Question

How many molecules are present in $1g$ of hydrogen?
(A) $6.02 \times {10^{23}}$
(B) $3.01 \times {10^{23}}$
(C) $1.50 \times {10^{23}}$
(D) $6.02 \times {10^{22}}$

Answer 1

Hint:To solve this question, we must first have some basic knowledge of Mole concept and Avogadro Number. First we need to find the number of moles of the given sample and then find the number of molecules in that sample and then only we can conclude the correct answ

Complete step-by-step solution:Before we move forward with the solution of this given question, let us first understand some basic concepts:
The mole concept is a convenient method of expressing the amount of a substance. Any measurement can be broken down into two parts – the numerical magnitude and the units that the magnitude is expressed in.The number $6.02 \times {10^{23}}$ is popularly known as the Avogadro constant and is often denoted by the symbol $'{N_A}'$ . The elementary entities that can be represented in moles can be atoms, molecules, monatomic/polyatomic ions, and other particles (such as electrons).
Step 1: In this step we will find the number of moles of the given sample:
Number of moles $ = \frac{{Given\,\,mass}}{{molecular\,\,mass}} = \,\,\frac{{1g}}{{2g}} = 0.5$
Step 2: In this step we will find the number of molecules in 1 mole of Hydrogen:
Since we know that, Number of molecules in 1 mole of substance $ = \,\,{N_A}\,\, = \,\,6.02 \times {10^{23}}$
Therefore, required number of molecules in $0.5$ mole of Hydrogen $ = 0.5 \times 6.02 \times {10^{23}}\,\, = \,\,3.01 \times {10^{23}}$$ = \,\,$

So, clearly we can conclude that the correct answer is Option (B).

Note:The molecular mass of an element is the sum of the atomic masses of all its constituent elements. This quantity is also represented in terms of atomic mass units. Therefore, the molecular mass of water is equal to the sum of the atomic masses of its constituents – hydrogen and oxygen.