Law of Multiple Proportions

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Two elements, R and Q, combine to form two binary compounds. In the first compound, 14.0 g of R combines with 3.00 g of Q. In the second compound, 7.00 g of R combines with 4.50 g of Q. Show that these data are in accord with he law of multiple proportions. If the formula of the second compound is RQ, what is the formula of the first compound?

Thanks.

R + Q = R?Q?
14   3

R + Q = RQ
7    4.5

The Law of multiple proportions says that when two elements form a series of compounds (such as R and Q above), the ratio of Q per 1g R in compound 1 to Q per 1g R in compoound 2 will be small whole numbers. You can show this by the following.
Compound 1. 3g Q/14g R = 0.214g Q/1g R
Compound 2. 4.5g Q/7g R = 0.643g Q/1g R

Now take the ratio of the amounts of Q/ 1 g R and we have 0.214/0.643 = 1/3 and 1:3 is the ratio of small whole numbers for Q between compounds 1 and 2. You can do the same thing by using 1 g Q as the base and calculating the ratio between the amounts of R between compounds 1 and 2. I will leave that for you to do. The first one will be 14g R/3g Q = ?? etc.

As for the formula, if the second one is RQ, then we look at the ratio. Copying from above,
R + Q = R?Q?
14   3

R + Q = RQ
7    4.5

R14/7Q3/4.5 =
R2Q0.666 =
R2/0.666Q0.666/0.666 =
R3Q1 =
R3Q
Check my thinking. Check my arithmetic.
I hope this helps.

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