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?
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
To find the lowest whole number mass ratio of nitrogen that combines with a given mass of oxygen, we need to calculate the ratio of nitrogen to oxygen for both compounds and then simplify the ratio to its lowest whole number form.
Let's start with Compound A:
Given: 2.8 g of nitrogen per 1.6 g of oxygen
To calculate the mass ratio, we divide the mass of nitrogen by the mass of oxygen:
2.8 g ÷ 1.6 g = 1.75
Next, let's calculate the mass ratio for Compound B:
Given: 5.6 g of nitrogen per 9.6 g of oxygen
Again, we divide the mass of nitrogen by the mass of oxygen:
5.6 g ÷ 9.6 g = 0.5833333333333333
Now, we need to simplify these ratios to their lowest whole number form.
For Compound A:
The mass ratio is 1.75, which means that for every 1.75 g of nitrogen, there is 1 g of oxygen. To simplify this ratio to its lowest whole number form, we multiply both sides by 4 (to convert 1.75 to a whole number):
1.75 × 4 = 7 : 4
Therefore, the simplified mass ratio for Compound A is 7 : 4.
For Compound B:
The mass ratio is 0.5833333333333333, which means that for every 0.5833333333333333 g of nitrogen, there is 1 g of oxygen. To simplify this ratio to its lowest whole number form, we can multiply both sides by a number that makes the nitrogen mass a whole number (for convenience, we can choose 3):
0.5833333333333333 × 3 = 1.75 : 3
Therefore, the simplified mass ratio for Compound B is 7 : 12.
To find the lowest whole number mass ratio of nitrogen that combines with a given mass of oxygen, we need to compare the ratios of Compound A and Compound B. The common factor between the two ratios is 7. Therefore, the lowest whole number mass ratio of nitrogen to oxygen is 7 : 4.