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Chapter 2: Problem 40

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 \(\mathrm{RQ}\), what is the formula of the first compound?

Short Answer

Expert verified
The data are in accord with the law of multiple proportions, as the ratio of the masses of R in the two compounds is 1:2, which is a small whole number ratio. Since the formula of the second compound is RQ, the first compound has twice as much R, making the formula of the first compound \(\mathrm{R_2Q}\).

Step by step solution

01

Calculate the ratio of the mass of R in both compounds

In the first compound, the mass of R is 14.0 g and the mass of Q is 3.00 g. In the second compound, the mass of R is 7.00 g and the mass of Q is 4.50 g. Now let's calculate the ratio of the masses of R in these two compounds: Ratio = (Mass of R in second compound / Mass of Q in the second compound) / (Mass of R in first compound / Mass of Q in the first compound)
02

Evaluate the ratio and determine whole-number proportions

Now we'll plug in the given mass values: Ratio = (7.00 g / 4.50 g) / (14.0 g / 3.00 g) Ratio = (7.00 / 4.50) / (14.0 / 3.00) After evaluating, we get: Ratio = (7/4.5) / (14/3) = (7/4.5) × (3/14) = 1/2 The ratio is 1:2, which is a ratio of small whole numbers, so the data are in accord with the law of multiple proportions.
03

Find the formula of the first compound

Since the ratio is 1:2, this means that for the same amount of Q, the first compound has twice as much R as the second compound. Given that the formula for the second compound is RQ, the formula for the first compound will have twice the number of R atoms than the second one. Therefore, the formula for the first compound is \(\mathrm{R_2Q}\).

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