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Chapter 2: Problem 103

Two elements, \(\mathrm{R}\) and \(\mathrm{Q}\), combine to form two binary compounds. In the first compound, \(14.0 \mathrm{~g}\) of \(\mathrm{R}\) combines with \(3.00 \mathrm{~g}\) of \(\mathrm{Q}\). In the second compound, \(7.00 \mathrm{~g}\) of \(\mathrm{R}\) combines with \(4.50 \mathrm{~g}\) of \(\mathrm{Q}\). 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

Expert verified
The formula of the first compound is R₃Q, and the data are in accord with the Law of Multiple Proportions.

Step by step solution

01

Determine the ratio of weights in the first compound

Divide the weight of the element R in the first compound by the weight of element Q in the first compound: Ratio of weights in the first compound = \(\frac{14.0\,\mathrm{g\,of\,R}}{3.00\,\mathrm{g\,of\,Q}} = \frac{14}{3}\)
02

Determine the ratio of weights in the second compound

Divide the weight of the element R in the second compound by the weight of element Q in the second compound: Ratio of weights in the second compound = \(\frac{7.00\,\mathrm{g\,of\,R}}{4.50\,\mathrm{g\,of\,Q}} = \frac{7}{4.5}\)
03

Calculate the ratio of both weight ratios

Now, we will find the ratio of the two weight ratios. If this ratio is a simple whole number, the data follow the Law of Multiple Proportions: $$\frac{\frac{14.0\,\mathrm{g\,of\,R}}{3.00\,\mathrm{g\,of\,Q}}}{\frac{7.00\,\mathrm{g\,of\,R}}{4.50\,\mathrm{g\,of\,Q}}} = \frac{\frac{14}{3}}{\frac{7}{4.5}}$$
04

Simplify the ratio

Simplify the ratio by cross-multiplying and reducing it to a whole number: $$\frac{\frac{14}{3}}{\frac{7}{4.5}} = \frac{14 \times 4.5}{3 \times 7} = \frac{63}{21}$$ The simplified ratio is \(\frac{63}{21} = 3\), which is a simple whole number.
05

Determine the formula of the first compound

Since the ratio of weight ratios turned out to be 3, the proportion of R and Q in the first compound would be 3 times that in the second compound. Since the second compound's formula is RQ, the first compound's formula would be R₃Q (3 times Q for each R). Therefore, the formula of the first compound is R₃Q, and the data are in accord with the Law of Multiple Proportions.

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Most popular questions from this chapter

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