To solve the problem step by step, we will follow the outlined process in the video transcript while ensuring clarity and precision.
### Step 1: Calculate Initial Moles of Acetic Acid
Given:
- Volume of acetic acid solution (V1) = 100 mL = 0.1 L
- Molarity of acetic acid (C1) = 0.3 M
Using the formula:
\[
\text{Moles} = \text{Volume (L)} \times \text{Molarity (M)}
\]
\[
\text{Initial moles of acetic acid} = 0.1 \, \text{L} \times 0.3 \, \text{mol/L} = 0.03 \, \text{mol} = 30 \, \text{mmol}
\]
### Step 2: Calculate Final Moles of Acetic Acid
Given:
- Final concentration of acetic acid (C2) = 0.125 M
Using the same formula:
\[
\text{Final moles of acetic acid} = 0.1 \, \text{L} \times 0.125 \, \text{mol/L} = 0.0125 \, \text{mol} = 12.5 \, \text{mmol}
\]
### Step 3: Calculate Moles of Acetic Acid Adsorbed
Now, we can find the moles of acetic acid that were adsorbed by subtracting the final moles from the initial moles:
\[
\text{Moles adsorbed} = \text{Initial moles} - \text{Final moles}
\]
\[
\text{Moles adsorbed} = 30 \, \text{mmol} - 12.5 \, \text{mmol} = 17.5 \, \text{mmol}
\]
### Step 4: Calculate the Mass of Acetic Acid Adsorbed
Next, we need to find the mass of acetic acid adsorbed. First, we calculate the molecular weight of acetic acid (CH3COOH):
- Carbon (C) = 12 g/mol × 2 = 24 g/mol
- Hydrogen (H) = 1 g/mol × 4 = 4 g/mol
- Oxygen (O) = 16 g/mol × 2 = 32 g/mol
Thus, the molecular weight of acetic acid is:
\[
\text{Molecular weight} = 24 + 4 + 32 = 60 \, \text{g/mol}
\]
Now, we can calculate the mass of acetic acid adsorbed:
\[
\text{Mass} = \text{Moles} \times \text{Molecular Weight}
\]
\[
\text{Mass adsorbed} = 17.5 \, \text{mmol} \times 60 \, \text{g/mol} = 1.05 \, \text{g} = 1050 \, \text{mg}
\]
### Step 5: Calculate Mass of Acetic Acid Adsorbed per Gram of Charcoal
Given that the mass of charcoal used is 0.8 g, we can find the mass of acetic acid adsorbed per gram of charcoal:
\[
\text{Mass per gram of charcoal} = \frac{\text{Mass adsorbed}}{\text{Mass of charcoal}} = \frac{1050 \, \text{mg}}{0.8 \, \text{g}} = 1312.5 \, \text{mg/g}
\]
Converting mg to g:
\[
\text{Mass per gram of charcoal} = \frac{1312.5 \, \text{mg}}{1000} = 1.3125 \, \text{g}
\]
### Final Answer
The mass of acetic acid adsorbed per gram of charcoal is approximately **1.31 g**.
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