Question

The following bases, and their conjugate acids (as the chlorides), are available in the lab: ammonia, \(\mathrm{NH}_{3} ;\) pyridine, \(\mathrm{C}_{5} \mathrm{H}_{5} \mathrm{~N} ;\) ethylamine, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{2}\). A buffer solution of \(\mathrm{pH} 9\) is to be prepared, and the total concentration of buffering reagents is to be \(0.5\) mole/liter, (a) Choose the best acidbase pair, (b) Give the recipe for preparing one liter of the solution, (c) Calculate the \(\mathrm{pH}\) of the solution after \(0.02 \mathrm{~mole}\) of NaOH has been added per liter.

Short answer

The best acid-base pair is ammonia and its conjugate acid, ammonium chloride (NH3 and NH4Cl). To prepare 1 L of the buffer solution, use 0.2813 moles of NH3 and 0.2187 moles of NH4Cl. After adding 0.02 moles of NaOH, the pH of the solution will be approximately 9.48.

Step-by-step solution

1. Identify the best acid-base pair

Given the list of bases and their conjugates, we want to identify the acid-base pair that will create a buffer solution with pH 9. We can do this by calculating the pKa values of the given acids. The ideal buffer will have a pKa closest to the desired pH. Conjugate acid-base pairs are given in the following format: base (conjugate acid as chloride) 1. Ammonia: \(\mathrm{NH_{3}} \ ( \mathrm{NH_{4}Cl})\) 2. Pyridine: \(\mathrm{C_{5}H_{5}N} \ ( \mathrm{C_{5}H_{5}NHCl})\) 3. Ethylamine: \(\mathrm{CH_{3}CH_{2}NH_{2}} \ (\mathrm{CH_{3}CH_{2}NH_{3}Cl})\) The pKa values are listed below: 1. Ammonia: pKa = 9.25 2. Pyridine: pKa = 5.25 3. Ethylamine: pKa = 10.75 Since we are looking for a buffer with a pH of 9, ammonia is the best choice as its conjugate acid has pKa closest to the desired pH.

2. Determine the recipe for preparing 1 L of the buffer solution

We will use the Henderson-Hasselbalch equation to calculate the ratio of \(\mathrm{NH_{3}}\) (base) and \(\mathrm{NH_{4}Cl}\) (conjugate acid) needed to prepare the buffer solution: \[pH = pKa + \log{\frac{[\mathrm{Base}]}{[\mathrm{Acid}]}}\] Plugging in the values, we get: \(9 = 9.25 + \log{\frac{[\mathrm{NH_{3}}]}{[\mathrm{NH_{4}^{+}]}}\) Now, we need to solve for the ratio: \(-0.25= \log{\frac{[\mathrm{NH_{3}}]}{[\mathrm{NH_{4}^{+}]}}\) \[10^{-0.25} = \frac{[\mathrm{NH_{3}}]}{[\mathrm{NH_{4}^{+}]}\] Let x moles of \(\mathrm{NH_{3}}\) be present and (0.5-x) moles of \(\mathrm{NH_{4}^{+}}\) (\(\mathrm{NH_{4}Cl}\)) to maintain the total concentration of 0.5 moles/L. \[10^{-0.25} = \frac{x}{(0.5-x)}\] Solving for x gives, \[x=0.2813\ \mathrm{moles\ of\ NH_{3}}\] \[(0.5-x)=0.2187\ \mathrm{moles\ of\ NH_{4}^{+}}\] One liter of the pH 9 buffer solution is prepared using 0.2813 moles of \(\mathrm{NH_{3}}\) and 0.2187 moles of \(\mathrm{NH_{4}Cl}\).

