# What does the term "simple" in the phrase "simple whole number ratio" mean in Gay Lussac's law?

What does the term "simple" mean in the phrase "simple whole number ratio" in Gay Lussac's law? I have searched this site as well as different sites on the internet. The answer to one question on this site states that it indicates that the numbers are small whole numbers. Another site stated that the terms of the ratio are not decimal numbers while another site states that the terms of the ratio are in simplest terms that is reduced form.

• – user7951
Jan 1 '17 at 16:49

3/2 is simple. 45498334/9232493 is not.

The reason it works is because reactions of gases producing gases involve relatively simple compounds. If they were complicated, the molecular weight would likely be high enough that the substance would not be a gas.

This is akin to Loong's comment about the Law of Multiple Proportions, which also mentions "small whole number ratios." The difference is that for the Law of Multiple Proportions, "small" ratios doesn't apply in the case of something like palytoxin ($\ce{C129H223N3O54}$).

But palytoxin isn't a gas. For the reason mentioned above, you're almost certain to get simple coefficients for gas to gas reactions.

• So "small" here only means that it is not large and not anything else like decimal, in simplest terms. Correct?
– MrAP
Jan 2 '17 at 1:15
• Yes. It's just from the fact that the stoichiometric ratios for gas reactants producing gas products are small and simple.
– Zhe
Jan 2 '17 at 1:45
• One more question: Don't you mean that the volumes are simple after reducing them to the lowest terms? Otherwise they may be large(since we can take any volume of gases as reactants) but still, they have a common factor and on dividing them by this common factor they become small (simple), i.e., to say that, in the ratio of the volumes in their lowest terms, the volumes are simple.
– MrAP
Feb 4 '17 at 19:43
• This doesn't have anything to do with volumes. It's just ratios of atoms. You just happen to be using gases, so assuming their ideal (they're not) you could argue that the number of moles are related to the volumes, but that hides the information encoded in the stoichiometry of each substance.
– Zhe
Feb 5 '17 at 15:13
• What do you mean by saying " but that hides the information encoded in the stoichiometry of each substance"?
– MrAP
Feb 5 '17 at 15:52

It means that both terms are reduced to the smallest whole number possible so that the numerator and denominator are co prime.