Question

What is the percent nitrogen in each of the following compounds? (a) \(\mathrm{NaNO}_{3}\) (b) \(\mathrm{NH}_{4} \mathrm{Cl}\) (c) \(\mathrm{N}_{2} \mathrm{H}_{4}\) (d) \(\mathrm{N}_{2} \mathrm{O}\)

Short answer

The percent nitrogen in NaNO3, NH4Cl, N2H4 and N2O is 16.48%, 26.23%, 87.34% and 63.63% respectively.

Step-by-step solution

Recall Atomic Weights

Use the Periodic Table to obtain the atomic weights of the elements in the compounds. Nitrogen = 14.01, Sodium = 22.99, Oxygen = 16.00, Hydrogen = 1.01, and Chlorine = 35.45.

Calculate % Nitrogen in NaNO3

First, calculate the molar mass of NaNO3: \(22.99 + 14.01 + 3 × 16.00 = 85.00 g/mol\). The % nitrogen is calculated by taking the mass of nitrogen in one mole of the compound and dividing it by the molar mass of the compound, then multiply it by 100: \(14.01/85.00 × 100 = 16.48%\).

Calculate % Nitrogen in NH4Cl

Calculate the molar mass of NH4Cl: \(14.01 + 4 × 1.01 + 35.45 = 53.49 g/mol\). The % nitrogen here is: \(14.01/53.49 × 100 = 26.23%\).

Calculate % Nitrogen in N2H4

Calculate the molar mass of N2H4 = \(2 × 14.01 + 4 × 1.01 = 32.06 g/mol\). The % nitrogen here is: \(28.02/32.06 × 100 = 87.34%\).

Calculate % Nitrogen in N2O

Calculate the molar mass of N2O: \(2 × 14.01 + 16.00 = 44.02 g/mol\). The % nitrogen here is: \(28.02/44.02 × 100 = 63.63%\).

Key concepts

Atomic Weights

Atomic weights, also known as atomic masses, are fundamental to many aspects of chemistry, including the determination of percent composition by mass. They represent the average mass of atoms of an element, taking into account the existence of different isotopes and their abundances.

For example, in our exercise, nitrogen has an atomic weight of 14.01, reflecting its isotopic composition. These weights can be found on the periodic table and are measured in atomic mass units (amu). When calculating percent composition, we use these atomic weights to determine how much each element contributes to the overall mass of a compound.

Molar Mass Calculation

The molar mass of a compound is the mass of one mole of that compound, which is calculated by summing the atomic weights of all the atoms in the compound's formula. Essentially, it's the mass in grams of 6.022 × 10²³ (Avogadro's number) molecules or formula units of that compound.

For instance, the molar mass of NaNO₃ is calculated by adding the atomic weights of one sodium (Na), one nitrogen (N), and three oxygen (O) atoms, yielding 85.00 g/mol. Knowing the molar mass allows us to relate a compound's mass to the number of moles, a key step in finding percent composition by mass.

Mole Concept

The mole is a foundational concept in chemistry, acting as a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure. One mole is defined as the amount of a substance that contains as many entities (atoms, molecules, ions, etc.) as there are atoms in 12 grams of carbon-12.

This number, Avogadro's number, is approximately 6.022 × 10²³ and represents the number of atoms or molecules in one mole of a substance. Understanding the mole concept is crucial when working with chemical reactions and quantifying substances, as seen in our percent composition calculations.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It involves calculations that use the mole concept to predict the mass of reactants needed or products formed in a chemical reaction.

In the context of percent composition, stoichiometry is not directly applied to calculate the percent by mass of an element in a compound. However, the underlying principles, specifically the mole concept and molar mass calculations, are fundamental to understanding stoichiometry. For more complex problems that involve chemical reactions, a thorough grasp of stoichiometry would be necessary to quantify the changes in composition.