Question

What amount (moles) is represented by each of these samples? a. \(150.0 \mathrm{~g} \mathrm{Fe}_{2} \mathrm{O}_{3}\) b. \(10.0 \mathrm{mg} \mathrm{NO}_{2}\) c. \(1.5 \times 10^{16}\) molecules of \(\mathrm{BF}_{3}\)

Short answer

The amount of moles represented by each sample is as follows: a. 0.940 moles of Fe2O3. b. \(2.17\times10^{-4}\) moles of NO2. c. \(2.49 \times 10^{-8}\) moles of BF3.

Step-by-step solution

Determine the molar mass of each substance

We will first determine the molar mass of each substance using the atomic masses of the elements. a. For Fe2O3, Molar mass = 2(atomic mass of Fe) + 3(atomic mass of O) = 2(55.8)+3(16) = 111.6 + 48 = 159.6 g/mol b. For NO2, Molar mass = atomic mass of N + 2(atomic mass of O) = 14 + 2(16) = 14 + 32 = 46 g/mol

Find the amount(moles) for sample a

To find the number of moles of Fe2O3, divide the given mass (150.0 g) by its molar mass (159.6 g/mol) Moles of Fe2O3 = \( \frac{150.0 \mathrm{~g}}{159.6 \mathrm{~g/mol}} \) = 0.940 moles

Find the amount(moles) for sample b

Convert the mass of NO2 from mg to g (1 mg = \(1 \times 10^{-3}\) g): 10.0 mg = 10.0 x \(10^{-3}\) g = 0.010 g Now divide the mass of NO2 (0.010 g) by its molar mass (46 g/mol): Moles of NO2 = \( \frac{0.010 \mathrm{~g}}{46 \mathrm{~g/mol}} \) = \(2.17\times10^{-4}\) moles

Find the amount(moles) for sample c

Divide the number of BF3 molecules (1.5 x \(10^{16}\)) by Avogadro's number (6.022 × \(10^{23}\) molecules/mol): Moles of BF3 = \( \frac{1.5 \times 10^{16} \mathrm{~molecules}}{6.022 \times 10^{23} \mathrm{~molecules/mol}} \) = \(2.49 \times 10^{-8}\) moles Results: a. 0.940 moles of Fe2O3. b. \(2.17\times10^{-4}\) moles of NO2. c. \(2.49 \times 10^{-8}\) moles of BF3.

Key concepts

Molar Mass Calculation

Understanding the concept of molar mass is crucial when dealing with chemical compounds and reactions. Molar mass is defined as the mass of one mole of a substance in grams per mole (g/mol). It is numerically equivalent to the average atomic or molecular mass of all the isotopes of that substance, when expressed in atomic mass units (amu).

For compounds such as Fe₂O₃ or NO₂, the molar mass is the sum of the molar masses of each element multiplied by its subscript in the chemical formula. Let's dive into an example:

• For iron(III) oxide (Fe₂O₃), we calculate molar mass by adding together the molar masses of iron (Fe) and oxygen (O), considering there are two atoms of iron and three atoms of oxygen in each molecule. Hence, the calculation involves multiplying the atomic mass of iron (55.8 g/mol) by 2 and the atomic mass of oxygen (16 g/mol) by 3, and then summing these products together.

Remember, the molar mass allows us to convert between grams and moles of a substance, which is a foundational step in solving many stoichiometric problems.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and molecules and the macroscopic world we can measure and observe. One mole is defined as exactly 6.022 x 10²³ particles of a substance, which may be atoms, molecules, ions, or electrons – this number is known as Avogadro's number. The concept is used to express amounts of a chemical substance and could be seen as the chemist's equivalent to a dozen, except that it applies to an incredibly large number of particles.

When we say that we have one mole of iron(III) oxide, it means we have 6.022 x 10²³ formula units of Fe₂O₃. To determine the number of moles in a given mass, we use the formula:

• Number of moles = Given mass (g) / Molar mass (g/mol)

In practice, for a sample of Fe₂O₃ weighing 150.0 g, when we know the molar mass is 159.6 g/mol, we can calculate the moles as shown in the step-by-step solution provided. Thus, through the mole concept, we can relate a substance's mass to the number of particles it contains.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10²³, is an essential constant in chemistry. It represents the number of atoms, ions, or molecules in one mole of any substance and is named after the Italian scientist Amedeo Avogadro, who proposed this concept. A clear understanding of Avogadro's number underpins many aspects of chemistry, especially stoichiometry, where it allows chemists to count particles by weighing them.

For instance, if we have 1.5 x 10¹⁶ molecules of BF₃, to find the amount in moles, we simply divide the number of molecules by Avogadro's number:

• Moles of BF₃ = Number of molecules / Avogadro's number

By performing this calculation, we can find the corresponding moles, which can then be used to continue calculations in a chemical equation or to determine the mass of the sample if needed. Avogadro's number universally applies to all substances, so it remains consistent whether we're considering a mole of carbon, oxygen, or any chemical species.