100 mL of 0.6 M acetic acid is shaken with 2 g activatid carbon . The final concetration solution after adsorption is 0.5 M. what is the amount of acetifc acid adsorbed per gram of carbon ?

Options

A. 0.6 g
B. 0.3 g
C. 1.2 g
D. none of these

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the initial moles of acetic acid
We start with a 0.6 M solution of acetic acid and a volume of 100 mL.

\[ \text{Moles of acetic acid} = \text{Concentration} \times \text{Volume} = 0.6 \, \text{mol/L} \times 0.1 \, \text{L} = 0.06 \, \text{moles} \]

### Step 2: Calculate the final concentration and moles of acetic acid
The final concentration of acetic acid after adsorption is given as 0.5 M.

\[ \text{Final moles of acetic acid} = \text{Final concentration} \times \text{Volume} = 0.5 \, \text{mol/L} \times 0.1 \, \text{L} = 0.05 \, \text{moles} \]

### Step 3: Calculate the change in moles of acetic acid
The change in moles of acetic acid due to adsorption can be calculated as:

\[ \text{Change in moles} = \text{Initial moles} - \text{Final moles} = 0.06 \, \text{moles} - 0.05 \, \text{moles} = 0.01 \, \text{moles} \]

### Step 4: Calculate the mass of acetic acid adsorbed
To find the mass of acetic acid adsorbed, we need to convert moles to grams. The molar mass of acetic acid (CH₃COOH) is approximately 60 g/mol.

\[ \text{Mass of acetic acid adsorbed} = \text{Change in moles} \times \text{Molar mass} = 0.01 \, \text{moles} \times 60 \, \text{g/mol} = 0.6 \, \text{g} \]

### Step 5: Calculate the amount of acetic acid adsorbed per gram of carbon
Since 2 g of activated carbon adsorbs 0.6 g of acetic acid, we can find out how much is adsorbed per gram of carbon.

\[ \text{Amount adsorbed per gram of carbon} = \frac{0.6 \, \text{g}}{2 \, \text{g}} = 0.3 \, \text{g} \]

### Final Answer:
The amount of acetic acid adsorbed per gram of carbon is **0.3 g**.

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