Section 4: The Law of Multiple Proportions

Captivated Chemistry Module 1: The Atom Section 4: The Law of Multiple Proportions

Given that you haven’t had very much exposure to chemical formulas, other than the ones you’ve read on the back of your shampoo bottle or seen in a pharmaceutical commercial, which of the following formulas seems the most plausible? In other words, which one seems most likely to be a real chemical compound?

CCl2F2

CCl1.21F3.42

Ever been so bored that you read the ingredients list on the back of your shampoo?

You probably answered the first one, simply because of all the compounds you know (think of water or carbon dioxide), none of them have decimal values as subscripts. Why not? Because elements cannot be subdivided smaller than individual atoms. It is of course possible to subdivide atoms of course, they can be divided into protons, neutrons, electrons, and even smaller particles. However, upon doing so, they lose their identity as particular elements. The reason you would never see the formula CCl1.21F3.42 is because it there is no such thing as 0.21 of a chlorine atom or 0.42 of a fluorine atom.

This simple idea is expressed in a somewhat more complicated way in the Law of Multiple Proportions. The Law of Multiple Proportions states that when two elements combine with each other to form different compounds, the masses of one element that combine with a fixed mass of the second element can be expressed as small, whole number ratios.
That’s a mouthful. It is best understood by looking at an example.

Phosphorous trichloride
Phosphorous pentachloride
Suppose that you have samples of two compounds, PCl3 and PCl5.  Through careful elemental analysis, you discover that the PCl3 sample contains 22.6% phosphorous by mass and 77.4% chlorine by mass.  The other compound, PCl5, contains 14.9% phosphorous by mass and 85.1% chlorine by mass.  Do these compounds abide by the Law of Definite Proportions?  They don’t have a choice!  
Sample % P %Cl Ratio of Cl to P
PCl3 22.6 77.4 3.42
PCl5 14.9 85.1 5.71
  Now, what did the law say?  The masses of one element that combine with a fixed mass of a second can be expressed as small whole number ratios.  To find this ratio, we would simply need to divide the ratios of Cl to P (the last column above).  5.71/3.42 works out to about 1.66.  Is that a ratio of small whole numbers?  It is if it is expressed as a fraction!  It would be 5/3, or a 5:3 ratio. Put another way, this simply means that chlorine can combine with phosphorous in groups of 5 or 3, but not in some fractional amount. You might be wondering why this is all so confusing.  The answer is simple.  You have grown up in a world where we all know that atoms combine in specific proportions, not random proportions.  You probably knew in kindergarten that the formula for water was specifically two hydrogens for every one oxygen.  The truth is that today, because we already know this, the Law of Multiple Proportions does more to confuse than to inform about the existence of atoms.  The take away for you from all of this should simply be that there was a time in history when this fact of the Law of Multiple Proportions was absolutely pivotal in our discovery of the atom.
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