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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?


R + Q = R?Q?
14 &nbsp 3

R + Q = RQ
7&nbsp &nbsp 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 &nbsp 3

R + Q = RQ
7&nbsp &nbsp 4.5

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

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