Question

How many molecules are in each sample? a. \(6.5 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}\) b. \(389 \mathrm{~g} \mathrm{CBr}_{4}\) c. \(22.1 \mathrm{~g} \mathrm{O}_{2}\) d. \(19.3 \mathrm{~g} \mathrm{CeH}_{10}\)

Short answer

a. H2O sample contains approximately 2.171 x 10^23 molecules. b. CBr4 sample contains approximately 7.064 x 10^23 molecules. c. O2 sample contains approximately 4.158 x 10^23 molecules. d. CeH10 sample contains approximately 7.439 x 10^22 molecules.

Step-by-step solution

Calculate the Molar Mass of Each Compound

Determine the molar mass of each compound by adding the atomic masses of its elements. For H2O, the molar mass is 18.02 g/mol (2*1.01 for H + 16.00 for O). For CBr4, the molar mass is 331.63 g/mol (12.01 for C + 4*79.90 for Br). For O2, the molar mass is 32.00 g/mol (2*16.00 for O). For CeH10, the molar mass is 156.2 g/mol (140.1 for Ce + 10*1.01 for H).

Calculate the Number of Moles for Each Sample

Use the formula moles = mass (in grams) / molar mass (in g/mol). For H2O, 6.5 g / 18.02 g/mol = 0.3607 moles. For CBr4, 389 g / 331.63 g/mol = 1.173 moles. For O2, 22.1 g / 32.00 g/mol = 0.6906 moles. For CeH10, 19.3 g / 156.2 g/mol = 0.1236 moles.

Convert Moles to Molecules

Multiply the number of moles by Avogadro's number (6.022 x 10^23 molecules/mol) to find the number of molecules. For H2O, 0.3607 moles * 6.022 x 10^23 molecules/mol = 2.171 x 10^23 molecules. For CBr4, 1.173 moles * 6.022 x 10^23 molecules/mol = 7.064 x 10^23 molecules. For O2, 0.6906 moles * 6.022 x 10^23 molecules/mol = 4.158 x 10^23 molecules. For CeH10, 0.1236 moles * 6.022 x 10^23 molecules/mol = 7.439 x 10^22 molecules.

Key concepts

Molar Mass Calculation

Understanding the molar mass calculation is a fundamental step in chemistry that relates to the mass of one mole of a substance. It is simply the sum of the atomic masses of all the atoms in a molecule. To calculate it, you need to know the atomic weight of each element in the substance, which you can find on the periodic table.

For instance, water (H₂O) has a molar mass that we calculate by adding twice the atomic mass of hydrogen (approximately 1.01 grams per mole) to the atomic mass of oxygen (approximately 16.00 grams per mole). This calculation results in a molar mass of 18.02 grams per mole for water. It's important to be precise with atomic weights and account for all atoms present in the compound to ensure accurate calculations.

Avogadro's Number

The essence of Avogadro's number is a constant that represents the number of units in one mole of any substance and is a cornerstone of the mole concept in chemistry. Avogadro's number is approximately 6.022 x 10²³ units/mol.

It allows chemists to count molecules, atoms, or ions by weighing macroscopic amounts of matter and calculating the number of moles contained in that mass. Whether you are counting molecules of water or molecules of carbon tetrabromide, Avogadro's number remains the same, acting as a bridge between the microscopic and macroscopic worlds in chemistry.

Moles to Molecules Conversion

The moles to molecules conversion is a vital aspect of quantitative chemistry. Once the number of moles has been calculated, this number can be converted into the actual number of molecules using Avogadro's number. The formula is straightforward: you simply multiply the number of moles by 6.022 x 10²³ molecules/mol.

As an example, if you have 1 mole of water, you actually have 6.022 x 10²³ water molecules. This conversion is crucial for understanding the composition of a sample at the molecular level and is integral for calculations in chemical reactions and stoichiometry.

Stoichiometry

The term stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction. It revolves around the law of conservation of mass which states that mass can neither be created nor destroyed in a chemical reaction. Thus, stoichiometry involves using balanced chemical equations to calculate the mass of reactants required to produce a certain amount of product or vice versa.

It heavily relies on the mole concept, as it allows chemists to convert between mass and moles of substances. This conversion is at the heart of chemical calculations, helping to predict yields of reactions and to calculate the necessary proportions of reactants for experiments. Stoichiometry is fundamental for reaction prediction, product formation analysis, and is essential in the design of chemical syntheses and processes.