Question

In a certain experiment, 'V' volume of acid is added to alcohol to obtain a concentration of 1 part by 400. If the surface area of the solution is A, then the thickness of a molecule of the acid is-
1. \(\sqrt{400A}\)
2. \(\frac{400}{AV}\)
3. \(\frac{V}{400A}\)
4. \(\frac{400\sqrt V}{A}\)

Answer 1

Correct Answer - Option 3 : \(\frac{V}{400A}\)

The correct answer is option 3) i.e. \(\frac{V}{400A}\)

CONCEPT:

• For estimating measurements as small as the size of a molecule, a commonly used method is the oleic acid experiment.
  • Oleic acid is a soapy liquid with large molecular size of the order of 10^–9 m.
  • 1 cm³ of oleic acid is mixed in alcohol to make a solution of 20 cm³. 1 cm³ of this solution is further diluted to 20 cm³ of alcohol.
  • Thus, the concentration of the solution is equal to 1 part by 20 × 20 cm³ of solution.
  • Lycopodium powder is sprinkled on the surface of the water in a large trough and one drop of this solution is added in the water.
  • As the lycopodium powder weakens the surface tension, the oleic acid drop spreads into a thin, large and circular film of molecular thickness on water surface.
  • The diameter of the thin film is measured to get its area A.
  • If n drops each of V cm³ of oleic acid were added in the water, the volume of n drops = nV cm³ 

Then the amount of oleic acid in this solution =  \(nV(\frac{1}{20 \times 20}) cm^3\)

The thickness of the acid film, \(t = \frac{volume \: of \:the \: film}{area\: of\: the\: film} = \frac{nV}{20\times 20 A}\: cm\)

• This will be the size of the molecule of oleic acid.

EXPLANATION:

Given that:

Amount of acid = V

Concentration = \(\frac{1}{400}\)

Area of the acid film = A

∴ Thickness, \(t= \frac{V}{400A}\)