Question

How do you calculate the molar masses of the following atmospheric molecules: \[{\text{CO}}\]and \[{{\text{N}}_{\text{2}}}{\text{O}}\]?

Answer 1

Hint:The molar mass of the compound represents the mass of one mole of that compound. The unit of the molar mass is ${\text{g/mol}}$.The molar mass of the molecule is determined by taking the sum of atomic masses in gram per mole of all the atoms of the molecule.

Complete step-by-step answer:Here, two molecules are given that is carbon dioxide \[{\text{CO}}\]and dinitrogen oxide \[{{\text{N}}_{\text{2}}}{\text{O}}\].

As we know a molecule is formed from atoms, the sum of the atomic masses of the atoms in (gram per mol)in the molecules gives the molar mass of the molecule.

Here, the first molecule given is carbon dioxide \[{\text{CO}}\]. It contains carbon and oxygen atoms. Hence, the molar mass of \[{\text{CO}}\] is the sum of atomic masses of carbon and oxygen atoms.
\[{\text{Molar}}\,{\text{mass}}\,{\text{of}}\,{\text{CO = Molar}}\,{\text{mass}}\,{\text{of}}\,{\text{C}}\,{\text{ + }}\,{\text{Molar}}\,{\text{mass}}\,{\text{of}}\,{\text{O}}\]
The atomic mass of carbon is \[{\text{12}}{\text{.011}}\,{\text{g/mol}}\]and the molar mass of oxygen is \[{\text{15}}{\text{.999}}\,{\text{g/mol}}\].
Now, substitute the values of the atomic masses in the above equation to obtain the molar mass of the carbon monoxide.

\[{\text{Molar}}\,{\text{mass}}\,{\text{of}}\,{\text{CO = }}\left( {{\text{12}}{\text{.011}}\,{\text{g/mol}}} \right){\text{ + }}\left( {{\text{15}}{\text{.999}}\,{\text{g/mol}}} \right)\]
\[{\text{Molar}}\,{\text{mass}}\,{\text{of}}\,{\text{CO = 28}}{\text{.01}}\,{\text{g/mol}}\]

Thus, the molar mass of \[{\text{CO}}\] is \[{\text{28}}{\text{.01}}\,{\text{g/mol}}\].

Now, the second molecule is dinitrogen oxide \[{{\text{N}}_{\text{2}}}{\text{O}}\].It contains nitrogen and oxygen atoms. Hence, the molar mass of \[{{\text{N}}_{\text{2}}}{\text{O}}\] is the sum of atomic masses of nitrogen and oxygen atoms.
\[{\text{Molar}}\,{\text{mass}}\,{\text{of}}\,{{\text{N}}_{\text{2}}}{\text{O = }}\left( {{\text{2}} \times {\text{Molar}}\,{\text{mass}}\,{\text{of}}\,{\text{N}}\,} \right){\text{ + }}\,{\text{Molar}}\,{\text{mass}}\,{\text{of}}\,{\text{O}}\]
The molar mass of nitrogen is \[{\text{14}}{\text{.0067}}\,{\text{g/mol}}\]and molar mass of oxygen is \[{\text{15}}{\text{.999}}\,{\text{g/mol}}\].
\[{\text{Molar}}\,{\text{mass}}\,{\text{of}}\,{{\text{N}}_{\text{2}}}{\text{O = }}\left( {{\text{2}} \times {\text{14}}{\text{.0067}}\,{\text{g/mol}}\,} \right){\text{ + }}\,\left( {{\text{15}}{\text{.999}}\,{\text{g/mol}}} \right)\]
\[{\text{Molar}}\,{\text{mass}}\,{\text{of}}\,{{\text{N}}_{\text{2}}}{\text{O = }}\left( {{\text{28}}{\text{.0134}}\,{\text{g/mol}}\,} \right){\text{ + }}\,\left( {{\text{15}}{\text{.999}}\,{\text{g/mol}}} \right)\]
\[{\text{Molar}}\,{\text{mass}}\,{\text{of}}\,{{\text{N}}_{\text{2}}}{\text{O = }}44.0124\,{\text{g/mol}}\,\]
Thus, the molar mass of \[{{\text{N}}_{\text{2}}}{\text{O}}\] is \[44.01\,{\text{g/mol}}\,\].

Note:The mole concept is used to determine the amount of the substance which is obtained by taking the ratio of the mass of the substance to the molar mass of the substance.The molecular formula \[{\text{CO}}\]represents the carbon monoxide molecule and \[{{\text{N}}_{\text{2}}}{\text{O}}\] represents a dinitrogen oxide molecule.