Question

The density of water is 1 g/ml. The volume of water drop is 1.8 ml. The number of molecules present in one water drop is:
A. \[6.023\, \times \,{10^{23}}\]
B. $6.023\, \times \,{10^{21}}$
C. $3.011\, \times \,{10^{11}}$
D. $6.023 \times \,{10^{22}}$

Answer 1

Hint: The given density of water is 1 g/ml and the volume of one drop is 1.8 ml. The Avogadro constant (NA or L) is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. Its SI unit is the reciprocal mole, and it is defined \[NA{\text{ }} = {\text{ }}6.02214076 \times {10^{23}}{\text{ }}mo{l^{ - 1}}\].

Complete step by step answer:
$D\, = \,\dfrac{{mass}}{{volume}}$
From density, it can be said that 1 g of water has volume of 1 ml.
Thus, 1.8 ml of water has a mass of 1.8 g.
1 mole of water weighs 18 g.
Thus, 1.8 g of water corresponds to 0.1 mole.
1 mole of water contains \[6.023\, \times \,{10^{23}}\] molecules.
Hence, 0.1 mole of water will contain $6.023 \times \,{10^{22}}$ molecules.

So, the correct answer is Option D.

Additional information:
The value of the Avogadro constant was chosen so that the mass of one mole of a chemical compound, in grams, is numerically equal (for all practical purposes) to the average mass of one molecule of the compound, in daltons (universal atomic mass units); one dalton being $\dfrac{1}{{12}}$ of the mass of one carbon-12 atom, which is approximately the mass of one nucleon (proton or neutron). Twelve grams of carbon contains one mole of carbon atoms. The mole (symbol: mol) is the unit of measurement for the amount of substance in the International System of Units (SI). A mole of a substance or a mole of particles is defined as containing exactly \[6.023\, \times \,{10^{23}}\] particles, which may be atoms, molecules, ions, or electrons.

Note: The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density. Increasing the temperature of a substance (with a few exceptions) decreases its density by increasing its volume.