Question

Calculate the mass percent composition of nitrogen in each nitrogen-containing compound. a. \(\mathrm{N}_{2} \mathrm{O}\) b. NO c. \(\mathrm{NO}_{2}\) d. \(\mathrm{HNO}_{3}\)

Short answer

The mass percent compositions of nitrogen are: a. 36.84% in N2O, b. 46.68% in NO, c. 30.43% in NO2, d. 22.22% in HNO3.

Step-by-step solution

Calculate the Molar Mass of N2O

First, determine the total molar mass of N2O by adding the molar masses of nitrogen (N) and oxygen (O). There are 2 nitrogen atoms and 1 oxygen atom. The molar mass of nitrogen is approximately 14.01 g/mol, and oxygen is approximately 16.00 g/mol. Thus, the molar mass of N2O is: 2(14.01 g/mol) + 1(16.00 g/mol).

Determine the Mass Percent Composition of Nitrogen in N2O

Divide the total mass of nitrogen in one molecule of N2O by the total molar mass of N2O and multiply by 100 to get the mass percent composition. So, you get: (2 * 14.01 g/mol) / molar mass of N2O * 100.

Calculate the Molar Mass of NO

Find the total molar mass of NO by adding the molar masses of nitrogen and oxygen. There is 1 nitrogen atom and 1 oxygen atom. Molar mass of NO is: 1(14.01 g/mol) + 1(16.00 g/mol).

Determine the Mass Percent Composition of Nitrogen in NO

Divide the mass of nitrogen in one molecule of NO by the total molar mass of NO and multiply by 100 to get the mass percent composition. So, you get: (1 * 14.01 g/mol) / molar mass of NO * 100.

Calculate the Molar Mass of NO2

Find the total molar mass of NO2 by adding the molar masses of nitrogen and two oxygen atoms. The molar mass of NO2 is: 1(14.01 g/mol) + 2(16.00 g/mol).

Determine the Mass Percent Composition of Nitrogen in NO2

Divide the mass of nitrogen in one molecule of NO2 by the total molar mass of NO2 and multiply by 100. So, you get: (1 * 14.01 g/mol) / molar mass of NO2 * 100.

Calculate the Molar Mass of HNO3

Find the total molar mass of HNO3 by adding the molar masses of hydrogen (H), nitrogen, and three oxygen atoms. The molar mass of HNO3 is: 1(1.01 g/mol) + 1(14.01 g/mol) + 3(16.00 g/mol).

Determine the Mass Percent Composition of Nitrogen in HNO3

Divide the mass of nitrogen in one molecule of HNO3 by the total molar mass of HNO3 and multiply by 100. So, you get: (1 * 14.01 g/mol) / molar mass of HNO3 * 100.

Key concepts

Molar Mass Calculation

Understanding how to calculate molar mass is fundamental in mastering chemistry. Molar mass, expressed in grams per mole (g/mol), is the weight of one mole of a substance. One mole corresponds to Avogadro's number (approximately 6.022 x 10²³) of particles (atoms, molecules, ions, or electrons) of a given substance.
Calculating the molar mass involves summing up the atomic masses of all the atoms present in a molecule. If you consider nitrogen (N) with an atomic mass of approximately 14.01 g/mol, for a molecule like N₂O which contains two nitrogen atoms, you would calculate its molar mass by adding twice the atomic weight of nitrogen plus the atomic weight of oxygen (16.00 g/mol).

• The molar mass of N₂O: 2(14.01 g/mol) + 1(16.00 g/mol) = 44.02 g/mol

Such calculations apply to any chemical compound, and molar mass serves as a bridge between the mass of a material and the amount of material present in moles.

Chemical Composition

Chemical composition refers to the identity and ratio of the elements that make up a substance. Every compound has a unique composition exemplified by its chemical formula. The mass percent composition of an element within a compound is a way of expressing this ratio. It shows what percentage of the compound's total mass is made up of a particular element.
When dealing with nitrogen-containing compounds such as NO or NO₂, the mass percent of nitrogen can be found by dividing the mass of nitrogen atoms in one mole of the compound by the compound's molar mass. Multiplying the quotient by 100 converts the fraction into a percentage. This percentage is essential for scientists and engineers who need to know the precise composition of materials for various applications.
For instance:
From the previous section, the molar mass of NO is 30.01 g/mol. With nitrogen's molar mass at 14.01 g/mol, the mass percent composition of nitrogen is:

• (1 * 14.01 g/mol) / 30.01 g/mol * 100 ≈ 46.65%

This calculation is crucial for understanding the properties and reactions of the compound.

Stoichiometry

Stoichiometry is the section of chemistry that involves quantitative relationships between reactants and products in a chemical reaction. At the core of stoichiometry is the balanced chemical equation, which provides the ratio of moles of each reactant and product involved in the reaction. This balancing act ensures the conservation of mass and atoms according to the law of conservation of matter.
Mass percent composition plays a key role in stoichiometry, especially when dealing with complex reactions. Knowing the mass percent of an element in a substance gives valuable information to predict the amounts of other elements or compounds that will react with or be produced from a given quantity of the substance.
For example, in the calculation of mass percent composition of nitrogen in HNO₃, one must consider that in stoichiometric problems, the starting point is often the amount of one reactant or product. Using the calculated mass percent composition:

• The molar mass of HNO₃: 63.01 g/mol
• Mass percent of nitrogen in HNO₃: (1 * 14.01 g/mol) / 63.01 g/mol * 100 ≈ 22.23%

This information helps determine how much nitrogen is available for reactions involving HNO₃, thereby allowing for the precise calculation of reactants or products in a chemical reaction.