Question

1 g of charcoal having surface area \[3.02 \times {10^2}\] is mixed in 100 ml of 0.5 M acetic acid solution ,after few times concentrations of solution becomes 0.49 M what will be surface area occupied by one molecule of acetic acid?
\[
A. {\text{ }}2 \times {{10}^{ - 19}}{m^2} \\
B. {\text{ }}5 \times {{10}^{ - 19}}{m^2} \\
C. {\text{ }}6 \times {{10}^{20}}{m^2} \\
D. {\text{ }}{{10}^{ - 3}}{m^2}
\]

Answer 1

Hint:Charcoal is lightweight black carbon residue or an amorphous form of carbon which is produced by strongly heating wood. It is generally present in the form of powder. It is highly porous, has high absorption power and possesses a large surface area. The surface area of any solid object is actually a measure of the total area which the object’s surface occupies.

Complete answer:
In the given question, we have been provided with the surface area of charcoal, concentration of solution and molarity of the reduced acetic acid. And we have to find out the surface area of charcoal occupied by one molecule acetic acid. To solve this question, first we will have to determine the total number of molecules of acetic acid getting absorbed.
Molarity of acetic acid = 0.5M (Given)
Volume of acetic acid solution = 100 ml = 0.1L (Given)
We know that
\[Number{\text{ }}of{\text{ }}moles = Molarity(M) \times Volume(L)\]
From this formula, we will calculate the number of moles of acetic acid.
\[Number{\text{ }}of{\text{ }}moles{\text{ }}of{\text{ }}acetic{\text{ }}acid = 0.5 \times 0.1 = 0.05\]
Similarly we can calculate the moles of acetic acid left after adsorption\[ = 0.49M{\text{ }}\times{\text{ }}0.1L = 0.049\]
Hence, number of moles of acetic acid adsorbed\[ = 0.05 - 0.049 = 0.001{\text{ }}mole\]
We know that 1 mole of any substance contains \[6.023\times{10^{23}}\]molecules
Therefore, 0.001 mole of adsorbed acetic acid corresponds to \[6.023\times{10^{20}}\]molecules
Now, Surface area of charcoal = \[3.02 \times {10^2}\](Given)
\[
  Surface{\text{ }}area{\text{ }}occupied{\text{ }}by{\text{ }}each{\text{ }}molecule = \dfrac{{Total{\text{ }}surface{\text{ }}area{\text{ }}of{\text{ }}charcoal}}{{Number{\text{ }}of{\text{ }}molecules{\text{ }}of{\text{ }}acetic{\text{ }}acid}} \\
   = \dfrac{{3.02 \times {{10}^2}}}{{6.023 \times {{10}^{20}}}} = 5 \times {10^{ - 19}}{m^2} \\
\]

Hence, the correct answer is Option B. ${\text{ }}5 \times {{10}^{ - 19}}{m^2}$

Note:
Acetic acid (\[C{H_3}COOH\]), also known as ethanoic acid, is one of the most important carboxylic acids. The health benefits of acetic acid involve lowering blood pressure, reducing inflammation and keeping blood sugar spikes at bay. It also has an alkaline effect that helps in running the systems in your body smoothly.