Problem 24 - Chemistry The Science in Context

Question

Which substance in each of the following pairs of quantities contains more moles of nitrogen? a. 2 moles of \(\mathrm{Li}_{3} \mathrm{N}\) or 0.5 mole of \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\). b. 1 mole of \(\mathrm{NO}\) or 0.4 mole of \(\mathrm{NO}_{2}\). c. 3 moles of \(\mathrm{NF}_{3}\) or 1 mole of \(\mathrm{N}_{2} \mathrm{O}_{5}\).

Step-by-Step Solution

Answer

a. 2 moles of Li3N or 0.5 moles of Ca(NO3)2 b. 1 mole of NO or 0.4 moles of NO2 c. 3 moles of NF3 or 1 mole of N2O5 Answer: a. Li3N b. NO c. NF3

Step 1: Pair a: Finding moles of nitrogen in Li3N

We're given 2 moles of Li3N, and there is 1 mole of nitrogen (N) for every mole of Li3N. Therefore, the moles of nitrogen in 2 moles of Li3N are: 2 moles of Li3N * (1 mole of N / 1 mole of Li3N) = 2 moles of N

Step 2: Pair a: Finding moles of nitrogen in Ca(NO3)2

We're given 0.5 moles of Ca(NO3)2, and there are 2 moles of nitrogen (N) for every mole of Ca(NO3)2. Therefore, the moles of nitrogen in 0.5 moles of Ca(NO3)2 are: 0.5 moles of Ca(NO3)2 * (2 moles of N / 1 mole of Ca(NO3)2) = 1 mole of N

Step 3: Pair a: Comparing moles of nitrogen

In pair a, Li3N has 2 moles of nitrogen, and Ca(NO3)2 has 1 mole of nitrogen. So, Li3N contains more moles of nitrogen.

Step 4: Pair b: Finding moles of nitrogen in NO

We're given 1 mole of NO, and there is 1 mole of nitrogen (N) for every mole of NO. Therefore, the moles of nitrogen in 1 mole of NO are: 1 mole of NO * (1 mole of N / 1 mole of NO) = 1 mole of N

Step 5: Pair b: Finding moles of nitrogen in NO2

We're given 0.4 moles of NO2, and there is 1 mole of nitrogen (N) for every mole of NO2. Therefore, the moles of nitrogen in 0.4 moles of NO2 are: 0.4 moles of NO2 * (1 mole of N / 1 mole of NO2) = 0.4 moles of N

Step 6: Pair b: Comparing moles of nitrogen

In pair b, NO has 1 mole of nitrogen, and NO2 has 0.4 moles of nitrogen. So, NO contains more moles of nitrogen.

Step 7: Pair c: Finding moles of nitrogen in NF3

We're given 3 moles of NF3, and there is 1 mole of nitrogen (N) for every mole of NF3. Therefore, the moles of nitrogen in 3 moles of NF3 are: 3 moles of NF3 * (1 mole of N / 1 mole of NF3) = 3 moles of N

Step 8: Pair c: Finding moles of nitrogen in N2O5

We're given 1 mole of N2O5, and there are 2 moles of nitrogen (N) for every mole of N2O5. Therefore, the moles of nitrogen in 1 mole of N2O5 are: 1 mole of N2O5 * (2 moles of N / 1 mole of N2O5) = 2 moles of N

Step 9: Pair c: Comparing moles of nitrogen

In pair c, NF3 has 3 moles of nitrogen and N2O5 has 2 moles of nitrogen. So, NF3 contains more moles of nitrogen. In conclusion, the substances containing more moles of nitrogen in each pair are: a. Li3N b. NO c. NF3

Key Concepts

Chemical Formulas

Chemical formulas are concise ways to represent chemical substances, showing the types and numbers of atoms involved in a molecule. They provide crucial insights into the molecular composition, aiding in the understanding of reactions and stoichiometries.
The chemical formula

consists of element symbols (from the periodic table) and numerical subscripts,

and reflects the ratio of atoms within the compound.

For example, in the formula for lithium nitride, ext {Li}_3 ext {N}, it indicates there are 3 lithium (Li) atoms paired with 1 nitrogen (N) atom. Another example is calcium nitrate, ext {Ca(NO}_3)_2, which denotes each molecule comprises 1 calcium (Ca) atom and 2 nitrate ( ext {NO}_3) groups.
Understanding these formulas is essential for calculating the number of specific atoms, such as nitrogen, in a given sample—one of the key skills tested in the exercise provided.

Stoichiometry

Stoichiometry is the aspect of chemistry that involves quantitative relationships in chemical reactions. It helps to derive the quantity of reactants or products in a chemical process. This includes determining how many moles of a particular element are present in compounds.
It incorporates principles like:

• mole ratios derived from balanced chemical equations,
• and conversion factors based on the molecular composition of substances.

For instance, in the exercise, if you know that for every 1 mole of lithium nitride ( ext {Li}_3 ext {N}), there is 1 mole of nitrogen, you can easily find the moles of nitrogen in any sample size of lithium nitride. Similarly, recognizing that calcium nitrate ( ext {Ca(NO}_3)_2) contains 2 moles of nitrogen per mole gives clarity on how moles of nitrogen are determined.
Stoichiometry not only allows for such calculations but also enables the prediction of yields and the efficiency of chemical processes.

Molecular Composition

Molecular composition involves the makeup of molecules based on the specific atoms and their quantities. Understanding this concept is crucial for performing accurate chemical analyses and solving problems like the comparison of nitrogen moles in different substances, as seen in the exercise.
The key aspects include:

• Identifying the different types of atoms within a molecule,
• and calculating the proportion of each atom, particularly when comparing similar compounds.

For example, the formula ext {NF}_3 indicates one nitrogen atom in each formula unit, while ext {N}_2 ext {O}_5 suggests two nitrogen atoms per formula unit. By understanding these patterns, one can succinctly solve which substances contain more moles of a particular element.
This knowledge forms the basis for analyzing molecular structures and their practical applications in areas like material science and environmental chemistry.