To find the concentration of the original acetic acid solution, we can use the concept of acid-base titration and the given information.
In this problem, acetic acid (CH3COOH) is a weak acid that can react with sodium hydroxide (NaOH), a strong base. The reaction between these two compounds results in the formation of water and sodium acetate (CH3COONa).
First, let's understand the calculation steps:
1. Determine the number of moles of NaOH used:
- Concentration of NaOH = 0.100 M
- Volume of NaOH used = 20.0 mL = 0.0200 L
- Moles of NaOH used = Concentration x Volume
2. Determine the number of moles of CH3COOH:
- The reaction between NaOH and CH3COOH is 1:1, so the moles of NaOH used are equal to the moles of CH3COOH initially present in the solution.
3. Calculate the initial concentration of CH3COOH:
- Volume of CH3COOH = 40.0 mL = 0.0400 L
- Concentration of CH3COOH = Moles of CH3COOH / Volume of CH3COOH
Now, let's calculate the concentration of the original acetic acid solution step by step:
Step 1: Determine the number of moles of NaOH used:
Moles of NaOH used = 0.100 M x 0.0200 L = 0.00200 mol
Step 2: Determine the number of moles of CH3COOH:
Since the reaction between NaOH and CH3COOH is 1:1, the moles of NaOH used are equal to the moles of CH3COOH initially present in the solution.
Moles of CH3COOH = 0.00200 mol
Step 3: Calculate the initial concentration of CH3COOH:
Concentration of CH3COOH = Moles of CH3COOH / Volume of CH3COOH
Concentration of CH3COOH = 0.00200 mol / 0.0400 L
Concentration of CH3COOH = 0.0500 M
Therefore, the concentration of the original acetic acid solution is 0.0500 M.