Antimony forms 2 chlorides having widely different properties. One of the chlorides is a solid that melts at 73*C and contains 46.5% chlorine by mass. The other is a liquid that boils at 140*C and contains 59.3% chlorine by mass. Show how these results illustrate the low of multiple proportions .

Answer 1

Sb(1)Cl(1) and Sb(2)Cl(2) means the first Sb compound and the second Sb compound.
.....Sb(1)...Cl(1).......Sb(2)...Cl(2)
.....53.5%..46.5%........40.7%..59.3%

What we want to do first is to determine the mass Cl that combines with 1 g Sb.
That is 46.5 x (1/53.5) = 0.869 for #1
That is 59.3 x (1/40.7) = 1.457 for #2

The numbers for #1 and #2 should be in the ratio of small whole numbers. Let's see if they are.
0.869 for #1
1.457 for #2.

The easy way to find the ratio is to divide the smallest number by itself which assures us of getting 1.00 for that value. Then we divide the other number by the same small number. This gives us
0.869/0.869 = 1.00
1.457/0.869 = 1.67
which shows that 1.00 to something doesn't work (1.67 isn't a whole number). BUT we can try other small numbers. To do this the easy way is to just multiply each of the numbers above by 2,3,4,5,6 etc as a trial and error and see if those small whole numbers will work.
1.00 x 2 = 2.00
1.67 x 2 = 3.34
No again since 3.34 isn't a whole number. Try 3
1.00 x 3 = 3.00
1.00 x 1.67 = 5.01 which can be rounded to 5.00. (Why is it not EXACTLY 5.0? Because we have rounded above and used only three significant figures.
Bingo! small whole numbers; therefore, the formula for the first one is SbCl3 and the formula for the second one is SbCl5. PLEASE NOTE that the formulas were determined WITHOUT using the atomic mass of Sb or Cl. This is an important concept since atomic masses were not known years and years ago BUT the formulas could be determined anyway.