Question

Calculate the mass of one molecule of ${H_2}O$ .
A. $29.88 \times {10^{23}}g$
B. $2.988 \times {10^{23}}g$
C. $0.2988 \times {10^{23}}g$
D. $2.988 \times {10^{ - 23}}g$

Answer 1

Hint: Basically, mole concept is used for expressing the amount of a substance. A mole is defined as the amount of substance that contains exactly $6.022 \times {10^{23}}$ elementary entities of the given substance. It is also known as Avogadro number or the number of units in one mole of any substance.

Formula used:
 $Mass = \,\dfrac{{molecular\,weight}}{{Avogadro\,number}}$

Complete step by step answer:
The mole is the unit of measurement for amount of substance in the International system of units. It was introduced in the year 1869 by the German chemist Wilhelm Ostwald .Further, a mole of a substance or mole of particles is exactly $6.022 \times {10^{23}}$ particles which may be atoms, molecules, ions or electrons or we can say that a mole is the amount of substance that contain exactly $6.022 \times {10^{23}}$ entities of the given substance. This number is known as Avogadro’s number and is denoted by ${N_A}$ .
Now, we have to calculate the mass of one mole of ${H_2}O$ . The molecular weight of water is 18g/mol and hence one mole of water weighs 18g.
Further, one mole of water contains $6.022 \times {10^{23}}$ water molecules so, mass of one water molecule is given as:
 $ = \dfrac{{18}}{{6.023 \times {{10}^{23}}}}$
 $ = 2.988 \times {10^{ - 23}}$

Hence, option D is correct.

Note: The number of moles of a molecule may not always be equal to the number of moles of its constituent elements. Moreover, Avogadro’s number creates a bridge between the macroscopic world and the microscopic world by relating the amount of substance to the number of particles. It also provides the relationship between other physical constants and properties.