Question

Formula Mass and the Mole Concept for Compounds How many molecules are in each sample? $$\begin{array}{ll}{\text { a. } 6.5 \mathrm{g} \mathrm{H}_{2} \mathrm{O}} & {\text { b. } 389 \mathrm{g} \mathrm{CBr}_{4}} \\ {\text { c. } 22.1 \mathrm{g} \mathrm{O}_{2}} & {\text { d. } 19.3 \mathrm{g} \mathrm{C}_{8} \mathrm{H}_{10}}\end{array}$$

Short answer

a. Approx. 2.17 x 10^23 molecules of H2O, b. Approx. 1.24 x 10^24 molecules of CBr4, c. Approx. 4.17 x 10^23 molecules of O2, d. Approx. 1.24 x 10^23 molecules of C8H10.

Step-by-step solution

Calculate the Molar Mass of each Compound

Determine the molar mass for each compound by adding the atomic masses of its constituent elements. The atomic masses are approximately: H = 1.01 g/mol, O = 16.00 g/mol, C = 12.01 g/mol, Br = 79.90 g/mol.

Convert grams to moles

Use the formula: Number of moles = Mass of sample (g) / Molar mass of compound (g/mol) to calculate the number of moles for each compound.

Calculate the Number of Molecules

Use Avogadro's number, which is approximately 6.022 x 10^23 molecules/mol, to convert the number of moles of each compound to the number of molecules.

Calculate the Number of Molecules for Each Compound

For each compound, multiply the number of moles found in Step 2 by Avogadro's number to find the total number of molecules in the sample.

Key concepts

Molar Mass Calculation

Understanding the molar mass of a compound is fundamental in chemistry, as it bridges the gap between the microscopic world of atoms and molecules and the macroscopic world we measure in the lab. 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, you sum the atomic masses of all the atoms in the molecule. For example, water (H_2O) has a molar mass of approximately 18.02 g/mol, calculated by adding twice the atomic mass of hydrogen (1.01 g/mol) to the atomic mass of oxygen (16.00 g/mol). Accurate molar mass calculation is crucial for converting between mass and moles, a key step in various quantitative chemistry problems.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is a constant that represents the number of particles, usually atoms or molecules, in one mole of a substance. It is named after Amedeo Avogadro, who first proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules it contains.

When solving chemistry problems involving the mole concept, it's crucial to use Avogadro's number to convert from moles to the actual number of particles of a substance, thereby relating macroscopic quantities to the number of microscopic entities. For example, when given the amount of substance in grams, you determine the number of moles and then apply Avogadro's number to find out how many molecules are present.

Molecular Formula

The molecular formula provides the exact number of each type of atom present in a molecule. For instance, glucose has a molecular formula of C_6H_12O_6, indicating it contains 6 carbon, 12 hydrogen, and 6 oxygen atoms. Calculating the molecular formula from empirical data often involves determining the molar mass of the compound and its empirical formula mass.

It's essential for accurately calculating the molar mass because, without the correct formula, the sum of the atomic masses would not represent the actual substance in question. Hence, a reliable molecular formula ensures proper stoichiometric calculations and is a fundamental step in quantifying chemical reactions.

Stoichiometry

Stoichiometry is the part of chemistry that pertains to measuring the quantities of reactants and products in chemical reactions. It is based on the conservation of mass, where the mass of the reactants equals the mass of the products in a chemical reaction.

Stoichiometry relies on balanced chemical equations and the mole concept to predict how much product will result from a given amount of reactant or how much reactant is needed to create a desired amount of product. It's the quantification of the relationships between the amounts of substances involved in a reaction and requires a solid understanding of the molar mass, Avogadro's number, and the molecular formula to make accurate predictions and calculations.