Question $1$: In each case, calculate the appropriate ratio to show that the information given is consistent with the law of multiple proportions.

$($a$)$ Both ammonia $(N{H}_3)$ and hydrazine $(N_2{H}_4)$ are composed of nitrogen and hydrogen. Ammonia contains $0\mathrm{.}2158g$ hydrogen for every gram of nitrogen. Hydrazine contains $0\mathrm{.}1439g$ hydrogen for every gram of nitrogen.

$($b$)$ Two of the compounds that consist of nitrogen and oxygen are nitric oxide, also known as nitrogen monoxide $(NO)$ and nitrous oxide $(N_{2}O),$ which is also known as dinitrogen monoxide. Nitric oxide contains $1\mathrm{.}142g$ oxygen for every gram of nitrogen, Nitrous oxide contains $0\mathrm{.}571g$ oxygen for every gram of nitrogen.