1 g of charcoal adsorbs 100 mL of 0.5 MCH3COOH to form a monolayer and...
To solve this problem, we need to use the concept of adsorption and the formula for surface area.
Given:
Mass of charcoal (m) = 1 g
Volume of acetic acid (V) = 100 mL = 0.1 L
Initial molarity of acetic acid (M1) = 0.5 M
Final molarity of acetic acid (M2) = 0.49 M
Surface area of charcoal (A) = 3.01 x 10^2 m^2/g
The amount of acetic acid adsorbed by the charcoal can be calculated using the equation:
n = (M1 - M2) x V
where n is the number of moles of acetic acid adsorbed.
Substituting the given values:
n = (0.5 - 0.49) x 0.1
n = 0.01 x 0.1
n = 0.001 mol
Now, we can calculate the number of molecules of acetic acid adsorbed:
Number of molecules (N) = n x Avogadro's number
where Avogadro's number is 6.022 x 10^23 mol^-1
N = 0.001 x 6.022 x 10^23
N = 6.022 x 10^20 molecules
To find the surface area adsorbed by each molecule of acetic acid, we divide the total surface area of charcoal by the number of molecules:
Surface area per molecule = A/N
Substituting the given values:
Surface area per molecule = (3.01 x 10^2)/(6.022 x 10^20)
Surface area per molecule = 5 x 10^-19 m^2
Therefore, the surface area of charcoal adsorbed by each molecule of acetic acid is 5 x 10^19 m^2.
Hence, the correct answer is option A: 5 x 10^19.
1 g of charcoal adsorbs 100 mL of 0.5 MCH3COOH to form a monolayer and...