A solution is made by containing 15 mL of 17.5 M acetic acid with 5.52 g of sodium acetate and diluting to total volume of 1.50 L. Calculate the pH
To calculate the pH of the solution, we need to use the concept of acid-base equilibrium in a solution. In this case, acetic acid (CH3COOH) is a weak acid that partially dissociates in water to form acetate ions (CH3COO-) and hydrogen ions (H+).
Step 1: Calculate the moles of acetic acid and sodium acetate:
First, we need to convert the mass of sodium acetate (5.52 g) to moles. Since the molar mass of sodium acetate (CH3COONa) is 82.03 g/mol:
Moles of sodium acetate = mass of sodium acetate / molar mass
= 5.52 g / 82.03 g/mol
≈ 0.0673 mol
Next, we calculate the moles of acetic acid using the given molarity and volume:
Moles of acetic acid = molarity × volume
= 17.5 M × 0.015 L
= 0.2625 mol
Step 2: Calculate the moles of acetate ions:
Since acetic acid is a weak acid, it does not dissociate completely in water. However, when we add sodium acetate to the solution, it provides acetate ions, increasing their concentration.
Moles of acetate ions = moles of sodium acetate
= 0.0673 mol
Step 3: Calculate the total moles of acetic acid and acetate ions:
Total moles = moles of acetic acid + moles of acetate ions
= 0.2625 mol + 0.0673 mol
≈ 0.3298 mol
Step 4: Calculate the concentration of the acid and its conjugate base:
In a solution of acetic acid and acetate ions, we can calculate the concentration of the acid and its conjugate base:
Concentration of acetic acid = moles of acetic acid / total volume in liters
= 0.2625 mol / 1.5 L
= 0.175 M
Concentration of acetate ions = moles of acetate ions / total volume in liters
= 0.0673 mol / 1.5 L
= 0.045 M
Step 5: Calculate the pH using the Henderson-Hasselbalch equation:
The Henderson-Hasselbalch equation relates the pH of a solution to the concentration of the acid and its conjugate base:
pH = pKa + log (concentration of acetate ions / concentration of acetic acid)
The pKa value for acetic acid is approximately 4.76.
Plugging in the values, we get:
pH = 4.76 + log (0.045 M / 0.175 M)
Now we can use a scientific calculator to evaluate the log term and find the pH of the solution.