Two samples of a compound containing only nitrogen and oxygen are decomposed into their constituent elements. The first sample produces 2.602 g of nitrogen and 6.400 g of oxygen. The second sample produces 3.903 g of nitrogen. If these two samples are consistent with the law of constant composition, how much oxygen is produced by the second sample?
According to the law of constant composition both samples should have equal mass ratios of O and N.
In sample one we have 2.602g of N and 6.4g of O.
`N:O = 2.602/6.4`
For second sample also this mass ratio is applicable.
In the second sample we have 3.903g of N. Let us say we have xg of O.
`N:O = 3.903:x`
`2.602/6.4 = 3.903:x`
`2.602x = 3.903xx6.4`
`x = 9.6`
So from the second sample we get 9.6g of O.
The ratio of nitrogen to oxygen will be the same no matter what the starting quantities are.
The ratio of nitrogen to oxygen will be:
Therefore, you can use a simple proportion:
`2.602/6.400 = 3.903/x`
Solve for "x" by cross multiplying:
`2.602x = 24.9792`
`x = 9.600`
9.600 grams of oxygen would be produced in the second sample. Remember that you need four sig figs as well since all your given values have four sig figs.