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Chapter 2: Problem 37

Hydrazine, ammonia, and hydrogen azide all contain only nitrogen and hydrogen. The mass of hydrogen that combines with \(1.00 \mathrm{~g}\) of nitrogen for each compound is \(1.44 \times 10^{-1} \mathrm{~g}\). \(2.16 \times 10^{-1} \mathrm{~g}\), and \(2.40 \times 10^{-2} \mathrm{~g}\), respectively. Show how these data illustrate the law of multiple proportions.

Short Answer

Expert verified
The mass of hydrogen that combines with 1.00 g of nitrogen for each compound, Hydrazine, Ammonia, and Hydrogen azide, are \(1.44 \times 10^{-1}\) g, \(2.16 \times 10^{-1}\) g, and \(2.40 \times 10^{-2}\) g, respectively. Comparing the mass ratios, we have the ratios of Hydrazine to Ammonia: 2:3, and Ammonia to Hydrogen azide: 3:1. Since the ratios are in small whole numbers, these data illustrate the law of multiple proportions.

Step by step solution

01

Write down the given information

We have three compounds formed by the combination of nitrogen and hydrogen: 1. Hydrazine (\(1.44 \times 10^{-1}\) g of hydrogen for 1 g of nitrogen) 2. Ammonia (\(2.16 \times 10^{-1}\) g of hydrogen for 1 g of nitrogen) 3. Hydrogen azide (\(2.40 \times 10^{-2}\) g of hydrogen for 1 g of nitrogen)
02

Compare the mass ratios of hydrogen per 1 g of nitrogen

We will find the ratio between each pair of compounds: Ratio of Hydrazine to Ammonia: \( \frac{1.44 \times 10^{-1}}{2.16 \times 10^{-1}} \) Ratio of Ammonia to Hydrogen azide: \( \frac{2.16 \times 10^{-1}}{2.40 \times 10^{-2}} \)
03

Calculate the ratios

Calculate the mass ratios between the compounds: For Hydrazine to Ammonia: \( \frac{1.44 \times 10^{-1}}{2.16 \times 10^{-1}} = 0.6667 \) For Ammonia to Hydrogen azide: \( \frac{2.16 \times 10^{-1}}{2.40 \times 10^{-2}} = 9 \)
04

Simplify the ratios into small whole numbers

The first ratio is not a whole number, so we will multiply both ratios in order to simplify them into whole numbers. For Hydrazine to Ammonia: \( 0.6667 * 3 = 2 \) For Ammonia to Hydrogen azide: \( 9 * 1 = 9 \) Now we have simplified the ratios as: Ratio of Hydrazine to Ammonia: 2:3 Ratio of Ammonia to Hydrogen azide: 3:1
05

Conclude the result

The ratios of the mass of hydrogen that combines with 1.00 g of nitrogen for each compound follow the law of multiple proportions as the ratios between the compounds are in small whole numbers. Therefore, the given data illustrates the law of multiple proportions.

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