To determine the surface area of charcoal adsorbed by each molecule of acetic acid (CH3COOH), we can break down the problem into several logical steps. First, we need to calculate the total number of moles of acetic acid in the solution, then find out how many molecules that corresponds to, and finally relate that to the surface area of the charcoal used for adsorption.
Step 1: Calculate the Total Moles of Acetic Acid
We start with the concentration of acetic acid, which is given as 0.5 M (molar). This means there are 0.5 moles of acetic acid in 1 liter of solution. Since we have 100 ml (or 0.1 L) of this solution, we can calculate the total moles of acetic acid:
- Volume of solution = 100 ml = 0.1 L
- Concentration of CH3COOH = 0.5 M
- Total moles of CH3COOH = Concentration × Volume = 0.5 moles/L × 0.1 L = 0.05 moles
Step 2: Convert Moles to Molecules
Next, we need to convert the moles of acetic acid into molecules. We use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules/mole:
- Total molecules of CH3COOH = Total moles × Avogadro's number
- Total molecules = 0.05 moles × \(6.022 \times 10^{23}\) molecules/mole ≈ \(3.01 \times 10^{22}\) molecules
Step 3: Calculate the Surface Area of Charcoal Used
Now, we know that 1 g of charcoal can adsorb the acetic acid to form a monolayer. The surface area of the charcoal is given as \(3.01 \times 10^{2} \, \text{m}^2/\text{g}\). Therefore, for 1 g of charcoal, the total surface area is:
- Surface area of 1 g of charcoal = \(3.01 \times 10^{2} \, \text{m}^2\)
Step 4: Calculate the Surface Area per Molecule of Acetic Acid
Finally, we can find the surface area available for each molecule of acetic acid by dividing the total surface area of the charcoal by the total number of molecules:
- Surface area per molecule = Total surface area / Total number of molecules
- Surface area per molecule = \(3.01 \times 10^{2} \, \text{m}^2 / 3.01 \times 10^{22} \, \text{molecules}\)
- Surface area per molecule ≈ \(1.00 \times 10^{-20} \, \text{m}^2\)
Final Result
Thus, the surface area of charcoal adsorbed by each molecule of acetic acid is approximately \(1.00 \times 10^{-20} \, \text{m}^2\). This calculation illustrates how a relatively small amount of charcoal can provide a significant surface area for adsorption, which is crucial in various applications such as filtration and catalysis.
