Question

The volume of one mole of water at 277 K is 18 ml. One ml of water contains 20 drops. The number of molecules in one drop of water will be ($N_A$ = $6 \times {10^{23}}$ )
A. $1.07 \times {10^{21}}$
B. $1.67 \times {10^{21}}$
C. $2.67 \times {10^{21}}$
D.$1.67 \times {10^{20}}$

Answer 1

The number of atoms in one mole of any substance is equal to Avogadro’s Number i.e. $6.02 \times {10^{23}}$ atoms per mole. On multiplying the molar mass of the substance to the number of moles, we can get the grams of the substance contained in that particular mole of the substance. Atomic weight when multiplied to the number of moles results in its gram weight.
Formula used:
Grams = moles $\times$atomic weight and 1mole $= 6.023 \times {10^{23}}$no. molecules.

Complete step by step answer:
A mole is a standard unit of measurement of an amount of a substance. Substances react in the simple ratios of their moles. One mole consists of Avogadro number of atoms i.e. $6.022 \times {10^{23}}$atoms. The number of atoms in 12.0 grams of Carbon-12 is the same as Avogadro’s number as it is for 1 mole of carbon i.e. a sample of 12 grams of carbon is equal to its one mole. It is similar to a dozen.
The molar mass is the number of grams present in one mole of a substance. It is also the average atomic weight of a substance. For example, carbon has an atomic weight of 12 amu, so its molar mass is 12 grams per mole. The formula for converting moles to gram is written as-
Grams = moles $\times$ atomic weight
Now, given, the volume of one mole of water at 277 K is 18 ml. One ml of water contains 20 drops Therefore, the number of drops in one mole is, $20 \times 18$.
1mole $= 6.023 \times {10^{23}}$no. molecules. Therefore $20 \times 18$ drops contain $= 6.023 \times {10^{23}}$ no. of molecules.
Therefore, 1drop of water contains

$$= \dfrac{{6.023 \times {{10}^{23}}}}{{20 \times 18}} \\\ = \dfrac{{6.023 \times {{10}^{23}}}}{{360}} \\\ = 1.67 \times {10^{21}} \\\$$

Therefore, the correct option is B.

Note:
Molecular mass means the weight of the 1-mole amount of a compound. According to the mole concept, we know 1 mole of any substance is equal to its molecular weight. 1 mole is equal to Avogadro’s number of atoms i.e. $6.023 \times {10^{23}}$ .