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Chapter 2: Problem 14

Phosphorus forms two compounds with chlorine. In the first compound, \(1.000 \mathrm{g}\) of phosphorus is combined with \(3.433 \mathrm{g}\) chlorine, and in the second, \(2.500 \mathrm{g}\) phosphorus is combined with \(14.308 \mathrm{g}\) chlorine. Show that these results are consistent with Dalton's law of multiple proportions.

Short Answer

Expert verified
The ratios of the masses of chlorine that combine with a fixed mass of phosphorus in the two compounds are approximately 5/3. This is a simple whole number ratio, thus proving these results to be consistent with Dalton's law of multiple proportions.

Step by step solution

01

Identify given data

Identify and list the given data. The mass of phosphorus and chlorine in the first compound is 1.000 g and 3.433 g respectively. For the second compound, the masses are 2.500 g and 14.308 g respectively.
02

Calculate the mass ratios

Calculate the ratios of the masses of chlorine that combine with a fixed mass of phosphorus for both compounds. For the first compound, it's \(\frac{3.433g}{1.000g} = 3.433\). For the second compound, it's \(\frac{14.308g}{2.500g} = 5.7232\). These are not simple whole numbers but they might be in lowest terms.
03

Simplify the ratios

To check if these ratios simplify to whole numbers, calculate the ratio of the two previous ratios. That is, \(\frac{5.7232}{3.433} = 1.667 ≈ 5/3\). Thus, we can conclude that the ratios are indeed whole numbers when in lowest terms, confirming Dalton's law.

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