Question

A 1.50 g sample of nitrous oxide contains \[2.05 \times {10^{22}}\]\[{N_2}O\] molecules. How many nitrogen atoms are in this sample? How many nitrogen atoms are in 44.0 g of nitrous oxide?

Answer 1

Hint:The nitrous oxide is known as the laughing gas. It is used widely as an anesthetic and used in medical applications. Whereas 1 mole is the basic unit for measuring the amount of substances. It contains the elementary entities which are equal to the Avogadro number. The Avogadro number is equal to \[6.023 \times {10^{23}}\] elementary entities.

Complete step-by-step answer:
So in the first part we need to calculate the number of nitrogen atoms present in the given sample. So in the question it is given that it contains \[2.05 \times {10^{22}}\] molecules of nitrous oxide. But in the \[{N_2}O\] molecule we have 2 atoms of nitrogen which is indicated in the formula. So to calculate the number of nitrogen atoms in any amount of nitrous oxide we will simply multiply the amount of the given sample by 2. To understand more clearly look at the following statements.
1 molecule of nitrous oxide contains = 2 atoms of nitrogen
\[2.05 \times {10^{22}}\] molecules of nitrous oxide contain= \[2.05 \times {10^{22}} \times 2 = 4.1 \times {10^{22}}\] atoms of nitrogen
So \[2.05 \times {10^{22}}\] molecules of nitrous oxide contain \[4.1 \times {10^{22}}\] atoms of nitrogen.
So in the next part of the question we need to calculate the nitrogen atoms in 44g of nitrous oxide.
so we will find the number of moles in 44g of nitrous oxide. The molar mass of nitrous oxide is 44\[gmo{l^{ - 1}}\] so,
44g of nitrous oxide contain =1 mole of nitrous oxide
So the given 44g of nitrous oxide will contains =\[\dfrac{{44}}{{44}}\]= 1mole
So we know that 1 mole of any substance contains \[6.023 \times {10^{23}}\] molecules. So 44g of nitrous oxide contains \[6.023 \times {10^{23}}\] molecules. So
1 molecule of nitrous oxide contains = 2 atoms of nitrogen
\[6.023 \times {10^{23}}\] molecules of nitrous oxide contain = \[6.023 \times {10^{23}} \times 2 = 1.204 \times {10^{24}}\] \[6.023 \times {10^{23}} \times 2 = 1.204 \times {10^{24}}\] atoms of nitrogen
So 44g of nitrous oxide contains \[1.204 \times {10^{24}}\] atoms of nitrogen.

Note:If we need to calculate the number of moles of the substance from the given volume then we need to divide the given volume by 22.4. But if the mass would be given then we will divide the given mass by the molar mass of the substance. We calculate the strength of the substance in terms of molarity and normality.