To find the pH of the resulting mixture when 100 ml of 0.1 M acetic acid (CH₃COOH) is mixed with 200 ml of 0.03 M sodium hydroxide (NaOH), we can follow these steps:
### Step 1: Calculate the number of moles of CH₃COOH
- Molarity (M) = moles/volume (L)
- Volume of CH₃COOH = 100 ml = 0.1 L
- Molarity of CH₃COOH = 0.1 M
\[
\text{Moles of CH₃COOH} = \text{Molarity} \times \text{Volume} = 0.1 \, \text{mol/L} \times 0.1 \, \text{L} = 0.01 \, \text{mol} = 10 \, \text{mmol}
\]
### Step 2: Calculate the number of moles of NaOH
- Volume of NaOH = 200 ml = 0.2 L
- Molarity of NaOH = 0.03 M
\[
\text{Moles of NaOH} = \text{Molarity} \times \text{Volume} = 0.03 \, \text{mol/L} \times 0.2 \, \text{L} = 0.006 \, \text{mol} = 6 \, \text{mmol}
\]
### Step 3: Determine the limiting reagent
- We have 10 mmol of CH₃COOH and 6 mmol of NaOH.
- Since NaOH is the limiting reagent, it will completely react with CH₃COOH.
### Step 4: Calculate the remaining moles of CH₃COOH after reaction
\[
\text{Remaining CH₃COOH} = \text{Initial CH₃COOH} - \text{NaOH used} = 10 \, \text{mmol} - 6 \, \text{mmol} = 4 \, \text{mmol}
\]
### Step 5: Calculate the moles of the salt formed (sodium acetate, CH₃COONa)
- The moles of salt formed will be equal to the moles of NaOH reacted, which is 6 mmol.
### Step 6: Calculate the total volume of the solution
\[
\text{Total Volume} = 100 \, \text{ml} + 200 \, \text{ml} = 300 \, \text{ml} = 0.3 \, \text{L}
\]
### Step 7: Calculate the concentrations of the remaining acetic acid and the formed salt
- Concentration of CH₃COOH:
\[
[\text{CH₃COOH}] = \frac{4 \, \text{mmol}}{0.3 \, \text{L}} = \frac{4 \times 10^{-3} \, \text{mol}}{0.3 \, \text{L}} = 0.01333 \, \text{M}
\]
- Concentration of CH₃COONa:
\[
[\text{CH₃COONa}] = \frac{6 \, \text{mmol}}{0.3 \, \text{L}} = \frac{6 \times 10^{-3} \, \text{mol}}{0.3 \, \text{L}} = 0.02 \, \text{M}
\]
### Step 8: Use the Henderson-Hasselbalch equation to find the pH
\[
\text{pH} = pK_a + \log\left(\frac{[\text{Salt}]}{[\text{Acid}]}\right)
\]
Given \( pK_a = 4.74 \):
\[
\text{pH} = 4.74 + \log\left(\frac{0.02}{0.01333}\right)
\]
Calculating the ratio:
\[
\frac{0.02}{0.01333} \approx 1.5
\]
Thus,
\[
\text{pH} = 4.74 + \log(1.5) \approx 4.74 + 0.18 = 4.92
\]
### Final Answer:
The pH of the resulting mixture is **4.92**.
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