Question

What is the mass of (a) 1 mole of nitrogen atoms? (b) 4 moles of the aluminum atom (Atomic mass of aluminum = 27)? (c) 10 moles of sodium sulfite $(N{a_2}S{O_3})$?

Answer 1

Moles are used to measure the amount of matter present in a given sample of a substance. To be more specific, it helps in measuring the number of atoms or molecules present in the given sample of the substance. One mole of any substance contains $6.022 \times {10^{23}}$ atoms or molecules.

Complete step by step answer:
Before we move forward with the solution to this question, let us discuss some important concepts.
1.Mole: a mole is a physical quantity that represents the amount of mass of the substance required to have a collective of $6.022 \times {10^{23}}$ atoms of the given substance. Mole is a widely used unit for calculating the amount of matter of a substance. One mole of any substance weighs about the same as the molecular mass of that substance.
2.Hydrogen has an atomic number of 1. This means that there is only 1 electron present in its 1s orbital. Hence to satisfy its duplet, and exist as a stable element, hydrogen gas is a diatomic molecule.
Molecular mass means the weight of the 1-mole amount of a compound. And according to the mole concept, we know 1 mole of any substance is equal to its molecular weight. And 1 mole is also equal to Avogadro’s number of atoms i.e. $6.023 \times {10^{23}}$.
The molar mass is the number of grams present in one mole of a substance. It is also the average atomic weight of a substance. For example, carbon has an atomic weight of 12 amu, so its molar mass is 12 grams per mole. The formula for converting moles to gram is written as-
Grams = moles $\times$ atomic weight
(a)The molecular mass of nitrogen is 14. So, the mass of 1 mole of nitrogen atoms is 14 gm.
(b)Atomic mass of aluminum is 27. So, the mass of 4 moles of an aluminum atom is $(4 \times 27) = 108$.
(c) mass of 10 moles of sodium sulfite $(N{a_2}S{O_3})$ is,

$$Grams = moles \times atomic\,weight \\\ \Rightarrow Grams = 10 \times atomic\,weight(N{a_2}S{O_3}) \\\ \Rightarrow Grams = 10 \times \left[ {(23 \times 2) + (32 + 3 \times 16)} \right] \\\ \Rightarrow Grams = 10 \times \left[ {(46) + (32 + 48)} \right] \\\ \Rightarrow Grams = 10 \times \left[ {(46) + (80)} \right] \\\ \Rightarrow Grams = 10 \times \left[ {126} \right] \\\ \Rightarrow Grams = 1260gm \\\$$

Note: Avogadro's number is defined as the number of elementary particles (molecules, atoms, compounds, etc.) per mole of a substance. With Avogadro's number, scientists can discuss and compare very large numbers, which is useful because substances in everyday quantities contain very large numbers of atoms and molecules.