Question

Methane contains 75 % carbon and 25% hydrogen, by mass. Carbon dioxide contains 27.27 % carbon and 72.73% oxygen, by mass. Water contains 11.11 % hydrogen and 88.89% oxygen, by mass. Show that the data illustrates the law of reciprocal proportion. 

Answer 1

Methane and carbon dioxide, both contains carbon and hence, carbon may be considered as the third element. Now, let the fixed mass of carbon = 1 gm. Then, 

the mass of hydrogen combined with 1 gm carbon in methane = 25/25 = 1/3 gm.

and the mass of oxygen combined with 1 gm carbon in carbon dioxide = 72.73 / 27.27 = 8/3 gm.

Hence, the mass ratio of hydrogen and oxygen combined with the fixed mass of carbon, r₁  = 1/8 : 8/3 = 1/8

Now, the mass ratio of hydrogen and oxygen in water, r₂ =11.11 / 88.89 = 1/8

As r₁ and r₂ are same , the data is according to the law of reciprocal proportion.