Calculate the PH OF A SOLUTION prepared by mixing 15.0mL OF 0.50 M OF NaOH AND 30.0mL OF 0.50 M BENZOIC ACID SOLUTION?( Benzoicacid is monoprotic and its dissociation constant is 6.5*10^-5)

Write the equation and set up an ICE chart. This mixture will prepare a buffer. Use the Henderson-Hasselbalch equation to solve for pH.

To calculate the pH of the solution prepared by mixing NaOH and benzoic acid, we need to determine the moles of benzoic acid and NaOH, and then calculate the concentration of each component in the final solution.

First, let's calculate the moles of benzoic acid and NaOH:
Moles of benzoic acid = concentration x volume = 0.50 M x 0.030 L = 0.015 moles
Moles of NaOH = concentration x volume = 0.50 M x 0.015 L = 0.0075 moles

Next, let's determine the concentration of each component in the final solution:
Total volume of the solution = volume of benzoic acid solution + volume of NaOH solution = 0.030 L + 0.015 L = 0.045 L

Concentration of benzoic acid in the final solution = moles/volume = 0.015 moles/0.045 L = 0.333 M
Concentration of NaOH in the final solution = moles/volume = 0.0075 moles/0.045 L = 0.167 M

Now, let's calculate the pH of the solution using the dissociation constant of benzoic acid:

pKa = -log[Ka]
pKa = -log[6.5 x 10^-5]
pKa ≈ 4.19

Since benzoic acid is monoprotic, it will fully dissociate into benzoate ions (C6H5COO-) and a hydrogen ion (H+) in water. Therefore, the concentration of H+ ions will be equal to the concentration of benzoic acid, which is 0.333 M.

pH = -log[H+]
pH = -log[0.333]
pH ≈ 0.477

Therefore, the pH of the solution prepared by mixing 15.0 mL of 0.50 M NaOH and 30.0 mL of 0.50 M benzoic acid solution is approximately 0.477.

To calculate the pH of the solution, we need to determine the concentration of the hydronium ion (H3O+) or its negative logarithm, the pH.

Here's how you can calculate it step-by-step:

Step 1: Determine the number of moles of NaOH and benzoic acid used in the solution.

First, calculate the number of moles of NaOH:
Moles of NaOH = Concentration of NaOH (in M) × Volume of NaOH (in L)
Moles of NaOH = 0.50 M × 0.015 L = 0.0075 moles

Next, calculate the number of moles of benzoic acid:
Moles of benzoic acid = Concentration of benzoic acid (in M) × Volume of benzoic acid (in L)
Moles of benzoic acid = 0.50 M × 0.030 L = 0.015 moles

Step 2: Determine the concentration of hydronium ions produced from benzoic acid.

Since benzoic acid is a monoprotic acid, it will only donate one H+ ion in solution. Therefore, the concentration of hydronium ions produced is the same as the concentration of benzoic acid.

Concentration of H3O+ ions = Concentration of benzoic acid = 0.50 M

Step 3: Determine the concentration of hydroxide ions (OH-) produced from NaOH.

NaOH is a strong base and completely dissociates in water, yielding one hydroxide ion for each molecule of NaOH. Hence, the concentration of hydroxide ions is the same as the concentration of NaOH.

Concentration of OH- ions = Concentration of NaOH = 0.50 M

Step 4: Determine the concentration of hydronium ions remaining after the reaction between benzoic acid and NaOH.

Since benzoic acid reacts with NaOH to form water, the moles of hydronium ions in solution are reduced by the same number of moles as the moles of benzoic acid used.

Moles of H3O+ remaining = Initial moles of H3O+ - Moles of benzoic acid used
Moles of H3O+ remaining = 0.50 M - 0.015 moles = 0.485 moles

Step 5: Determine the final concentration of hydronium ions.

To determine the final concentration of hydronium ions, divide the moles of hydronium ions remaining by the total volume of the mixture (NaOH + benzoic acid).

Concentration of H3O+ ions = Moles of H3O+ remaining / Total volume of the mixture
Concentration of H3O+ ions = 0.485 moles / (0.015 L + 0.030 L) = 0.485 moles / 0.045 L = 10.78 M

Step 6: Determine the pH of the solution.

The pH is the negative logarithm (base 10) of the concentration of hydronium ions.

pH = -log[H3O+]
pH = -log(10.78)
pH ≈ -1.03

Therefore, the pH of the solution is approximately -1.03.