Question

How many molecules are present in one gram of hydrogen gas?
A. $6.02 \times {10^{23}}$
B. $3.01 \times {10^{23}}$
C. $2.5 \times {10^{23}}$
D. $1.5 \times {10^{23}}$

Answer 1

We need to know and study Avogadro’s Number which defines the number of units in one mole of any substance. One mole of a substance is defined as the molecular weight of a substance in grams. It is a proportionality factor that is used to relate the number of constituent particles in a sample with the amount of substance in that sample. Its SI unit is the mole inverse and is equal to $6.02214076 \times {10^{23}}mo{l^{ - 1}}$.

Complete step by step answer:
We know that one mole of a substance contains$6.02214076 \times {10^{23}}$atoms. The number of moles of any substance is calculated by dividing the weight of the given substance by its atomic weight. We will use the concept of moles and Avogadro’s number to obtain the solution.
Let us now calculate the number of moles of the given substances and calculate the number of atoms accordingly.
We know that 1 mole of hydrogen gas contains $6.02 \times {10^{23}}$ atoms. One molecule of hydrogen gas contains 2 atoms of hydrogen. Therefore, 1 gram of hydrogen gas will contain
$\dfrac{{1 \times 6.02 \times {{10}^{23}}}}{2}$ (Atomic weight of hydrogen is 1).
=$3.01 \times {10^{23}}$ molecules.
Hence the total number of molecules in 1 gram of hydrogen gas is $3.01 \times {10^{23}}$.

Therefore, option B is correct.

Note: It must be noted that Avogadro’s number is calculated based on the charge of electrons. The charge on an electron based on modern experiments is estimated to be $1.60217653 \times {10^{ - 19}}\;coulombs$ per electron. Dividing the charge on a mole of electrons by the charge on a single electron the Avogadro's number of $6.02214154 \times {10^{23}}\;$ particles per mole is obtained.