Enough water is added to 0.35 g of benzoic acid to make 1000 mL of solution. What is the pH?
Ionization Constant for Benzoic Acid Ka = 6.5 × 10–5
Molar Mass Benzoic Acid 122. g·mol–1
(A) 1.9 (B) 2.6 (C) 3.4 (D) 4.2
A straight Ksp problem. You need to convert 0.35 g benzoic acid to mols. mols = g/molar mass.
2.6
To calculate the pH of the solution, we need to consider the ionization of benzoic acid in water. Benzoic acid is a weak acid, so it partially dissociates in water.
The balanced equation for the ionization of benzoic acid is:
C₆H₅COOH (aq) ⇌ C₆H₅COO⁻ (aq) + H⁺ (aq)
The ionization constant for benzoic acid (Ka) is given as 6.5 × 10⁻⁵. This represents the equilibrium constant for the above reaction.
To determine the concentration of H⁺ ions in the solution and subsequently calculate the pH, we will use the formula for the concentration of H⁺ ions in a weak acid solution.
[H⁺] = √(Ka × [acid])
First, we need to calculate the concentration of benzoic acid in the solution.
Moles of benzoic acid = mass / molar mass
Moles of benzoic acid = 0.35 g / 122 g·mol⁻¹
Moles of benzoic acid = 0.00287 mol
Concentration of benzoic acid = moles / volume
Concentration of benzoic acid = 0.00287 mol / 1 L
Concentration of benzoic acid = 0.00287 M
Now, we can calculate the concentration of H⁺ ions.
[H⁺] = √(Ka × [acid])
[H⁺] = √(6.5 × 10⁻⁵ × 0.00287)
[H⁺] = √(1.86655 × 10⁻⁷)
[H⁺] ≈ 4.325 × 10⁻⁴ M
Finally, we can calculate the pH using the formula:
pH = -log[H⁺]
pH = -log(4.325 × 10⁻⁴)
pH ≈ 3.36
Therefore, the pH of the solution is approximately 3.36, which is closest to option (C) 3.4.
To find the pH of the solution, we first need to calculate the concentration of benzoic acid in the solution.
Step 1: Calculate the moles of benzoic acid:
Moles = mass / molar mass
Moles = 0.35 g / 122 g·mol–1
Moles = 0.00287 mol
Step 2: Calculate the concentration of benzoic acid:
Concentration (in mol/L) = moles / volume (in L)
Concentration = 0.00287 mol / 1 L
Concentration = 0.00287 M
Now that we know the concentration of benzoic acid in the solution, we can calculate the concentration of H+ ions using the ionization constant (Ka) of benzoic acid.
Step 3: Calculate the concentration of H+ ions:
Ka = [H+][C6H5COO-] / [C6H5COOH]
Assuming complete ionization, we can approximate [C6H5COO-] as 0 and simplify the equation:
Ka = [H+][0] / [C6H5COOH]
[H+] = Ka × [C6H5COOH]
[H+] = (6.5 × 10–5) × (0.00287 M)
[H+] = 1.8705 × 10–7 M
Step 4: Calculate the pH of the solution:
pH = -log[H+]
pH = -log(1.8705 × 10–7)
pH ≈ 6.73
Since the pH is approximately 6.73, none of the answer choices (A) 1.9, (B) 2.6, (C) 3.4, (D) 4.2) match the calculated pH.