Question

A drop of olive oil of radius 0.30mm spreads into a nearly circular film of radius 12cm on the water surface. Estimate the molecular size of olive oil.

Answer 1

Here olive oil spread as a film, supposing it is 1 molecule thick on water surface, then the thickness of the film will give the estimate of diameter of molecule

So, we have

d = Volume of oil drop ÷ Area of film

d = 4/3 π (0.03)³ ÷ π (12)²

d = 4/3 (0.000027) ÷ 144

d = 0.000036 ÷ 144

d = 0.00000025

or d = 2.5 x 10^(-7) cm

Answer 2

Hello Dear.

Here is the answer---

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Given ⇒

Radius of the one drop olive oil = 0.3 mm.
                                                   = 0.03 cm.

We know, the drop is generally spherical i shape,
Thus volume of the drop = (4/3)π r³
                                        = 4π × 0.000009
                                        = 0.000036 cm³

As per as the Question,Water Surface is circular in shape,

Radius of the Water Surface(r)  =12 cm.

∴  Area = π r².
            = π × (12)².
            = 144 π cm².


∵    $Molecular Size = \frac{Volume of one drop}{Area of Water Surface}$

⇒ $Molecular Size = \frac{0.000036 \pi}{144 \pi }$
⇒ Molecular Size = 0.25 × 10⁻⁶
                            = 2.5 × 10⁻⁷ m.


∴ Molecular Size of the one drop of the olive oil is 2.5 × 10⁻⁷ m.


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Hope it helps.

Have a Good Day.