Problem 13 - Chemistry: The Central Science in SI Units, Global Edition

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

The oxygen-to-nitrogen mass ratios for the four compounds are approximately 0.571, 1.142, 2.284, and 2.855. These values can be approximated by simple whole-number ratios (1, 2, 4, and 5), supporting Dalton's atomic theory which states that elements combine in simple whole-number ratios to form compounds.

Step 1: Calculate the mass of oxygen per gram of nitrogen in each compound.

To find the ratio of the mass of oxygen to the mass of nitrogen in a compound, we divide the mass of oxygen in the compound by the mass of nitrogen. For the given problem, there are four different compounds formed, and we can calculate the oxygen-to-nitrogen mass ratio for each of them. Mass of Nitrogen = 30.82 g Compound 1: Mass of Oxygen: 17.60 g Oxygen-to-nitrogen mass ratio = \( \frac{17.60}{30.82} \) Compound 2: Mass of Oxygen: 35.20 g Oxygen-to-nitrogen mass ratio = \( \frac{35.20}{30.82} \) Compound 3: Mass of Oxygen: 70.40 g Oxygen-to-nitrogen mass ratio = \( \frac{70.40}{30.82} \) Compound 4: Mass of Oxygen: 88.00 g Oxygen-to-nitrogen mass ratio = \( \frac{88.00}{30.82} \) Now, let's compute these ratios.

Step 2: Compute the ratios of oxygen-to-nitrogen mass.

Compute the oxygen-to-nitrogen mass ratios by dividing the mass of oxygen by the mass of nitrogen for each compound. Compound 1: Oxygen-to-nitrogen mass ratio = \( \frac{17.60}{30.82} \approx 0.571 \) Compound 2: Oxygen-to-nitrogen mass ratio = \( \frac{35.20}{30.82} \approx 1.142 \) Compound 3: Oxygen-to-nitrogen mass ratio = \( \frac{70.40}{30.82} \approx 2.284 \) Compound 4: Oxygen-to-nitrogen mass ratio = \( \frac{88.00}{30.82} \approx 2.855 \)

Step 3: Analyze the results in the context of Dalton's atomic theory.

Dalton's atomic theory states that elements combine in simple whole-number ratios to form compounds. Therefore, if a pattern exists in the ratios obtained in step 2, it would support Dalton's atomic theory. Let's examine the oxygen-to-nitrogen mass ratios calculated previously: Compound 1: 0.571 Compound 2: 1.142 Compound 3: 2.284 Compound 4: 2.855 Observe that these mass ratios can be approximated by simple whole-number ratios: Compound 1: 1 Compound 2: 2 Compound 3: 4 Compound 4: 5 These approximations show that the compounds are formed according to simple whole-number ratios of oxygen to nitrogen atoms, which supports Dalton's atomic theory.

Key Concepts

Chemical Compounds

Chemical compounds are substances made from two or more elements that are chemically bonded together. In this exercise, the compounds are formed by the combination of nitrogen and oxygen. Each different ratio of oxygen to nitrogen represents a different chemical compound.

• The process of bond formation results in stable substances with distinct properties.
• Compounds are characterized by a specific ratio of elements, determining their unique structure and properties.

When nitrogen and oxygen combine to form these compounds, they follow specific atomic and mass ratios, leading to unique compounds like Nitrogen dioxide (NO2), Dinitrogen tetroxide (N2O4), and others. Understanding the composition and structure of these compounds helps us grasp foundational concepts in chemistry, such as how elements interact and the laws governing these interactions. This exercise highlights the diversity in chemical compounds when varying the amounts of combining elements.

Mass Ratios

Mass ratios are crucial when discussing chemical compounds as they describe the proportion of each element present in a compound. In the exercise, we calculated the mass of oxygen that combines with a fixed mass of nitrogen (30.82 g) to form various compounds.

• By dividing the mass of oxygen by the mass of nitrogen, we obtain the mass ratios of each compound.
• For example, the mass ratio for compound 1 is calculated as \( \frac{17.60}{30.82} \approx 0.571 \).

These ratios allow chemists to determine the fixed amounts of each element that combine during chemical reactions. In sum, mass ratios provide insight into the stoichiometry of compounds and ensure the conservation of mass during reactions. This idea aligns with the law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction.

Law of Multiple Proportions

The law of multiple proportions is a fundamental concept stemming from Dalton’s atomic theory. It states that when two elements form more than one compound, the ratios of the masses of one element that combine with a constant mass of the second element are in simple whole-number ratios.

• In this exercise, this law is illustrated by the different ratios of oxygen that combine with 30.82 g of nitrogen.
• These ratios—\(0.571\), \(1.142\), \(2.284\), and \(2.855\)—show a pattern of approximations to whole numbers: \(1:2:4:5\).

This pattern demonstrates how variations in the amounts of elements combined lead to compounds with different properties, yet still follow a predictable and rational order of whole number ratios. This law is key to understanding chemical multi-compound formation and supports the idea that matter is composed of fixed ratios of relatively tiny particles, known as atoms.

Atomic Theory Concepts

Dalton’s atomic theory was groundbreaking as it introduced the idea that matter is composed of atoms, the indivisible building blocks of elements. This concept underpins our understanding of how elements combine to form compounds and how they follow specific patterns as observed in the law of multiple proportions.

• According to Dalton, atoms of different elements can combine in fixed whole number ratios to form compounds.
• This theory explains why the oxygen-to-nitrogen mass ratios in the exercise align with simple whole numbers.

Atomic theory provides the framework for understanding chemical reactions, chemical bonding, and the conservation of mass in reactions. It is foundational to modern chemistry and helps explain the reactivity, composition, and properties of matter. Through Dalton’s vision, scientists today can predict the behavior of elements and compounds with remarkable precision, using these basic yet profound concepts that started the journey into understanding the atomic nature of matter.