Multiple Choice
Using the Henderson-Hasselbalch equation, what is the pH of a buffer system that contains 0.87 M dimethylamine ((CH3)2NH) and 0.68 M dimethylammonium ion ((CH3)2NH2+)? The Kb of dimethylamine is 5.9 × 10⁻⁴.
18. Aqueous Equilibrium
Henderson-Hasselbalch Equation
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The Kb of C6H5NH2 (aniline) is 3.9 × 10−10. Determine pH of a buffer solution made up of 500 mL of 1.4 M C6H5NH2 and 230 mL of 2.3 M C6H5NH3+.
A
4.81
B
9.62
C
9.29
D
4.71
Verified step by step guidance1
Start by understanding the components of the buffer solution. Aniline (C6H5NH2) is a weak base, and C6H5NH3+ is its conjugate acid. The buffer solution consists of both these components.
Use the Henderson-Hasselbalch equation to find the pH of the buffer solution: \( \text{pH} = \text{pKa} + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right) \). First, calculate the pKa from the given Kb using the relation \( \text{pKa} = 14 - \text{pKb} \).
Calculate the concentration of C6H5NH2 and C6H5NH3+ in the buffer solution. Use the formula \( C = \frac{n}{V} \) where \( n \) is the number of moles and \( V \) is the total volume of the solution. Find the moles of each component using their initial concentrations and volumes, then divide by the total volume (500 mL + 230 mL).
Substitute the concentrations of the base (C6H5NH2) and the acid (C6H5NH3+) into the Henderson-Hasselbalch equation. Ensure the concentrations are in the same units (Molarity, M).
Calculate the logarithmic term \( \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right) \) and add it to the pKa value to find the pH of the buffer solution.
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