To solve the problem of selecting the best indicator for the titration of 20 mL of 0.02 M acetic acid (CH₃COOH) with 0.02 M sodium hydroxide (NaOH), we can follow these steps:
### Step 1: Write the Reaction
The reaction between acetic acid and sodium hydroxide can be written as:
\[ \text{CH}_3\text{COOH} + \text{NaOH} \rightarrow \text{CH}_3\text{COONa} + \text{H}_2\text{O} \]
### Step 2: Calculate the Initial Moles
Calculate the initial moles of acetic acid and sodium hydroxide:
- Moles of CH₃COOH = Volume (L) × Concentration (M) = \( 0.020 \, \text{L} \times 0.02 \, \text{mol/L} = 0.0004 \, \text{mol} \)
- Moles of NaOH = Volume (L) × Concentration (M) = \( 0.020 \, \text{L} \times 0.02 \, \text{mol/L} = 0.0004 \, \text{mol} \)
### Step 3: Determine the Final Concentration of the Salt
At the equivalence point, all the acetic acid will react with sodium hydroxide to form sodium acetate (CH₃COONa). The total volume after mixing will be:
\[ \text{Total Volume} = 20 \, \text{mL} + 20 \, \text{mL} = 40 \, \text{mL} = 0.040 \, \text{L} \]
The concentration of sodium acetate (the salt formed) will be:
\[ \text{Concentration of CH}_3\text{COONa} = \frac{\text{Moles of CH}_3\text{COONa}}{\text{Total Volume}} = \frac{0.0004 \, \text{mol}}{0.040 \, \text{L}} = 0.01 \, \text{M} \]
### Step 4: Calculate the pH at the Equivalence Point
At the equivalence point, we can use the formula for calculating the pH of a solution of a salt:
\[ \text{pH} = \frac{1}{2} \left( pK_w + pK_a + \log C \right) \]
Where:
- \( pK_w = 14 \)
- \( pK_a = 4.74 \)
- \( C = 0.01 \, \text{M} \)
Calculating:
1. \( \log(0.01) = -2 \)
2. Substitute the values:
\[ \text{pH} = \frac{1}{2} \left( 14 + 4.74 - 2 \right) = \frac{1}{2} \left( 16.74 \right) = 8.37 \]
### Step 5: Select the Best Indicator
Now, we need to determine which indicator has a pH transition range that includes 8.37:
1. **Bromothymol blue**: pH range 6.0 - 7.6 (not suitable)
2. **Thymolphthalein**: pH range 9.3 - 10.5 (not suitable)
3. **Malachite green**: pH range 11.4 - 13 (not suitable)
4. **M-Cresol purple**: pH range 7.4 - 9.0 (suitable)
Since 8.37 falls within the range of M-Cresol purple, it is the best indicator for this titration.
### Conclusion
The best indicator for the titration of 20 mL of 0.02 M CH₃COOH with 0.02 M NaOH is **M-Cresol purple**.
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