Question

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

The mass of hydrogen combining with 1.00 g of nitrogen in hydrazine, ammonia, and hydrogen azide are given as \(1.44 \times 10^{-1}\) g, \(2.16 \times 10^{-1}\) g, and \(2.40 \times 10^{-2}\) g, respectively. By calculating the ratios of the mass of hydrogen in each compound to the mass of hydrogen in hydrogen azide, we get 0.6 (or 3/5) for hydrazine and 0.9 (or 9/10) for ammonia. Multiplying these ratios by the least common denominator (10) results in the simple whole number ratios of 6:9:1 for hydrazine, ammonia, and hydrogen azide, thus illustrating the Law of Multiple Proportions.

Step-by-step solution

Arrange the Data

In the problem, we are given the masses of hydrogen that combine with 1.00 g of nitrogen in three different compounds. Let's arrange the data for easy comparison: 1. Hydrazine: \(1.44 \times 10^{-1}\) g of hydrogen per 1.00 g of nitrogen 2. Ammonia: \(2.16 \times 10^{-1}\) g of hydrogen per 1.00 g of nitrogen 3. Hydrogen azide: \(2.40 \times 10^{-2}\) g of hydrogen per 1.00 g of nitrogen

Calculate the Ratios

Now, we need to find the ratios of the masses of hydrogen that combine with 1.00 g of nitrogen in these compounds. We can take the compound with the smallest mass of hydrogen (hydrogen azide) as the reference and calculate the ratios of the mass of hydrogen in other compounds to that in hydrogen azide. 1. Ratio of hydrogen in hydrazine to hydrogen azide: \(\frac{1.44 \times 10^{-1}}{2.40 \times 10^{-2}}\) 2. Ratio of hydrogen in ammonia to hydrogen azide: \(\frac{2.16 \times 10^{-1}}{2.40 \times 10^{-2}}\)

Simplify the Ratios

Let's simplify the calculated ratios: 1. Ratio of hydrogen in hydrazine to hydrogen azide: \(\frac{1.44 \times 10^{-1}}{2.40 \times 10^{-2}} = \frac{1.44}{2.40} \approx 0.6\) 2. Ratio of hydrogen in ammonia to hydrogen azide: \(\frac{2.16 \times 10^{-1}}{2.40 \times 10^{-2}} = \frac{2.16}{2.40} \approx 0.9\) Now, we need to find the smallest whole numbers that are in the same ratio as the calculated ones. Notice that 0.6 = 3/5 and 0.9 = 9/10. Taking the least common denominator (LCM) of 5 and 10, we obtain 10. We'll multiply both ratios by 10 to get whole numbers: 1. Ratio of hydrogen in hydrazine to hydrogen azide: \(\frac{3}{5} \times 10 = 6\) 2. Ratio of hydrogen in ammonia to hydrogen azide: \(\frac{9}{10} \times 10 = 9\)

Conclusion

The ratios of the mass of hydrogen that combine with a fixed mass of nitrogen in hydrazine, ammonia, and hydrogen azide are in a 6:9:1 proportion, which are indeed simple whole numbers. This confirms that the given data illustrates the Law of Multiple Proportions.

Key concepts

Understanding Chemical Composition

The chemical composition of a substance describes the proportion of each element within that substance. Much like a recipe might call for specific amounts of flour, sugar, and eggs to make a cake, chemical compounds require elements in certain proportions to form.

Let's use the example provided in the exercise to deepen our understanding. Hydrazine, ammonia, and hydrogen azide are all composed of nitrogen and hydrogen, but they differ in the ratio in which these elements combine. That is where the law of multiple proportions comes into play, providing a foundational understanding of how elements combine to form chemical compounds.

When we look at the mass of hydrogen that can combine with a fixed mass of nitrogen (1.00 g in this case), we see that it can vary depending on the compound. This variable ratio is a direct reflection of each compound's unique chemical composition and indicates that the same elements can form more than one compound by combining in different ratios - an idea at the heart of chemical versatility.

Delving into Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the substances involved in chemical reactions. Think of it as the 'mathematics' of chemistry.

In our example, stoichiometry allows us to calculate the precise amounts of nitrogen and hydrogen that combine to form different compounds. By determining the mass ratios, we can deduce the molecular formulas of the compounds in question. The exercise directs us to compare the mass of hydrogen that combines with a constant mass of nitrogen in three distinct nitrogen-hydrogen compounds. Using stoichiometry, we recognize that these mass ratios are simple whole numbers relative to each other, perfectly illustrating the law of multiple proportions. Understanding stoichiometry not only helps us solve textbook problems but also equips us with the tools to predict the outcomes of reactions, design chemical processes, and even develop new products.

Exploring Molecular Ratios

Molecular ratios express how many atoms of one element combine with another in a chemical compound. These ratios are at the core of how we understand compounds at the molecular level.

Reviewing our exercise, we see that nitrogen and hydrogen combine in different molecular ratios to form a variety of compounds. To interpret these molecular ratios, we use the mass ratios of hydrogen to nitrogen as a reference. By doing this, we are able to compare the different molecular structures that result from varying these ratios. For instance, a molecular ratio of hydrogen to nitrogen in ammonia is different from that in hydrazine, which leads to their distinct chemical and physical properties.

Understanding how to evaluate and apply molecular ratios is critical for students in mastering chemistry. These ratios do not only aid in predicting the proportions in which elements will combine but also give insight into the molecular geometry and empirical formulas, which pave the way for understanding more complex chemical behaviors.