Question

# The density of a liquid (molar mass 70) is 1.2g/mL. If 2 mL of liquid contains 35 drops, the number of molecules of liquid in one drop is: A. $\dfrac{1.2}{35}\times {{\text{N}}_{\text{A}}}$ B. $\dfrac{1}{35}\times {{\text{N}}_{\text{A}}}$ C. $\dfrac{1.2}{{{\left( 35 \right)}^{2}}}\times {{\text{N}}_{\text{A}}}$ D. $1.2\text{ }{{\text{N}}_{\text{A}}}$

Hint: Find the number of drops in the molar mass of the liquid using the density of liquid. Then, find the molecules of liquid using Avogadro’s number and mole concept. The Avogadro’s number is denoted by ${{\text{N}}_{\text{A}}}$ and says that $6.022\times {{10}^{23}}$ molecules or atoms present in one mole of substance.

Let us solve this question step by step:
Step (1)- The density of liquid is 1.2 g/mL.
It means that 1 mL has 1.2 grams.
Then, 2 mL of liquid will have $1.2\times 2$ or 2.4 grams.
So, it means that 2.4 grams of liquid will have 35 drops or 35 drops will make up 2.4 grams of liquid.

Step (2)- We know that 1 mole of liquid will have ${{\text{N}}_{\text{A}}}$ molecules.
1 mole means molar mass of the liquid.
Molar mass of liquid is 70 grams.
So, 70 grams of liquid will have ${{\text{N}}_{\text{A}}}$ molecules.

Step (3)- The number of drops in 70 grams of liquid will be calculated by unitary method;
As, we already know, 2 = 2.5 gm of the liquid.
So, if 2.4 gm has 35 drops, then,
$\dfrac{70}{2.4}\times 35$ = 1020.8 drops.
That is 1021 drops (approximately) are present in 70 grams.
There are ${{\text{N}}_{\text{A}}}$ molecules in 1021 drops,

So the number of molecules present in one drop will be $\dfrac{{{\text{N}}_{\text{A}}}}{1021}\text{ or }\dfrac{{{\text{N}}_{\text{A}}}\times 2.4}{70\times 35}$.
As, 1021 has the value $\dfrac{70\times 35}{2.4}$.
The molecules in drop are $\dfrac{1.2}{35\times 35}\times {{\text{N}}_{\text{A}}}$ or $\dfrac{1.2}{{{\left( \text{35} \right)}^{2}}}\times {{\text{N}}_{\text{A}}}$.

The correct option is option ‘c’ which is the number of molecules of liquid in one drop are $\dfrac{1.2}{{{\left( \text{35} \right)}^{2}}}\times {{\text{N}}_{\text{A}}}$.
So, the correct answer is “Option C”.

Note: There is no such need to use direct formulae, when the answer can be obtained step-by-step conveniently. Moreover, there is no direct formula for this question. Remember that 1 mole equals the molar mass of any substance and it is also called a gram atomic mass. Also remember to find out the mass of 2 ml of the liquid using the density.