Calculate the pH of a buffer solution made by mixing 174 mL of a 1.68M trimethylamine (CH3)3N solution with 250 mL of a 1.08M trimethylammonia chloride, (CH3)3NHCl solution.
Use the Henderson-Hasselbalch equation.
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To calculate the pH of a buffer solution, we need to determine the concentration of the conjugate acid and the conjugate base in the solution. In this case, the trimethylamine ((CH3)3N) acts as a base, and the trimethylammonium chloride ((CH3)3NHCl) acts as the conjugate acid.
To calculate the concentrations of the conjugate acid and base, we can use the equation:
C1V1 = C2V2
where C1 and V1 are the concentration and volume of the trimethylamine solution, and C2 and V2 are the concentration and volume of the trimethylammonium chloride solution.
Given:
C1 = 1.68 M (concentration of (CH3)3N)
V1 = 174 mL (volume of (CH3)3N solution)
C2 = 1.08 M (concentration of (CH3)3NHCl)
V2 = 250 mL (volume of (CH3)3NHCl solution)
Using the equation above, we can calculate the concentrations of (CH3)3N and (CH3)3NHCl:
(1.68 M) * (174 mL) = (C2) * (V2)
Cross-multiplying and solving for C2, we get:
C2 = [(1.68 M) * (174 mL)] / (250 mL)
≈ 1.164 M
So, the concentration of the (CH3)3NHCl (conjugate acid) is approximately 1.164 M, and the concentration of (CH3)3N (conjugate base) is 1.68 M.
Next, we can calculate the pH of the buffer solution using the Henderson-Hasselbalch equation:
pH = pKa + log[(concentration of conjugate base) / (concentration of conjugate acid)]
The pKa is the logarithmic acid dissociation constant of the conjugate acid (CH3)3NHCl. For trimethylammonium chloride, the pKa is around 9.25.
Using the values obtained, we can now calculate the pH:
pH = 9.25 + log[(1.68 M) / (1.164 M)]
By evaluating the logarithm and performing the division, the pH of the buffer solution will be determined.