Question

Calculate the \(\mathrm{pH}\) of the \(0.20 \mathrm{M} \mathrm{NH}_{3} / 0.20 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) buffer. What is the \(\mathrm{pH}\) of the buffer after the addition of \(10.0 \mathrm{~mL}\) of \(0.10 \mathrm{M} \mathrm{HCl}\) to \(65.0 \mathrm{~mL}\) of the buffer?

Short answer

The initial pH of the \(NH_3 / NH_4Cl\) buffer system is 9.25, after the addition of \(10.0 \, mL\) of \(0.10 \, M\) \(HCl\) the pH of the system decreases due to the reaction. Using the provided calculations the final pH could be calculated.

Step-by-step solution

Calculate Initial pH

Firstly, use the Henderson-Hasselbalch equation to calculate the initial pH of the buffer using the formula \[pH = pKa + log\left( \frac{[NH_3]}{[NH_4^+]}\right)\]. Since the molarities of NH3 and NH4Cl are the same (0.20 M), their ratio is 1, therefore, the log part becomes 0. Using the provided pKa value of 9.25 for NH4+, the pH of the buffer initially is thus 9.25 + 0 = 9.25.

Calculate change in buffer species concentrations

After the addition of HCl, the HCl will react with NH3 and convert it to NH4+. Using the knowledge of stoichiometry and the volume and concentration of the added HCl (10.0 mL of 0.10 M, which will react to form 0.001 moles of NH4+), calculate the new concentrations of NH3 and NH4+. The initial volume of buffer is 65.0 mL. Therefore, when 10.0 mL of HCl is added the total volume of the solution is 75.0 mL and the new concentrations are: \[ [NH_3] = (0.20 * 65 - 0.001) / 75 ] = 0.17 M \] and \[ [NH_4^+] = (0.20 * 65 + 0.001) / 75 = 0.174M \].

Calculate final pH after HCl addition

Finally, substitute the found concentrations back into the Henderson-Hasselbalch equation to find the final pH of the buffer. Applying the equation with the new concentrations: \[ pH = 9.25 + log\left( \frac{0.17}{0.174}\right) \] which will give the new pH value.

Key concepts

Buffer Solution

When it comes to maintaining a stable pH level, buffer solutions play a crucial role. A buffer solution is a special type of solution that resists changes in its pH when small quantities of an acid or a base are added. Essentially, it is like having a protective barrier for your solution against unwanted pH fluctuations. Buffer solutions are typically made by mixing a weak acid with its conjugate base or a weak base with its conjugate acid. For example, the exercise you provided involves a buffer solution made from ammonia ( H_3 ) and ammonium chloride ( H_4Cl ). This combination works because H_3 is a weak base, while H_4^+ is its conjugate acid. To form a buffer, it's important that the concentrations of both the weak acid and its conjugate base (or the weak base and its conjugate acid) are similar. This allows the buffer to effectively neutralize added acids or bases. The beauty of this system is that it keeps the environment remarkably stable, which is why buffers are so vital in biological systems and various chemical applications.

Buffer solutions find their importance in the world of chemistry and biochemistry for a number of reasons:

• Maintaining blood pH: Our blood contains buffer systems to keep pH within a narrow range, crucial for health.
• Chemical reactions: Buffers maintain a consistent pH for reactions that are pH sensitive.
• Industrial processes: They help in maintaining the pH of different products and materials during manufacturing.

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a vital tool when dealing with buffer solutions. This equation gives a straightforward way to calculate the pH of a buffer solution. Its formula is written as:\[ pH = pK_a + \log\left( \frac{[\text{Base}]}{[\text{Acid}]} \right) \]In this expression, \( pK_a \) is the negative logarithm of the acid dissociation constant \( K_a \). It reflects how easily the acid donates protons in a solution. The terms \([\text{Base}]\) and \([\text{Acid}]\) refer to the concentrations of the base and acid in the buffer solution.Understanding how to use this equation is essential for solving pH calculation problems involving buffers. In our exercise, both the ammonia and the ammonium ion were present at the same concentration, leading to a straightforward use of this equation. The log term in the formula determines the relative contributions of the base and the acid in the buffer.Some significant points about using this equation:

• When the concentrations of the acid and the base are equal, the \( pH \) of the solution is equal to \( pK_a \).
• This equation is particularly useful for weak acids and bases.
• It helps in predicting the change in pH following the addition of small amounts of strong acids or bases.

This powerful tool is indispensable in both academic studies and practical applications, making acid-base equilibrium analyses simpler and more approachable.

Acid-Base Chemistry

Acid-base chemistry is a fundamental concept in chemistry that revolves around the reactions between acids and bases. Understanding this topic starts with the Bronsted-Lowry theory, which defines acids as proton donors and bases as proton acceptors. From this perspective, the main characters in our buffer system are ammonia (as a base) and ammonium ion (as an acid). In acid-base reactions, the transfer of protons affects the pH of the solution. The pH scale, a concise numerical scale, measures the acidity or basicity of a solution. It ranges from 0 (very acidic) to 14 (very basic), with 7 being neutral. Ammonia, being a weak base, and its conjugate acid ammonium ion, balance each other to maintain a specific pH. Let's explore a few important concepts in acid-base chemistry:

• Dissociation: Acids and bases dissociate in water to release protons or hydroxide ions. Weak acids and bases, however, do not fully dissociate.
• Conjugate Acid-Base Pairs: When a base gains a proton, it forms its conjugate acid, and when an acid loses a proton, it forms its conjugate base.
• pH and pKa: The pH is determined by the concentration of hydrogen ions in solution, while the pKa is a constant that provides insights into the acid's strength. Buffers leverage the pKa to resist pH changes.

This interplay of acids, bases, and their conjugates is critical for maintaining the stability of biological systems and facilitating numerous laboratory reactions. Understanding these principles helps not only with homework problems like the exercise but also in the practical application of controlling pH levels in various fields.