0.0025 moles New moles of NH4+ = 0.0375 + 0.010 = 0.0475 moles

Solution (a) - Calculate new pH

Using the Henderson-Hasselbalch equation, calculate the new pH for solution (a): pH = pKa + log ([NH3]/[NH4+]) The pKa of NH4+ is 9.25. pH = 9.25 + log (0.0025/0.0475) = 9.25 - 2.78 = 6.47

Solution (b) - Calculate moles before reaction

To calculate the moles of NH3 and NH4+ in solution (b), we will use the molarity and volume of the solution. Moles of NH3 = 0.50 moles/L * 0.250 L = 0.125 moles Moles of NH4+ = 1.50 moles/L * 0.250 L = 0.375 moles

Solution (b) - Determine moles after reaction

Upon addition of 0.010 moles of HCl, 0.010 moles of NH3 will react to produce 0.010 moles of NH4+. New moles of NH3 = 0.125 - 0.010 = 0.115 moles New moles of NH4+ = 0.375 + 0.010 = 0.385 moles

Solution (b) - Calculate new pH

Using the Henderson-Hasselbalch equation, calculate the new pH for solution (b): pH = pKa + log ([NH3]/[NH4+]) The pKa of NH4+ is 9.25. pH = 9.25 + log (0.115/0.385) = 9.25 - 1.25 = 8.00

Conclusion - Comparing Buffers

The calculated pH for the two buffered solutions after the addition of 0.010 moles of HCl are as follows: Solution (a): pH = 6.47 Solution (b): pH = 8.00 Thus, the two buffers differ in their pH values. The buffer capacity of solution (b) is higher, as it contains more NH3 and NH4+. A buffer with a greater capacity can resist changes in pH more effectively when an acidic or basic substance is added, making it more suitable for maintaining pH stability in various applications.

Key concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a fundamental formula used to calculate the pH of buffer solutions. This equation demonstrates the relation between the concentration of an acid and its conjugate base in a solution.
The formula is expressed as:
$$\text{pH}=\text{pKa}+\log \left(\frac{[{\text{A}}^{-}]}{[\text{HA}]}\right)$$Here, $\text{pKa}$ is the negative logarithm of the acid dissociation constant, $[{\text{A}}^{-}]$ denotes the concentration of the base (or the anion), and $[\text{HA}]$ is the concentration of the acid present in the buffer.
This equation is especially useful for weak acid and base combinations, making it easier to calculate how the pH changes when acids or bases are added to the buffer.
When using the Henderson-Hasselbalch equation, it assumes that only small amounts of base or acid are added, and the temperature remains constant. This approximation holds true in many practical scenarios, showcasing why it is such a staple in chemistry.

Noble gases

Noble gases are a group of chemical elements in group 18 of the periodic table, known for their exceptional stability and lack of reactivity.
These gases include helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and radon (Rn).

• Noble gases have a full outer shell of valence electrons, which makes them largely unreactive and perfectly stable under normal conditions.
• They are colorless, odorless, and have low chemical reactivity, which is why they often do not participate in forming compounds.
• In industrial and scientific applications, their lack of reactivity is advantageous, allowing them to function as inert environments for reactions or processes that require isolation from reactive elements.
• Despite their stability, under extreme conditions, some noble gases do form compounds, such as xenon hexafluoroplatinate.

These characteristics make noble gases distinctive, acting as an example of utmost stability in the periodic table.

pH calculations

Calculating pH involves understanding the balance of hydrogen ions (H+) in a solution. The pH scale ranges from 0 to 14, where:

• A pH of 7 is neutral, meaning a balanced concentration of H+ and OH- ions.
• pH values below 7 indicate an acidic solution, rich in H+ ions.
• pH values above 7 signal a basic (or alkaline) solution, where OH- ions are more prevalent.

To calculate the pH, the concentration of hydrogen ions is crucial. The basic formula used is:
$$\text{pH}=-\log [{\text{H}}^{+}]$$This formula relies on the principle that pH is a measure of the logarithmic abundance of H+ ions. Thus, a higher concentration of H+ results in a lower pH, whereas fewer H+ ions increase the pH value.
In buffer solutions, pH calculations typically involve understanding how the buffer resists changes. Calculations in such cases often employ the Henderson-Hasselbalch equation to adjust for any additional acids or bases introduced to the system, maintaining its equilibrium effectively.

Buffer capacity

Buffer capacity refers to a buffer's ability to resist pH changes upon the addition of an acid or a base.
It essentially measures how well a buffer can maintain its pH despite external influences.

• The buffer capacity is higher when there are larger quantities of the weak acid and its conjugate base present in the solution.
• Ideally, buffers work best when the concentrations of the acid and its base are equal, as this allows for optimal resistance to pH shifts.
• A higher buffer capacity allows a solution to maintain its pH level even when significant amounts of acid or base are added.
• This is crucial in many chemical and biological processes where stable pH conditions are necessary for the proper functioning of enzymes and biochemical reactions.

In practical applications, choosing a buffer with a suitable buffer capacity is essential for achieving precise control over the pH in environments such as laboratories, industrial processes, and even human bodies, where enzyme activity depends heavily on pH stability.