Question

1 gm atom of nitrogen represents:
A) $6.02 \times 10^{23} \mathrm{N}_{2}$ molecules
B) $22.4 \mathrm{L}$ of $\mathrm{N}_{2}$ at $\mathrm{NTP}$
C) $11.2 \mathrm{L}$ of $\mathrm{N}_{2}$ at $\mathrm{NTP}$
D) $28 \mathrm{gm}$ of nitrogen

Answer 1

Mole concept is a very important topic in chemistry. It forms the basis of the whole physical chemistry, because it allows us to determine the number of elementary particles in a sample of a pure substance by simply determining the mass of the sample.

Complete step-by-step answer:
-A mole of atoms of any element has a mass in grams equal to the atomic weight of the element. The number of particles in a mole is known as Avagadro's Constant. It is equal to $6.02 \times 10^{23}$.
-The atomic mass of an element is the mass of one atom of the element expressed in atomic mass units (amu). It accounts for the abundance of the various isotopes of the element and assigns an average value to the mass of one atom of the element.
For example, the atomic mass of carbon is 12.011 atomic mass units since carbon samples generally contain 98.89% of the carbon-12 isotope, 1.11% of carbon-13, and trace amounts of carbon-14. However, the atomic masses of these isotopes are different.
-The atomic mass of a carbon-12 atom is 12 atomic mass units, but that of a carbon-13 atom is 13 amu. The atomic mass of an element is roughly equal to the sum of all the protons and neutrons present in its nucleus.
-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.
-The atomic mass of hydrogen is 1.00794 amu and that of oxygen is 15.9994. Since water molecules contain 2 hydrogen atoms and only one oxygen atom, the molecular mass of water is 18.0154 amu.
-Discussing option A, it tells us that $1 \mathrm{gm}$ of nitrogen is $6.02 \mathrm{X} 10^{23} \mathrm{N}_{2}$ molecules. Let us see if that is true. $1 \mathrm{gm}$ atom of nitrogen $=6.02 \mathrm{X} 10^{23}$ atoms. Thus, $3.01 \mathrm{X} 10^{23}$ number of $\mathrm{N}_{2}$ molecules. Since, two atoms combine and form one nitrogen molecule. $1 \mathrm{gm}$ atom of nitrogen $=$ $3.01 \times 10^{23}$ number of $\mathrm{N}_{2}$ molecules.
-Discussing option $\mathrm{B}, 1$ mole of nitrogen $=1 / 2$ mole of nitrogen molecule. Thus if 1 mole of nitrogen molecule occupies $22.4 \mathrm{L} \mathrm{N}_{2}$ at NTP. Hence, 1 mole of nitrogen atoms occupies half of the total volume occupied by $\mathrm{N}_{2}$ at $\mathrm{NTP}$ i.e. $, 11.2 \mathrm{L}$.
-Discussing option $\mathrm{D},$ we know that 1 mole of nitrogen $=1 / 2$ mole of nitrogen molecule. Thus one mole of nitrogen molecules has 28 grams. Thus, 1 mole of $\mathrm{N}$ atoms has $14 \mathrm{gm}$ of nitrogen.

Clearly, the answer is C.

Note: We could also find the answer in a simpler way. As we have found that the molar mass of $\mathrm{N}_{2}$ gas is 28 ,it means that 28 g of $\mathrm{N}_{2}$ gas contains one mole and for finding the number of moles in 1 atom of nitrogen, it is easy to find out the ratio i.e., 2:1 to yield us the answer.