Question

A chemist finds that 30.82 gof nitrogen will react with 17.60 , $35.20,70.40,$ or 88.00 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

In conclusion, the mass of oxygen per gram of nitrogen in each compound is approximately 0.571, 1.142, 2.283, and 2.854. These ratios exhibit whole number relationships (1:2, 1:4, and 1:5) supporting Dalton's atomic theory, as they indicate elements combine in fixed proportions to form compounds.

Step-by-step solution

(Step 1: Calculate mass of oxygen per gram of nitrogen for each compound)

To find the mass of oxygen per gram of nitrogen in each compound, we will divide the mass of oxygen by the mass of nitrogen. For the first compound: $\frac{mass\mathrm{\_}of\mathrm{\_}oxygen}{mass\mathrm{\_}of\mathrm{\_}nitrogen}=\frac{17.60g}{30.82g}$ For the second compound: $\frac{mass\mathrm{\_}of\mathrm{\_}oxygen}{mass\mathrm{\_}of\mathrm{\_}nitrogen}=\frac{35.20g}{30.82g}$ For the third compound: $\frac{mass\mathrm{\_}of\mathrm{\_}oxygen}{mass\mathrm{\_}of\mathrm{\_}nitrogen}=\frac{70.40g}{30.82g}$ For the fourth compound: $\frac{mass\mathrm{\_}of\mathrm{\_}oxygen}{mass\mathrm{\_}of\mathrm{\_}nitrogen}=\frac{88.00g}{30.82g}$

(Step 2: Calculate the ratios)

Next, we will calculate the ratios by dividing the mass of oxygen by the mass of nitrogen for each compound. First compound ratio: $\frac{17.60g}{30.82g}=0.571$ Second compound ratio: $\frac{35.20g}{30.82g}=1.142$ Third compound ratio: $\frac{70.40g}{30.82g}=2.283$ Fourth compound ratio: $\frac{88.00g}{30.82g}=2.854$

(Step 3: Analyze the ratios)

Now, let's analyze the ratios and compare them with each other to find any relationships. We can see that the second compound has approximately twice the ratio of the first compound (1.142 ≈ 2 x 0.571). Similarly, the third compound has approximately four times the ratio of the first compound (2.283 ≈ 4 x 0.571). The fourth compound has approximately five times the ratio of the first compound (2.854 ≈ 5 x 0.571). These ratios show that the mass of oxygen combining with the fixed mass of nitrogen is in whole number ratios, which supports Dalton's atomic theory.

(Conclusion)

In conclusion, the mass of oxygen per gram of nitrogen in each compound and the resulting ratios support Dalton's atomic theory because they exhibit whole number relationships. These whole number relationships indicate that elements combine in fixed proportions to form compounds, which is a key principle of Dalton's atomic theory.

Key concepts

Chemical Compound Composition

Understanding the composition of chemical compounds is fundamental in the study of chemistry. Elements combine in specific proportions to form compounds, and these proportions are determined by the nature of the atoms involved. For instance, in the provided exercise, we have nitrogen reacting with varying amounts of oxygen to create different compounds.

Each compound is unique not only in the quantity of oxygen that reacts with nitrogen but also in the specific arrangement of the atoms within the compound. These distinct arrangements yield different properties and indicate that in chemical reactions, atoms are neither created nor destroyed but simply rearranged, highlighting the law of conservation of mass. This introduces the significance of knowing the constituent elements in a compound and their ratios, as they are key for predicting the outcomes of chemical reactions.

Law of Multiple Proportions

The law of multiple proportions is a cornerstone of chemical understanding that states when two elements form more than one compound, the masses of one element that combine with a fixed mass of the other are in the ratio of small whole numbers.

As demonstrated in the exercise, nitrogen combines with oxygen in different amounts to form various compounds. The ratios of the mass of oxygen per gram of nitrogen in these compounds—0.571, 1.142, 2.283, and 2.854—are all small whole numbers when compared to each other (1:2:4:5). This supports Dalton's atomic theory and provides insight into the discrete nature of atoms. It implies that atoms combine in simple whole number ratios, not arbitrarily, highlighting the predictability and consistency underlying chemical reactions.

Mass of Oxygen per Gram of Nitrogen

In the context of stoichiometry and chemical composition, it is often useful to consider the mass of one reactant that will combine with a fixed mass of another. Here, we focus on the mass of oxygen that reacts with one gram of nitrogen.

This calculation helps to determine the proportions in which these two elements combine to form different nitrogen oxides. By dividing the mass of oxygen by the mass of nitrogen for each compound—as demonstrated in the exercise—we determine the ratio in which oxygen and nitrogen combine, which further reveals their stoichiometric relationship in each of the nitrogen oxides. This is crucial for understanding the quantitative aspects of the formed chemical compounds.

Stoichiometry

Stoichiometry is the area of chemistry that pertains to the quantitative relationships between the reactants and products in a chemical reaction. It derives from the Greek words 'stoicheion' (element) and 'metron' (measure), effectively meaning the measurement of elements.

In practice, it involves calculations based on the balanced chemical equations of a reaction to predict how much of each substance is required or produced. The exercise showcases stoichiometry through the calculated mass ratios, which represent how quantities of one substance, like oxygen, relate to another, like nitrogen, in chemical compounds. Grasping stoichiometry is invaluable for students as it is used to predict the outcomes of reactions, determine the amount of materials needed for reactions, and is fundamental in applications ranging from laboratory experiments to industrial chemical processes.