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Question: One gram of charcoal having a surface area \(3.02 \times {10^2}{m^2}\) is mixed in 100ml of \(0.05M\...

One gram of charcoal having a surface area 3.02×102m23.02 \times {10^2}{m^2} is mixed in 100ml of 0.05M CH3COOH0.05M\,C{H_3}COOH to form a monolayer and the molarity of acetic acid is reduced to 0.49M. What will be the surface area of charcoal adsorbed by each molecule of acetic acid?
A. 2×10−19m22 \times {10^{ - 19}}{m^2}
B. 5×10−19m25 \times {10^{ - 19}}{m^2}
C. 6×1020m26 \times {10^{20}}{m^2}
D. 10−3m2{10^{ - 3}}{m^2}

Explanation

Solution

Surface area is basically a measure of the total area that the object occupies. To solve this question, we will first calculate the total molecules of acetic acid absorbed and then we will divide the surface area of charcoal by the number of molecules of acetic acid adsorbed.

Complete step by step answer:
Charcoal is basically made from coal, wood and many other substances. It is a black carbon residue produced by heating wood or other plant or animal materials. It is of various types such as common charcoal, sugar charcoal, activated charcoal, lump charcoal and many more.
Now, in the question, we have been given the surface area of charcoal, and the concentrations of the solution and the molarity of reduced acetic acid. We have to calculate the surface area of charcoal absorbed by each molecule of acetic acid. So, first of all we will calculate moles of acetic acid absorbed.
So, moles of CH3COOHC{H_3}COOH absorbed==initial moles- final moles
=(0.5×100×10−3)−(0.049×100×10−3)= (0.5 \times 100 \times {10^{ - 3}}) - (0.049 \times 100 \times {10^{ - 3}})
=0.05-0.049
=0.001
Now, number of molecules of CH3COOHC{H_3}COOH absorbed =0.001×6.02×1023 = 0.001 \times 6.02 \times {10^{23}}
=6.02×1020= 6.02 \times {10^{20}}
Now, the surface area given to us is 3.02×102m23.02 \times {10^2}{m^2}.
Therefore, surface area of charcoal absorbed in each molecule of 3.02×102m23.02 \times {10^2}{m^2},
=3.01×10206.02×1020= \dfrac{{3.01 \times {{10}^{20}}}}{{6.02 \times {{10}^{20}}}}
=5×10−19m2= 5 \times {10^{ - 19}}{m^2}

Hence, option B is correct.

Note: Acetic acid is carboxylic acid consisting of a methyl group that is attached to a carboxyl functional group. It is used as an antiseptic due to its antibacterial qualities. Medically, it has been employed to treat cancer by its direct injection into the tumor.