Question

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

Short answer

The formula of the first compound is R₃Q.

Step-by-step solution

Definition of multiple proportions

The law of multiple proportions explains that if two elements produce a series of compounds, then the ratio of the masses of the second element is combined with one gram of the first element. It is always reduced to whole numbers. The first compound 14grams of R reacts with 3 grams of Q.

Calculation of compounds

In other words, 1 gram of Q reacts with $4\frac{2}{3}$grams of R. Second compound, 7 grams of R reacts with 4.5 grams of Q. In other words, 1 gram of Q reacts with 1.55556 grams of R.Applying the law of multiple proportions (Q is the first element at a constant mass of one gram), the ratio of the mass of R creates a simple whole number ratio:

$$\begin{gathered} \frac{\text{Compound 1}}{\text{Compound 2}}=\frac{4.6667}{1.5556} \\ \frac{\text{Compound 1}}{\text{Compound 2}}=3 \end{gathered}$$

Conclusion

The formula of the second compound is RQ. The figures above show that one atom of R of the second compound is directly proportional to three atoms of compound1. Therefore, the formula of compound one is R₃Q.