Calculate the pH of a solution obtained by mixing 50 mL of 0.75 M CH3COOH with 15 mL of 1.6 M NaOH. (Ka of CH3COOH is 1.8 x 10-5)
To calculate the pH of the solution, we need to determine the concentration of the CH3COOH (acetic acid) and the NaOH (sodium hydroxide) in the final mixture.
First, let's determine the moles of CH3COOH and NaOH in each solution:
Moles of CH3COOH = volume (in liters) x concentration
= 0.050 L x 0.75 M (converting mL to L)
= 0.0375 moles
Moles of NaOH = volume (in liters) x concentration
= 0.015 L x 1.6 M
= 0.024 moles
Since NaOH is a strong base and fully dissociates in water, the number of moles of OH- produced is the same as the number of moles of NaOH added.
Now, let's determine the concentration of CH3COOH and OH- after the mixing of the solutions:
For CH3COOH:
The total volume of the final solution is the sum of the initial volumes:
Volume of CH3COOH = 50 mL = 0.050 L
Volume of NaOH = 15 mL = 0.015 L
Total volume = 0.050 L + 0.015 L = 0.065 L
Concentration of CH3COOH in the final solution = moles of CH3COOH / total volume
= 0.0375 moles / 0.065 L
= 0.577 M
For OH-:
The total moles of OH- in the final solution will be the same as the moles of NaOH added:
Moles of OH- in the final solution = 0.024 moles
Now, let's calculate the pOH of the solution using the concentration of OH-:
pOH = -log[OH-]
= -log(0.024 M)
Next, we can use the pOH to determine the pH of the solution. The pH and pOH are related by the equation:
pH + pOH = 14
Rearranging the equation, we can solve for pH:
pH = 14 - pOH
Finally, substitute the calculated pOH value into the equation to find the pH:
pH = 14 - (-log(0.024 M))
Using a calculator:
pH = 14 - (-1.62)
pH ≈ 15.62
Therefore, the pH of the solution obtained by mixing 50 mL of 0.75 M CH3COOH with 15 mL of 1.6 M NaOH is approximately 15.62.