Problem 22 - Chemistry: An Atoms-Focused Approach

Question

What is the pH of a buffer that is \(0.100 M\) methylamine and \(0.175 M\) methylammonium chloride at \(25^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

Question: Calculate the pH of a buffer solution containing 0.100 M methylamine and 0.175 M methylammonium chloride at 25°C using the Henderson-Hasselbalch equation. The Kb value for methylamine is \(4.4 \times 10^{-4}\). Answer: The pH of the buffer solution is approximately 3.02.

Step 1: Write down the general formula for the buffer solution

A buffer solution is a mixture of a weak base (methylamine) and its conjugate acid (methylammonium chloride). The general formula for a buffer solution can be written as: $$CH_3NH_2 + H_2O \longleftrightarrow CH_3NH_3^+ + OH^-$$ where methylamine (CH3NH2) is the weak base, and methylammonium ion (CH3NH3⁺) is the conjugate acid.

Step 2: Define the Henderson-Hasselbalch equation for a basic buffer

For a basic buffer solution, the Henderson-Hasselbalch equation can be written as: $$pH = pK_b + \log{\frac{[B]}{[HB^+]}}$$ where pH is the negative logarithm of the hydrogen ion concentration, pKb is the negative logarithm of the equilibrium constant Kb for methylamine (the weak base), [B] is the concentration of the weak base, and [HB⁺] is the concentration of the conjugate acid.

Step 3: Determine the equilibrium constant (Kb) of methylamine

The given exercise does not provide the equilibrium constant Kb for methylamine. The value can be found in a suitable chemistry reference or textbook. The Kb value for methylamine is known to be \(4.4 \times 10^{-4}\).

Step 4: Calculate pKb from Kb

Use the relationship between pKb and Kb to calculate the pKb value for methylamine: $$pK_b = -\log{K_b}$$ $$pK_b = -\log{(4.4 \times 10^{-4})}$$ $$pK_b \approx 3.36$$

Step 5: Apply the Henderson-Hasselbalch equation to calculate the pH of the buffer solution

Now, we can use the Henderson-Hasselbalch equation and the provided concentrations of methylamine (0.100 M) and methylammonium chloride (0.175 M) to calculate the pH: $$pH = pK_b + \log{\frac{[B]}{[HB^+]}}$$ $$pH = 3.36 + \log{\frac{0.100}{0.175}}$$ $$pH \approx 3.02$$ The pH of the buffer solution containing 0.100 M methylamine and 0.175 M methylammonium chloride at 25°C is approximately 3.02.