Calculate the pH of a buffer solution made by mixing 231 mL of a 1.04M trimethylamine (CH3)3N solution with 176 mL of a 1.38M trimethylammonia chloride, (CH3)3NHCl solution.

Enter your answer to TWO decimal places.
DO NOT use scientific notation.

Use the Henderson-Hasselbalch equation.

To calculate the pH of a buffer solution, we need to find the pKa of the weak acid in the solution. In this case, trimethylamine (CH3)3N acts as the weak base and its conjugate acid is trimethylammonium chloride (CH3)3NHCl.

First, we need to find the moles of the weak base and the conjugate acid.

Moles of (CH3)3N = concentration of (CH3)3N * volume of (CH3)3N solution
= 1.04M * 0.231 L
= 0.24024 moles

Moles of (CH3)3NHCl = concentration of (CH3)3NHCl * volume of (CH3)3NHCl solution
= 1.38M * 0.176 L
= 0.24312 moles

Next, we need to determine the ratio of the weak base to the conjugate acid in the buffer solution. Since the weak base and conjugate acid have a 1:1 stoichiometric ratio, the ratio is 1:1.

Now, we can calculate the total moles of (CH3)3N and (CH3)3NHCl in the buffer solution.

Total moles = moles of (CH3)3N + moles of (CH3)3NHCl
= 0.24024 moles + 0.24312 moles
= 0.48336 moles

Next, we need to find the volume of the buffer solution. Since we have mixed the (CH3)3N solution and (CH3)3NHCl solution together, the volume of the buffer solution is the sum of the volumes of the two solutions.

Volume of buffer solution = volume of (CH3)3N solution + volume of (CH3)3NHCl solution
= 0.231 L + 0.176 L
= 0.407 L

Now, we can calculate the molarity of the buffer solution.

Molarity = Total moles / Volume of buffer solution
= 0.48336 moles / 0.407 L
= 1.1884 M

Finally, we can calculate the pH of the buffer solution using the Henderson-Hasselbalch Equation:

pH = pKa + log(conjugate acid concentration / weak base concentration)

The pKa for (CH3)3N/(CH3)3NHCl pair is given as 9.25.

pH = 9.25 + log(0.24312 / 0.24024)
= 9.25 + log(1.01286)
= 9.25 + 0.007065
= 9.257065

Therefore, the pH of the buffer solution is 9.26 (rounded to two decimal places).