Question

nitrogen reacts with oxygen to form 2 compounds. Compund A contains 2.8 g of nitrogen for each 1.6 g of oxygen. Compound B contains 5.6g of nitrogen for each 9.6g of oxygen. What is the lowest whole number mass ratio of nitrogen that combines with a given mass of oxygen?

Answer 1

well, it would be

A 2.8/1.6= ???
or
B 5.6/9.6=???
obviously neither is a whole number.

Assume 100 g of Nitrogen.

then
m(2.8/1.6)+n(5.6/9.6)=k(100)

where k is an integer, and m,n are grams of oxygen in each compound.
But m+n=100

m=100-n
(100-n)(2.8/1.6)+n(5.6/9.6)=100 k
(100-n)1.75+ .583n=100k
-1.1666n=100k-175
n=-85.71k+150
if k=1, then n=14.3

m= 85.7

, k=1
in that, one has grams O=100, grams N= 14.3*2.8/1.6+85.7*5.6/9.8=25.7+50 g N or 75gN, so I get 3/4 ratio of N/O