Question

Consider 100.0 g samples of two different compounds consisting only of vanadium and oxygen. one compound contains 61.4 g of vanadium and the other has 76.1 g of vanadium. find the ratio:

Answer 1

Answer:

2:1

Explanation:

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.

1. Compound 1

Mass of O = 100.0 - 61.4 = 38.6 g

$r_{1} = \dfrac{\text{mass of O}}{\text{mass of V}} = \dfrac{ 38.6}{61.4} = 0.6287$

2. Compound 2

Mass of O = 100.0 - 76.1 = 23.9 g

$r_{2} = \dfrac{ 23.9}{76.1} = 0.3141$

3. Ratio of the ratios

$r = \dfrac{r_{1}}{r_{2}} = \dfrac{ 0.6287}{0.3141} = \dfrac{2.00}{1} \approx 2\\\\\text{The relative amounts of O per gram of V are in the ratio }\boxed{\mathbf{\dfrac{2}{1}}}$

For example. the compounds might be VO₂ and VO.