# 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...

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?

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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.

Mass ratio

`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.

Mass ratio

`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:

`2.602/6.400`

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.