Suppose you have added 200.0 mL of a solution containing 0.5000 moles of acetic acid per liter to 100.0 mL of 0.50000 M NaOH. What the is the final pH? The Ka of acetic acid is 1.77 x 10^-5.
To find the final pH of the solution, we need to calculate the concentration of acetic acid and the concentration of hydroxide ions (OH-) after the reaction occurs. Then we can use these concentrations to calculate the pH.
Step 1: Calculate the moles of acetic acid
Given that we have added 200.0 mL of a solution containing 0.5000 moles of acetic acid per liter, we can calculate the moles of acetic acid added:
0.5000 moles/L * 0.2000 L = 0.1000 moles
Step 2: Calculate the moles of NaOH
Given that we have 100.0 mL of 0.50000 M NaOH, we can calculate the moles of NaOH:
0.50000 moles/L * 0.1000 L = 0.0500 moles
Step 3: Determine the limiting reactant
To determine the limiting reactant, we compare the moles of acetic acid (0.1000 moles) and NaOH (0.0500 moles). Since we have an equal number of moles for each reactant and the balanced equation is 1:1, neither substance is in excess. Therefore, both the acetic acid and NaOH will completely react to form water and the acetate ion (CH3COO-).
Step 4: Calculate the final volume
The final volume of the solution is the sum of the volumes of the acetic acid solution (200.0 mL) and the NaOH solution (100.0 mL):
200.0 mL + 100.0 mL = 300.0 mL
Step 5: Calculate the molar concentration of CH3COOH
To calculate the molar concentration of acetic acid (CH3COOH), we convert the moles to liters and divide by the final volume (300.0 mL converted to 0.3000 L):
0.1000 moles / 0.3000 L = 0.3333 M
Step 6: Calculate the molar concentration of OH-
Since the reaction between acetic acid and NaOH is a neutralization reaction, the moles of OH- is equal to the moles of acetic acid. Therefore, the molar concentration of OH- is also 0.3333 M.
Step 7: Calculate pOH
To calculate pOH, we use the equation: pOH = -log10[OH-]
pOH = -log10(0.3333) ≈ 0.4771
Step 8: Calculate pH
Since pH + pOH = 14, we subtract pOH from 14 to find the pH:
pH = 14 - 0.4771 ≈ 13.5229
Therefore, the final pH of the solution is approximately 13.5229.