Q146CP - Chemistry: Molecular Nature Of Matter And Change

Question

Dinitrogen monoxide (${\mathbf{N}}_{\mathbf{2}}\mathbf{O}$; nitrous oxide) is a greenhouse gas that enters the atmosphere principally from natural fertilizer breakdown. Some studies have shown that the isotope ratios${}^{\mathbf{15}}\mathbf{N}$ of ${}^{\mathbf{14}}\mathbf{N}$ to  and of ${}^{\mathbf{18}}\mathbf{O}$ to ${}^{\mathbf{16}}\mathbf{O}$ in ${\mathbf{N}}_{\mathbf{2}}\mathbf{O}$ depending on the source, which can thus be determined by measuring the relative abundance of molecular masses in a sample of ${\mathbf{N}}_{\mathbf{2}}\mathbf{O}$. (a) What different molecular masses are possible for ${\mathbf{N}}_{\mathbf{2}}\mathbf{O}$? (b) The percent abundance of ${}^{\mathbf{14}}\mathbf{N}$ is 99.6%, and that of ${}^{\mathbf{16}}\mathbf{O}$is 99.8%. Which molecular mass of ${\mathbf{N}}_{\mathbf{2}}\mathbf{O}$ is least common, and which is most common?

Step-by-Step Solution

Answer

(a) Different types of molecular masses can be found like 48,47,46,45 and 44.

(b) The most common and least common molecular masses are 44 and 48 respectively.

Step 1: Finding different molecular masses

The different types of molecular masses can be found as,

$$\begin{gathered} \mathbf{If}\mathbf{ }{\mathbf{N}}_{\mathbf{2}}\mathbf{O}\mathbf{ }\mathbf{contain}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{isotopes}\mathbf{ }{}^{\mathbf{15}}\mathbf{N}\mathbf{,}{}^{\mathbf{15}}\mathbf{N}\mathbf{,}{}^{\mathbf{18}}\mathbf{O} \\ \mathbf{Molecular}\mathbf{ }\mathbf{mass}\mathbf{ }\mathbf{=}\mathbf{2}\mathbf{\times }\mathbf{15}\mathbf{+}\mathbf{18} \\ \mathbf{=}\mathbf{48} \\ \mathbf{If}\mathbf{ }{\mathbf{N}}_{\mathbf{2}}\mathbf{O}\mathbf{ }\mathbf{contain}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{isotopes}\mathbf{ }{}^{\mathbf{14}}\mathbf{N}\mathbf{,}{}^{\mathbf{15}}\mathbf{N}\mathbf{,}{}^{\mathbf{18}}\mathbf{O} \\ \mathbf{Molecular}\mathbf{ }\mathbf{mass}\mathbf{ }\mathbf{=}\mathbf{14}\mathbf{+}\mathbf{15}\mathbf{+}\mathbf{18} \\ \mathbf{=}\mathbf{47} \\ \mathbf{If}\mathbf{ }{\mathbf{N}}_{\mathbf{2}}\mathbf{O}\mathbf{ }\mathbf{contain}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{isotopes}\mathbf{ }{}^{\mathbf{14}}\mathbf{N}\mathbf{,}{}^{\mathbf{14}}\mathbf{N}\mathbf{,}{}^{\mathbf{18}}\mathbf{O} \\ \mathbf{Molecular}\mathbf{ }\mathbf{mass}\mathbf{ }\mathbf{=}\mathbf{14}\mathbf{\times }\mathbf{2}\mathbf{+}\mathbf{18} \\ \mathbf{=}\mathbf{46} \\ \mathbf{If}\mathbf{ }{\mathbf{N}}_{\mathbf{2}}\mathbf{O}\mathbf{ }\mathbf{contain}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{isotopes}\mathbf{ }{}^{\mathbf{15}}\mathbf{N}\mathbf{,}{}^{\mathbf{15}}\mathbf{N}\mathbf{,}{}^{\mathbf{16}}\mathbf{O} \\ \mathbf{Molecular}\mathbf{ }\mathbf{mass}\mathbf{ }\mathbf{=}\mathbf{15}\mathbf{\times }\mathbf{2}\mathbf{+}\mathbf{16} \\ \mathbf{=}\mathbf{46} \\ \mathbf{If}\mathbf{ }{\mathbf{N}}_{\mathbf{2}}\mathbf{O}\mathbf{ }\mathbf{contain}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{isotopes}\mathbf{ }{}^{\mathbf{14}}\mathbf{N}\mathbf{,}{}^{\mathbf{15}}\mathbf{N}\mathbf{,}{}^{\mathbf{16}}\mathbf{O} \\ \mathbf{Molecular}\mathbf{ }\mathbf{mass}\mathbf{ }\mathbf{=}\mathbf{15}\mathbf{+}\mathbf{14}\mathbf{+}\mathbf{18} \\ \mathbf{=}\mathbf{45} \\ \mathbf{If}\mathbf{ }{\mathbf{N}}_{\mathbf{2}}\mathbf{O}\mathbf{ }\mathbf{contain}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{isotopes}\mathbf{ }{}^{\mathbf{14}}\mathbf{N}\mathbf{,}{}^{\mathbf{14}}\mathbf{N}\mathbf{,}{}^{\mathbf{16}}\mathbf{O} \\ \mathbf{Molecular}\mathbf{ }\mathbf{mass}\mathbf{ }\mathbf{=}\mathbf{2}\mathbf{\times }\mathbf{14}\mathbf{+}\mathbf{16} \\ \mathbf{=}\mathbf{44} \end{gathered}$$

Step 2: Finding the most common and least common Molecular mass

As the percentage abundance of 14N and 16O is very high as compared to their respective isotopes, so, the most common one is 44 (both N¹⁴ and O¹⁶) and the least common is 48 (both O¹⁸ and N¹⁵).