Question

A chemist finds that \(30.82 \mathrm{~g}\) of nitrogen will react with \(17.60 \mathrm{~g}\), \(35.20 \mathrm{~g}, 70.40 \mathrm{~g},\) 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?

Short answer

The mass of oxygen per gram of nitrogen for the four compounds are approximately 0.571, 1.142, 2.284, and 2.855, respectively. These mass ratios are related by simple whole numbers (1, 2, 4, and 5 times the first ratio), supporting Dalton's atomic theory that elements combine in fixed, whole-number ratios to form compounds.

Step-by-step solution

Find the mass of oxygen per gram of nitrogen for each compound

We have four compounds with different masses of oxygen reacting with the same mass of nitrogen. We will find the mass of oxygen per gram of nitrogen for each compound by dividing the mass of oxygen by the mass of nitrogen. 1. For the compound with 17.60 g of oxygen: \(\frac{17.60}{30.82} = 0.571\) 2. For the compound with 35.20 g of oxygen: \(\frac{35.20}{30.82} = 1.142\) 3. For the compound with 70.40 g of oxygen: \(\frac{70.40}{30.82} = 2.284\) 4. For the compound with 88.00 g of oxygen: \(\frac{88.00}{30.82} = 2.855\) So the mass of oxygen per gram of nitrogen for the four compounds are approximately 0.571, 1.142, 2.284, and 2.855, respectively.

Discuss how the numbers support Dalton's atomic theory

Dalton's atomic theory states that elements combine in fixed proportions to form compounds. In this case, we can see that the mass ratios of oxygen to nitrogen are related by simple whole numbers. We can observe the following relationships between the mass ratios: 1. The mass ratio in compound 2 is approximately 2 times the mass ratio in compound 1 (1.142 / 0.571 ≈ 2) 2. The mass ratio in compound 3 is approximately 4 times the mass ratio in compound 1 (2.284 / 0.571 ≈ 4) 3. The mass ratio in compound 4 is approximately 5 times the mass ratio in compound 1 (2.855 / 0.571 ≈ 5) This shows that the compounds are formed by combining oxygen and nitrogen in fixed, whole-number ratios, supporting Dalton's atomic theory.

Key concepts

Law of Multiple Proportions

The law of multiple proportions is a key concept in chemistry, which asserts that when two elements form more than one compound, the ratios of the masses of the second element that combine with a fixed mass of the first element are simple whole numbers. This principle was vital in establishing the credibility of atomic theory and chemical reactions in the early 19th century.

In our exercise, we see different amounts of oxygen reacting with the same amount of nitrogen. These mass ratios of oxygen are found to be closely related to whole numbers when compared amongst each other. For instance, the ratios of oxygen to nitrogen vary in a simplistic and predictable manner that can be expressed as whole-number multiples (e.g. 0.571, 1.142, 2.284, 2.855 in an approximated relationship of 1:2:4:5).

• This observation strongly supports the law of multiple proportions as it suggests compounds are formed by specific integer proportion combinations.
• This manner of composition confirms Dalton's atomic theory, which affirmed that chemical compounds are formed in definite proportions.

Mass Ratios

In any chemical reaction, understanding mass ratios is fundamental as it tells us how elements combine by mass. Here, the chemist observed the reaction of a constant mass of nitrogen with varying masses of oxygen to form different compounds. By calculating the mass of oxygen that combines with a fixed mass of nitrogen, we determine an important ratio that describes the compound's composition.

In our example, a fixed mass of nitrogen reacts with various amounts of oxygen, yielding different mass ratios of the form oxygen/nitrogen:

• For the compound with 17.60 g of oxygen, the mass ratio is approximately 0.571.
• With 35.20 g of oxygen, the ratio is around 1.142.
• For 70.40 g of oxygen, the ratio becomes about 2.284.
• Finally, with 88.00 g of oxygen, it is roughly 2.855.

These ratios subsequently highlight how elements combine in specific measured patterns to create distinct chemical compounds. Understanding this concept helps in predicting the outcomes of chemical reactions and the necessary proportions for forming new substances.

Chemical Compounds

Chemical compounds are substances formed by the chemical combination of two or more different elements. Each compound is characterized by a specific ratio of atoms, which results in unique chemical and physical properties. Compounds like those produced from nitrogen and oxygen are a prime example of how specific quantitative relationships are established at the molecular level.

In our scenario, forming compounds of nitrogen and oxygen involves combining these elements in varied but precise ways, as indicated by our mass ratios. The uniqueness in each compound comes from this fixed atomic composition dictated by the ratios:

• Every compound is formed based on a specific mass ratio, ensuring a predetermined combination of nitrogen and oxygen atoms.
• This uniformity stems from the fact that compounds are bound by physical laws dictating atomic proportions, making chemical prediction and synthesis more logical and guided by quantitative data.

Understanding the formation of such compounds provides critical insight into the consistency and predictability of chemical reactions as a whole.

Nitrogen and Oxygen Reactions

The reactions between nitrogen and oxygen to form different compounds are a classic illustration of chemical transformations. These reactions showcase how elements bond under specific conditions to create new substances.

Within this context, a chemist observes various mass ratios of oxygen, overriding the same mass of nitrogen, leading to distinct chemical products. Each mass ratio indicates a reaction that results in a new compound with the fused properties of nitrogen and oxygen.

• The fixed amount of nitrogen acts as a constant, while altering the amount of oxygen demonstrates the change in compound formation.
• This directly correlates to our understanding of the law of multiple proportions, underlying chemical diversity arising from fixed elemental interactions.

Thus, studying these variations not only represents basic chemical principles but also enhances our comprehension of molecular formation mechanisms.