In each case, calculate the appropriate ratio to show that the information given is consistent with the law of multiple proportions. (a) Both ammonia (NH3) and hydrazine (N2H4) are composed of nitrogen and hydrogen. Ammonia contains 0.2158 g hydrogen for every gram of nitrogen. Hydrazine contains 0.1439 g 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 (N20), which is also known as dinitrogen monoxide. Nitric oxide contains 1.142 g oxygen for every gram of nitrogen. Nitrous oxide contains 0.571 g oxygen for every gram of nitrogen.

The Law of Multiple Proportions states that when two elements A and B combine to form two or more compounds, the masses of B that combine with a given mass of A are in the ratios of small whole numbers.

That is, if one compound has a ratio r₁ and the other has a ratio r₂, the ratio of the ratios r is in small whole numbers.

(a) Ammonia and hydrazine.

In ammonia, the mass ratio of H:N is r₁ = 0.2158/1

In hydrazine, the mass ratio of H:N is r₂ = 0.1439/1

The ratio of the ratios is:

[tex]r = \dfrac{r_{1}}{r_{2}} = \dfrac{ 0.2158}{0.1439} = \dfrac{1.500 }{1} = \dfrac{2.999}{2} \approx \mathbf{\dfrac{3}{2}}\\\\\text{The relative amounts of H in the two compounds are in the ratio }\boxed{\mathbf{\dfrac{3}{2}}}[/tex]

(b) Nitrogen oxides

In nitrogen monoxide, the mass ratio of O:N is r₁ = 1.142/1

In dinitrogen monoxide, the mass ratio of O:N is r₂ = 0.571/1

The ratio of the ratios is:

[tex]r = \dfrac{r_{1}}{r_{2}} = \dfrac{ 1.142}{0.571} = \dfrac{2.000 }{1} \approx \mathbf{\dfrac{2}{1}}\\\\\text{The relative amounts of O in the two compounds are in the ratio }\boxed{\mathbf{\dfrac{2}{1}}}[/tex]