Question

Calculate the mass in grams of each of the following samples. a. 10,000,000,000 nitrogen molecules b. \(2.49 \times 10^{20}\) carbon dioxide molecules c. 7.0983 moles of sodium chloride d. \(9.012 \times 10^{-6}\) moles of 1,2 -dichloroethane, \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}\)

Short answer

The mass of each sample is calculated as follows: a. \( \frac{10,000,000,000}{6.022 \times 10^{23}}\) × 28.02 g/mol b. \( \frac{2.49 \times 10^{20}}{6.022 \times 10^{23}}\) × 44.01 g/mol c. 7.0983 × 58.44 g/mol d. \( 9.012 \times 10^{-6} \) × ((2 × 12.01) + (4 × 1.008) + (2 × 35.45)) g/mol

Step-by-step solution

Calculate moles of nitrogen molecules

First, we need to find the moles of nitrogen molecules. To do this, divide the given number of nitrogen molecules (10,000,000,000) by Avogadro's number. Moles of nitrogen molecules = \( \frac{10,000,000,000}{6.022 \times 10^{23}} \)

Convert moles to grams

Now that we have the moles of nitrogen molecules, we can calculate the mass in grams. The molar mass of nitrogen gas, N₂, is 28.02 g/mol. Mass = (Moles of nitrogen molecules) x (Molar mass of nitrogen gas) Mass = \( \frac{10,000,000,000}{6.022 \times 10^{23}}\) × 28.02 g/mol #b. Calculate the mass of \(2.49 \times 10^{20}\) carbon dioxide molecules#

Calculate moles of carbon dioxide molecules

Divide the given number of carbon dioxide molecules by Avogadro's number. Moles of carbon dioxide molecules = \( \frac{2.49 \times 10^{20}}{6.022 \times 10^{23}} \)

Convert moles to grams

The molar mass of carbon dioxide, CO₂, is 44.01 g/mol. Mass = (Moles of carbon dioxide molecules) x (Molar mass of carbon dioxide) Mass = \( \frac{2.49 \times 10^{20}}{6.022 \times 10^{23}}\) × 44.01 g/mol #c. Calculate the mass of 7.0983 moles of sodium chloride#

Convert moles to grams

The molar mass of sodium chloride, NaCl, is 58.44 g/mol. Mass = (Moles of sodium chloride) x (Molar mass of sodium chloride) Mass = 7.0983 × 58.44 g/mol #d. Calculate the mass of \(9.012 \times 10^{-6}\) moles of 1,2-dichloroethane, C₂H₄Cl₂#

Calculate the molar mass

The molar mass of 1,2-dichloroethane is: - 2 carbon atoms: 2 × 12.01 g/mol - 4 hydrogen atoms: 4 × 1.008 g/mol - 2 chlorine atoms: 2 × 35.45 g/mol Molar mass = (2 × 12.01) + (4 × 1.008) + (2 × 35.45)

Convert moles to grams

Using the calculated molar mass, we can now calculate the mass of \(9.012 \times 10^{-6}\) moles of 1,2-dichloroethane. Mass = (Moles of 1,2-dichloroethane) x (Molar mass of 1,2-dichloroethane) Mass = \( 9.012 \times 10^{-6} \) × ((2 × 12.01) + (4 × 1.008) + (2 × 35.45)) g/mol

Key concepts

Molar Mass Calculation

Understanding the calculation of molar mass is fundamental in chemistry because it bridges the gap between atoms/molecules and the macroscopic world we can measure. The molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). To calculate the molar mass, we look at the substance's chemical formula and sum the average atomic masses of all the atoms in the molecule.

For example, to find the molar mass of water \text{(H\(_2\)O)}, you would add twice the atomic mass of hydrogen (approximately 1.008 g/mol) to the atomic mass of oxygen (approximately 16.00 g/mol). This gives us a molar mass for water of about 18.02 g/mol. When this concept is clear, a student can easily extend it to any compound, thereby determining how much of a substance they have in a sample.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10²³, is the number of atoms, molecules, or ions in one mole of substance. It is an enormous constant that allows chemists to count particles by weighing them. Understanding Avogadro's number is crucial when converting between the number of entities and the amount of substance in moles.

For instance, if you have exactly one mole of carbon atoms, you have 6.022 x 10²³ carbon atoms, and their total mass would be equal to the molar mass of carbon, 12.01 g. Knowing Avogadro's number enables students to perform calculations involving the number of molecules and their mass directly, and is quite helpful in solving problems related to the mole concept.

Converting Moles to Grams

Conversion from moles to grams is a straightforward process with a direct formula: Mass in grams = Number of moles x Molar mass of the substance. The molar mass acts as a conversion factor that translates moles, which count chemical entities, into grams, which are a more practical unit for measurement in the laboratory.

For example, if you have 2 moles of sodium chloride (NaCl), and the molar mass of NaCl is 58.44 g/mol, the mass of your sample is 2 moles x 58.44 g/mol = 116.88 grams. Students should become comfortable with this type of conversion because it frequently appears in chemical calculations and various scientific exercises.

Chemical Formula Stoichiometry

Stoichiometry revolves around the quantitative relationships between the reactants and products in a chemical reaction. By using the chemical formula of a substance within a balanced chemical equation, stoichiometry allows for predictions about the amounts of substances consumed and produced.

For example, in the combustion of propane (\text{C\(_3\)H\(_8\)}), the balanced equation is \text{C\(_3\)H\(_8\)} + 5\text{O\(_2\)} \rightarrow 3\text{CO\(_2\)} + 4\text{H\(_2\)O}. Knowing the moles of \text{C\(_3\)H\(_8\)} that react, you can calculate the moles of \text{CO\(_2\)} produced and, subsequently, the mass. These calculations are central to understanding the conservation of mass in reactions, optimizing chemical processes, and even assessing environmental impact.