What is the pH of a solution prepared by dissolving 12.2 g of benzoic acid in enough water to produce a 500 mL solution?
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To find the pH of a solution prepared by dissolving benzoic acid in water, we need to consider the dissociation of the acid in water. The dissociation of benzoic acid can be represented by the following equation:
C6H5COOH (benzoic acid) ⇌ C6H5COO- (benzoate ion) + H+ (hydrogen ion)
We can assume that benzoic acid is a monoprotic acid, which means that each molecule of benzoic acid will donate one hydrogen ion (H+) when it dissociates.
To find the pH of the solution, we need to calculate the concentration of hydrogen ions in the solution.
Step 1: Calculate the number of moles of benzoic acid:
First, we need to convert the mass of benzoic acid to moles. The molar mass of benzoic acid (C6H5COOH) is approximately 122.12 g/mol.
Number of moles = mass / molar mass
Number of moles = 12.2 g / 122.12 g/mol
Number of moles = 0.1 mol
Step 2: Calculate the concentration of hydrogen ions:
Since one molecule of benzoic acid donates one hydrogen ion in dissociation, the concentration of hydrogen ions will be the same as the concentration of benzoic acid in the solution.
Concentration of hydrogen ions = number of moles / volume of the solution
Concentration of hydrogen ions = 0.1 mol / 0.5 L
Concentration of hydrogen ions = 0.2 mol/L
Step 3: Calculate the pH:
The pH is a measure of hydrogen ion concentration and is defined as the negative logarithm (base 10) of the hydrogen ion concentration.
pH = -log[H+]
pH = -log[0.2]
pH ≈ 0.7
Therefore, the pH of the solution prepared by dissolving 12.2 g of benzoic acid in enough water to produce a 500 mL solution is approximately 0.7.
To find the pH of the solution prepared by dissolving benzoic acid, we first need to understand the properties of benzoic acid and how it behaves in water.
Benzoic acid (C₆H₅COOH) is a weak acid that partially dissociates in water, releasing hydrogen ions (H⁺). In this case, we assume it dissociates completely. The dissociation reaction is as follows:
C₆H₅COOH ⇌ C₆H₅COO⁻ + H⁺
The concentration of H⁺ ions in the solution determines its pH. The higher the concentration of H⁺ ions, the lower the pH value.
To calculate the pH, we need to follow the following steps:
1. Calculate the number of moles of benzoic acid:
- We know the mass of benzoic acid is 12.2 g.
- We can convert it to moles using the molar mass of benzoic acid (122.12 g/mol).
Moles of benzoic acid = mass / molar mass
= 12.2 g / 122.12 g/mol
2. Determine the molarity of the solution:
- We know the volume of the solution is 500 mL (0.5 L).
- We can calculate the molarity (M) using the formula:
Molarity = moles of solute / volume of solution in liters
3. Calculate the concentration of H⁺ ions:
- Since benzoic acid completely dissociates, the concentration of H⁺ ions will be the same as the molarity of the solution.
4. Calculate the pH:
- The pH is determined by the concentration of H⁺ ions using the formula:
pH = -log[H⁺]
So by going through these steps, you can determine the pH of the solution prepared by dissolving 12.2 g of benzoic acid in enough water to produce a 500 mL solution.