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Chapter 16: Problem 22

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

Short Answer

Expert verified
Question: Calculate the pH of a buffer solution containing 0.100 M methylamine and 0.175 M methylammonium chloride at 25掳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 by step solution

01

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鈦�) is the conjugate acid.
02

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鈦篯 is the concentration of the conjugate acid.
03

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 \(4.4 \times 10^{-4}\).
04

Calculate pKb from Kb

Use the relationship between pKb and Kb to calculate the pKb value for methylamine: $$pK_b = -\log{K_b}$$ $$pK_b = -\log{(4.4 \times 10^{-4})}$$ $$pK_b \approx 3.36$$
05

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掳C is approximately 3.02.

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