3. Calculate the new pH of the solution after adding 0.02 moles of NaOH

Adding 0.02 moles of NaOH will react with the \(\mathrm{NH_{4}^{+}}\) ions as follows: \[\mathrm{NH_{4}^{+} + OH^{-} \rightarrow NH_{3} + H_{2}O}\] Since NaOH reacts with the acid, the number of moles of base (NH3) will increase and the number of moles of acid (NH4+) will decrease. We find the new amounts of acid and base: - Acid: 0.2187 - 0.02 = 0.1987 moles - Base: 0.2813 + 0.02 = 0.3013 moles Now, we use the Henderson-Hasselbalch equation again to find the new pH of the solution: \[pH = pKa + \log{\frac{[\mathrm{Base}]}{[\mathrm{Acid}]}}\] Plugging in the new values: \[pH = 9.25 + \log{\frac{0.3013}{0.1987}}\] Calculating the new pH: \[pH \approx 9.48\] After the addition of 0.02 moles of NaOH, the pH of the solution will be approximately 9.48.

Key concepts

Acid-Base Pair

In chemistry, an acid-base pair is a set of two species that transform into each other by the gain or loss of a proton (H⁺ ion). This concept is fundamental because it describes how acids and bases interact in aqueous solutions. Each pair includes an acid and its conjugate base or a base and its conjugate acid.

For example, when ammonia (\( \mathrm{NH_{3}} \)) acts as a base, it accepts a proton to become its conjugate acid, ammonium ion (\( \mathrm{NH_{4}^{+}} \)). Conversely, if ammonium ion donates a proton, it reverts to ammonia. These reversible reactions are at the heart of buffering solutions, which aim to maintain a stable pH in varying conditions.

In the preparation of buffer solutions, selecting the optimal acid-base pair is crucial. This is because the chosen pair should possess a pKₐ value closest to the desired pH, enhancing the buffer's efficiency in resisting changes in pH.

pH Calculation

Calculating the pH of a solution is essential to understanding its acidity or basicity. pH itself is a measure of the concentration of hydrogen ions (H⁺) in a solution. Lower pH values indicate high H⁺ concentrations—an acidic environment, while higher pH values suggest lower H⁺ concentrations—a basic environment.

The equation \( \text{pH} = -\log_{10} [\text{H}^+ ] \) is used to determine pH from the concentration of hydrogen ions. In buffer solutions, the introduction of acids or bases shifts the concentration of the ions, thereby altering the pH.

When calculating pH, especially in buffer setups, it's important to consider the buffer capacity, meaning how well the solution can counter changes in pH. This involves comparing the amounts of the acid and base components, as changes due to added acids or bases will directly affect these balanced concentrations.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a vital tool for calculating the pH of buffer solutions. It relates pH, pKₐ (the negative log of the acid dissociation constant), and the concentration ratio of the base to its conjugate acid. The equation is expressed as:
\[\text{pH} = \text{pK}_a + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right)\]
This formula is particularly useful because it connects the pH of a solution directly to the ratio of base to acid, rather than their absolute concentrations. This means even if the solution is diluted or concentrated, the inherent buffer capacity remains consistent as long as the ratio is unchanged.

In practice, using the Henderson-Hasselbalch equation allows chemists to calculate the necessary proportions of an acid-base pair needed to achieve a target pH. It's crucial for adjusting buffer solutions to maintain stability in biological and chemical experiments.

Conjugate Acids and Bases

Conjugate acids and bases are integral to understanding how acid-base reactions function in solutions. They are formed when an acid donates a proton to become its conjugate base, or a base accepts a proton to become its conjugate acid.

This concept is pivotal in studying buffer solutions, as it governs the equilibrium between acids and bases. For example, the equilibrium in a buffer might involve ammonia (\( \mathrm{NH_{3}} \)) as a base and ammonium (\( \mathrm{NH_{4}^{+}} \)) as its conjugate acid. This pair can neutralize added acids or bases by shifting equilibrium as needed.

Conjugate pairs play a substantial role in calculating changes in pH, especially when additional acids or bases are introduced into the solution. They act as reservoirs to either absorb excess hydrogen ions or provide them, maintaining the stability of the solution's pH.