Problem 154 - Chemistry An Atoms First Approach

Question

Arrange the following substances in order of increasing mass percent of nitrogen. a. NO c. \(\mathrm{NH}_{3}\) b. \(\mathrm{N}_{2} \mathrm{O}\) d. SNH

Step-by-Step Solution

Answer

The order of increasing mass percent of nitrogen for the given substances is: SNH (29.79%) < NO (46.67%) < \(\mathrm{N}_{2} \mathrm{O}\) (63.64%) < \(\mathrm{NH}_{3}\) (82.35%), or d < a < b < c.

Step 1: Determine the molar mass of nitrogen

We first need to find the molar mass of nitrogen (N). The molar mass of an element can be found using the periodic table. Nitrogen has a molar mass of 14 g/mol.

Step 2: Calculate the molar mass of each molecule

Next, we will compute the molar mass of each molecule given in the problem: a. NO: Sum of the molar masses of N (14 g/mol) and O (16 g/mol) Molar mass = 14 + 16 = 30 g/mol b. \(\mathrm{N}_2 \mathrm{O}\): Molar mass of N2O = 2 x (14 g/mol) for nitrogen + 1 x (16 g/mol) for oxygen Molar mass = 2(14) + 16 = 44 g/mol c. \(\mathrm{NH}_3\): Molar mass of NH3 = 1 x (14 g/mol) for nitrogen + 3 x (1 g/mol) for hydrogen Molar mass = 14 + 3(1) = 17 g/mol d. \(\mathrm{SNH}\): Molar mass of SNH = 1 x (32 g/mol) for sulfur + 1 x (14 g/mol) for nitrogen + 1 x (1 g/mol) for hydrogen Molar mass = 32 + 14 + 1 = 47 g/mol

Step 3: Calculate the mass percent of nitrogen in each molecule

Now, we will calculate the mass percent of nitrogen in each molecule. a. NO: Mass percent of N = (14 / 30) × 100 = 46.67 % b. \(\mathrm{N}_2 \mathrm{O}\): Mass percent of N = (28 / 44) × 100 = 63.64 % c. \(\mathrm{NH}_3\): Mass percent of N = (14 / 17) × 100 = 82.35 % d. SNH: Mass percent of N = (14 / 47) × 100 = 29.79 %

Step 4: Arrange the molecules in order of increasing mass percent of nitrogen

Based on the mass percent calculations, we can arrange the molecules from lowest to highest mass percent of nitrogen: 1. SNH (29.79%) 2. NO (46.67%) 3. \(\mathrm{N}_{2} \mathrm{O}\) (63.64%) 4. \(\mathrm{NH}_{3}\) (82.35%) Therefore, the order of increasing mass percent of nitrogen is: d < a < b < c.

Key Concepts

Molar Mass Calculation

Understanding molar mass is the first step in many chemical calculations. Molar mass is defined as the mass of one mole of a given substance (chemical element or chemical compound) expressed in grams per mole. It corresponds to the sum of the masses of the individual elements (found on the periodic table) multiplied by their respective number of atoms in the formula.

For instance, in calculating the molar mass of water (H₂O), we take 2 times the molar mass of hydrogen (approximately 1 g/mol) plus 1 time the molar mass of oxygen (approximately 16 g/mol). This calculation leads to a molar mass for water of about 18 g/mol. It's essential to understand how to compute molar mass correctly as it impacts later calculations, such as percent composition.

Percent Composition

The percent composition of an element in a compound is a way of expressing the proportion of the mass of each element to the total mass of the compound. It's a reflection of the compound's composition, written as a percentage. To calculate it, you take the mass of the individual element (which can be found by multiplying the atom's molar mass by the number of atoms of that element in the molecule) and divide it by the molar mass of the entire compound. You then multiply the result by 100 to get a percentage.

For example, to find the mass percent of nitrogen in ammonia (NH₃), you would find the mass of one mole of nitrogen in the compound (14 g, since there's only one nitrogen atom in ammonia) and divide it by the molar mass of ammonia (17 g/mol). The result, once multiplied by 100, tells you the percent of the compound that is made up of nitrogen. Understanding percent composition allows students to understand the relative amounts of different elements in a compound and is useful in stoichiometry and analytical chemistry.

Chemical Formula

The chemical formula of a compound offers vital information on the types and numbers of atoms present. It is a representation using element symbols from the periodic table, along with numeric subscripts to indicate the number of each type of atom. The chemical formula is fundamental in understanding the composition of a molecule and leads into the calculation of its molar mass.

When the formula is known, one can determine the exact molar mass and percent composition. For instance, the formula CO₂ indicates carbon dioxide, a compound with one carbon atom and two oxygen atoms. Knowing this formula, its molar mass can be calculated by adding the mass of one carbon (about 12 g/mol) to twice the mass of oxygen (2 times approximately 16 g/mol), giving a total of about 44 g/mol. Accurate interpretation of chemical formulas is crucial for all subsequent calculations and understanding chemical reactions.