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Chapter 1: Problem 29

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 ratios of hydrogen to nitrogen in hydrazine, ammonia, and hydrogen azide are \(1.44 \times 10^{-1}, 2.16 \times 10^{-1},\) and \(2.40 \times 10^{-2}\), respectively. The ratios between these mass ratios are: hydrazine to ammonia \(\frac{2}{3}\), hydrazine to hydrogen azide \(6\), and ammonia to hydrogen azide \(\frac{9}{2}\). These ratios are small whole numbers, illustrating the law of multiple proportions.

Step by step solution

01

Calculate the mass ratios of hydrogen to nitrogen in each compound

For each compound, we are given the mass of hydrogen that combines with 1.00 g of nitrogen. Let's calculate the mass ratio for each compound: 1. For hydrazine: \( \frac{1.44 \times 10^{-1} \mathrm{g}}{1.00 \mathrm{g}} = 1.44 \times 10^{-1} \) 2. For ammonia: \( \frac{2.16 \times 10^{-1} \mathrm{g}}{1.00 \mathrm{g}} = 2.16 \times 10^{-1} \) 3. For hydrogen azide: \( \frac{2.40 \times 10^{-2} \mathrm{g}}{1.00 \mathrm{g}} = 2.40 \times 10^{-2} \)
02

Find the ratios between the mass ratios of each compound

Now we'll find the ratios between the mass ratios of hydrogen to nitrogen in each compound: 1. Ratio between hydrazine and ammonia: \( \frac{1.44 \times 10^{-1}}{2.16 \times 10^{-1}} = \frac{1.44}{2.16} \) 2. Ratio between hydrazine and hydrogen azide: \( \frac{1.44 \times 10^{-1}}{2.40 \times 10^{-2}} = \frac{1.44}{2.40 \times 10^{-1}} \) 3. Ratio between ammonia and hydrogen azide: \( \frac{2.16 \times 10^{-1}}{2.40 \times 10^{-2}} = \frac{2.16}{2.40 \times 10^{-1}} \)
03

Simplify the ratios

Now, we simplify these ratios to check if they are small whole numbers: 1. Ratio between hydrazine and ammonia: \( \frac{1.44}{2.16} = \frac{8}{12} = \frac{2}{3} \) (small whole numbers: 2 and 3) 2. Ratio between hydrazine and hydrogen azide: \( \frac{1.44}{2.40 \times 10^{-1}} = \frac{6}{1} \) (small whole numbers: 6 and 1) 3. Ratio between ammonia and hydrogen azide: \( \frac{2.16}{2.40 \times 10^{-1}} = \frac{9}{2} \) (small whole numbers: 9 and 2) The ratios between the mass ratios of hydrogen to nitrogen in each compound are small whole numbers, which proves that the given compounds and their respective data illustrate the law of multiple proportions.

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Most popular questions from this chapter

Indium oxide contains \(4.784 \mathrm{g}\) of indium for every \(1.000 \mathrm{g}\) of oxygen. In \(1869,\) when Mendeleev first presented his version of the periodic table, he proposed the formula \(\operatorname{In}_{2} \mathrm{O}_{3}\) for indium oxide. Before that time it was thought that the formula was InO. What values for the atomic mass of indium are obtained using these two formulas? Assume that oxygen has an atomic mass of \(16.00 .\)

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