References
Chapter 17: EOC
Assume you dissolve 0.178 g of the weak acid benzoic acid, , in enough water to make mL of solution and then titrate the solution with 0.187 M . ( for benzoic acid = .)
What was the pH of the original benzoic acid solution?
You didn't include the volume of water that dissolved the benzoic acid.
To find the pH of the original benzoic acid solution, we need to use the information provided and perform a calculation.
Step 1: Calculate the number of moles of benzoic acid dissolved.
The number of moles of benzoic acid can be calculated using the formula:
moles = mass / molar mass
Given:
mass of benzoic acid = 0.178 g
molar mass of benzoic acid = ?
To find the molar mass of benzoic acid, we need its molecular formula. It is mentioned in the question as the weak acid benzoic acid, but the molecular formula is missing. The molar mass can be found by adding the atomic masses of all the elements present in benzoic acid.
For benzoic acid (C7H6O2):
- Carbon (C) atomic mass = 12.011 g/mol
- Hydrogen (H) atomic mass = 1.008 g/mol
- Oxygen (O) atomic mass = 15.999 g/mol
Using the molecular formula, we can calculate the molar mass of benzoic acid:
molar mass = (7 × C atomic mass) + (6 × H atomic mass) + (2 × O atomic mass)
Step 1: Calculate the molar mass of benzoic acid.
molar mass = (7 × 12.011 g/mol) + (6 × 1.008 g/mol) + (2 × 15.999 g/mol)
molar mass = 84.086 g/mol + 6.048 g/mol + 31.998 g/mol
molar mass = 122.132 g/mol
Now, we can calculate the number of moles of benzoic acid:
moles = mass / molar mass
moles = 0.178 g / 122.132 g/mol
moles ≈ 0.001459 mol
Step 2: Calculate the number of moles of NaOH using the stoichiometry of the reaction.
The balanced chemical equation for the reaction between benzoic acid (C6H5COOH) and NaOH (NaOH) is as follows:
C6H5COOH + NaOH → C6H5COONa + H2O
From the equation, we can see that the mole ratio between benzoic acid and NaOH is 1:1. This means that the number of moles of NaOH used in the titration is also approximately 0.001459 mol.
Step 3: Calculate the volume of NaOH used.
We are given the concentration of NaOH (0.187 M) and the moles of NaOH (0.001459 mol). We can use the formula:
moles = concentration × volume
0.001459 mol = 0.187 M × volume
volume ≈ 0.0078 L or 7.8 mL
Step 4: Calculate the initial volume.
We know that the volume of the solution after dissolving benzoic acid is mL. Since we added 7.8 mL of NaOH, the initial volume of the benzoic acid solution would be the sum of the mL added to the mL of solution:
initial volume = mL + 7.8 mL
Step 5: Calculate the concentration of benzoic acid.
The concentration of benzoic acid can be calculated using the formula:
concentration = moles / volume
concentration = 0.001459 mol / ( mL + 7.8 mL)
Now, we have the concentration of benzoic acid, which we can use to calculate the pH using the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation for a weak acid is:
pH = pKa + log (concentration of conjugate base / concentration of weak acid)
However, the pKa value for benzoic acid (C6H5COOH) is missing from the question. Without this value, we cannot accurately calculate the pH of the benzoic acid solution.
Please provide the pKa value for benzoic acid to continue with the calculation.