Question

In which of the following pairs, do 1 g of each have an equal number of molecules ?
a.) ${N_2}O$ and CO
b.) ${N_2}$ and CO
c.) ${N_2}O$ and $C{O_2}$
d.) Both (b) and (c)

Answer 1

Hint: The two molecules with the same molar mass will have an equal number of molecules. The molar mass of a molecule is the sum of molar mass of its elements multiplied by the number of atoms present.

Complete step by step answer :
We know that if the molar mass of two compounds is the same then, both will have equal numbers of molecules. So, let us find the molar mass of two compounds. If any option has molecules with the same molar mass that will be the answer.
So, the first option has ${N_2}O$ and CO. The molar mass of ${N_2}O$ is 44 g/mol and for CO; it is 28 g/mol. So, 1 g of these molecules will have different numbers of molecules. So, it can not be the correct answer.
The second option has molecules ${N_2}$ and CO. The dinitrogen has molar mass of 28 g/mol and even CO has molar mass of 28 g/mol. So, 1 g of these compounds will have the same number of molecules. Thus, it can be the correct answer.
Now, the third option has ${N_2}O$ and $C{O_2}$. The ${N_2}O$ has molar mass of 44 g/mol and the $C{O_2}$ also has molar mass of 44 g/mol. So, 1 g of these two molecules will also have the same number of molecules. Thus, it can also be the correct answer.
So, the option b.) and c.) both are the correct answer.

Thus, the option d.) having both b.) and c.) is the correct answer.

Note: It must be noted that 1 mole of a substance is equal to Avogadro’s number of atoms or molecules. Further, 1 mole of an element or molecule is also equal to the molecular mass of that component. So, the molecules with equal molar mass will have equal number of moles and thus, equal number of atoms or molecules.