Problem 13 - Chemistry: The Central Science

Question

A chemist finds that \(30.82 \mathrm{~g}\) of nitrogen will react with \(17.60\), \(35.20,70.40\), or \(88.00 \mathrm{~g}\) of oxygen to form four different compounds. (a) Calculate the mass of oxygen per gram of nitrogen in each compound. (b) How do the numbers in part (a) support Dalton's atomic theory?

Step-by-Step Solution

Answer

(a) The mass ratios of oxygen to nitrogen for each compound are approximately 0.571, 1.142, 2.284, and 2.855. (b) The mass ratios support Dalton's atomic theory because they can be expressed as integer multiples (1, 2, 4, and 5) of the smallest ratio, demonstrating that elements combine in fixed integral ratios to form compounds.

Step 1: Calculate mass ratios of oxygen to nitrogen for each compound.

To find the mass ratio of oxygen to nitrogen, we need to divide the mass of oxygen by the mass of nitrogen for each compound. Let's denote the compounds as A, B, C, and D, with given masses of oxygen as 17.60 g, 35.20 g, 70.40 g, and 88.00 g, respectively. The mass of nitrogen is constant at 30.82 g for all compounds. Compound A: Mass ratio (O/N) = \( \frac{17.60}{30.82} \) Compound B: Mass ratio (O/N) = \( \frac{35.20}{30.82} \) Compound C: Mass ratio (O/N) = \( \frac{70.40}{30.82} \) Compound D: Mass ratio (O/N) = \( \frac{88.00}{30.82} \)

Step 2: Calculate the mass ratios for each compound.

Now we'll perform the calculations to find the mass ratios: Compound A: Mass ratio (O/N) = \( \frac{17.60}{30.82} \approx 0.571 \) Compound B: Mass ratio (O/N) = \( \frac{35.20}{30.82} \approx 1.142 \) Compound C: Mass ratio (O/N) = \( \frac{70.40}{30.82} \approx 2.284 \) Compound D: Mass ratio (O/N) = \( \frac{88.00}{30.82} \approx 2.855 \)

Step 3: Relate the mass ratios with Dalton's atomic theory.

Dalton's atomic theory states that elements combine in fixed ratios (called integral ratios) to form compounds. To determine if the mass ratios support Dalton's atomic theory, let's check if these ratios can be expressed as integer multiples by finding the lowest ratio and taking the ratios of all other compounds with respect to it. Looking at the calculated mass ratios, compound A has the smallest ratio (approximately 0.571). Now, let's divide each mass ratio by this smallest ratio: Compound A: \( \frac{0.571}{0.571} = 1 \) Compound B: \( \frac{1.142}{0.571} = 2 \) Compound C: \( \frac{2.284}{0.571} = 4 \) Compound D: \( \frac{2.855}{0.571} \approx 5 \) As seen above, the mass ratios for each compound can be expressed as integer multiples (1, 2, 4, and 5) of the smallest ratio. Hence, this supports Dalton's atomic theory.

Key Concepts

Mass Ratios

Mass ratios are a fundamental aspect of understanding compound formation in chemistry. When two elements, like nitrogen and oxygen, react to form compounds, they do so in proportions that can be represented by mass ratios.

To determine the mass ratio of oxygen to nitrogen in a compound, you simply divide the mass of oxygen by the mass of nitrogen used. This ratio tells you how much oxygen is needed to combine with a given amount of nitrogen.

• Compound A's mass ratio: approximately 0.571
• Compound B's mass ratio: approximately 1.142
• Compound C's mass ratio: approximately 2.284
• Compound D's mass ratio: approximately 2.855

Calculating these ratios allows us to see a consistent pattern, helping to support theoretical concepts like Dalton's atomic theory.

Compound Formation

Compound formation is an essential concept in chemistry, explaining how elements react to form new substances with unique properties. When nitrogen and oxygen react, they form compounds by combining in specific proportions.

This process occurs at the atomic level, where atoms of nitrogen bond with atoms of oxygen. Chemists measure the mass of each element involved to determine how much of one element combines with a given amount of another.

The creation of compounds from elements is rooted in the stability achieved when atoms share, gain, or lose electrons to form chemical bonds. Each compound formed can have very different chemical and physical properties, contributing to a vast diversity in matter.

Fixed Ratios

Dalton's atomic theory introduced the concept that elements combine in fixed ratios to form compounds. These ratios are not random but follow specific patterns based on the nature of the elements involved.

The theory helps us understand that for a chemical reaction between nitrogen and oxygen to create a stable compound, the elements must combine in integral ratios, meaning integer multiples of each other.

• In our example, we observed mass ratios: 1, 2, 4, and 5.
• These suggest that compounds formed from nitrogen and oxygen do so in simple whole-number proportions.

Such a pattern strongly supports the principles laid out in Dalton's theory, which holds that atoms don't combine randomly or in arbitrary amounts, but follow strict numerical relationships.

Nitrogen and Oxygen Reactions

Reactions involving nitrogen and oxygen are classic examples of how elements can combine to form multiple compounds, each with distinct properties. Such reactions illustrate key principles of chemical combination, including Dalton's law of multiple proportions.

For instance, nitrogen and oxygen can form compounds like nitrogen dioxide ( ext{NO}_2), dinitrogen tetroxide ( ext{N}_2 ext{O}_4), and others, each having different oxygen to nitrogen ratios. These ratios align with Dalton's theory, reinforcing how elements combine in fixed, simple ratios to form different products.

• Reactions can result in compounds with varying oxygen content, contributing to different mass ratios like 1, 2, 4, and 5.
• Such diversity arises from the flexible ways in which nitrogen atoms can bond with oxygen atoms.

The reaction between nitrogen and oxygen serves as a perfect illustration of fundamental concepts in chemical science, showing how elemental ratios produce a variety of compounds.