Question

Using the average atomic masses given inside the front cover of this book, calculate how many moles of each substance the following masses represent. a. \(1.47 \times 10^{-3} \mathrm{g}\) of iridium b. \(8.95 \mathrm{g}\) of lead(II) sulfide, \(\mathrm{PbS}\) c. \(293 \mathrm{mg}\) of copper(II) oxide, \(\mathrm{CuO}\) d. \(91.4 \mathrm{g}\) of iron(III) chloride, \(\mathrm{FeCl}_{3}\) e. \(2.67 \mathrm{g}\) of nitrogen gas, \(\mathrm{N}_{2}\) f. 89.2 g of carbon disulfide, \(\mathrm{CS}_{2}\) g. \(1.43 \mathrm{kg}\) of iron

Short answer

The moles for the given substances are: a. Iridium (Ir): \(7.64 \times 10^{-6} \, moles\) b. Lead(II) Sulfide (PbS): \(0.0374 \, moles\) c. Copper(II) Oxide (CuO): \(0.00368 \, moles\) d. Iron(III) Chloride (FeCl_3): \(0.563 \, moles\) e. Nitrogen Gas (N_2): \(0.0953 \, moles\) f. Carbon Disulfide (CS_2): \(1.17 \, moles\) g. Iron (Fe): \(25.6 \, moles\)

Step-by-step solution

(a. Moles of Iridium)

To find the moles of Iridium (Ir), we need to look up the average atomic mass of Ir, which is 192.22 g/mol. Given the mass of Iridium is \(1.47 \times 10^{-3} \mathrm{g}\), the number of moles can be calculated as: \[moles \: of \: Ir = \frac{1.47 \times 10^{-3} \mathrm{g}}{192.22 \mathrm{g/mol}} = 7.64 \times 10^{-6} \, moles\]

(b. Moles of Lead(II) Sulfide)

For Lead(II) Sulfide (PbS), we need to determine its molar mass. The average atomic masses of Pb and S are 207.2 g/mol and 32.07 g/mol, respectively. Hence, the molecular mass of PbS is \(207.2 + 32.07 = 239.27 \, \mathrm{g/mol}\). To find the number of moles, we can divide the given mass (8.95 g) by the molar mass: \[moles \: of \: PbS = \frac{8.95 \mathrm{g}}{239.27 \mathrm{g/mol}} = 0.0374 \, moles\]

(c. Moles of Copper(II) Oxide)

For Copper(II) Oxide (CuO), we need to determine its molar mass. The average atomic masses of Cu and O are 63.55 g/mol and 16.00 g/mol, respectively. Hence, the molecular mass of CuO is \(63.55 + 16.00 = 79.55 \, \mathrm{g/mol}\). To find the number of moles from the given mass (293 mg), first, convert it to grams: \(293 \: \mathrm{mg} = 0.293 \: \mathrm{g}\). Then, we can divide the mass by the molar mass: \[moles \: of \: CuO = \frac{0.293 \mathrm{g}}{79.55 \mathrm{g/mol}} = 0.00368 \, moles\]

(d. Moles of Iron(III) Chloride)

For Iron(III) Chloride (FeCl_3), we need to determine its molar mass. The average atomic masses of Fe and Cl are 55.85 g/mol and 35.45 g/mol, respectively. Hence, the molecular mass of FeCl_3 is \(55.85 + 3 \times 35.45 = 162.2 \, \mathrm{g/mol}\). To find the number of moles, we can divide the given mass (91.4 g) by the molar mass: \[moles \: of \: FeCl_3 = \frac{91.4 \mathrm{g}}{162.2 \mathrm{g/mol}} = 0.563 \, moles\]

(e. Moles of Nitrogen Gas)

For Nitrogen Gas (N_2), we need to determine its molar mass. The average atomic mass of N is 14.01 g/mol. Therefore, the molecular mass of N_2 is \(2 \times 14.01 = 28.02 \, \mathrm{g/mol}\). To find the number of moles, we can divide the given mass (2.67 g) by the molar mass: \[moles \: of \: N_2 = \frac{2.67 \mathrm{g}}{28.02 \mathrm{g/mol}} = 0.0953 \, moles\]

(f. Moles of Carbon Disulfide)

For Carbon Disulfide (CS_2), we need to determine its molar mass. The average atomic masses of C and S are 12.01 g/mol and 32.07 g/mol, respectively. Hence, the molecular mass of CS_2 is \(12.01 + 2 \times 32.07 = 76.15 \, \mathrm{g/mol}\). To find the number of moles, we can divide the given mass (89.2 g) by the molar mass: \[moles \: of \: CS_2 = \frac{89.2 \mathrm{g}}{76.15 \mathrm{g/mol}} = 1.17 \, moles\]

(g. Moles of Iron)

Back to Iron (Fe), we have its average atomic mass as 55.85 g/mol. The given mass of Iron is 1.43 kg, which we need to convert to grams: \(1.43 \: \mathrm{kg} = 1430 \: \mathrm{g}\). To find the number of moles, we can divide the mass by the molar mass: \[moles \: of \: Fe = \frac{1430 \mathrm{g}}{55.85 \mathrm{g/mol}} = 25.6 \, moles\]

Key concepts

Atomic Mass

The atomic mass of an element, often referred to in textbooks as atomic weight, is the average mass of atoms of an element measured in atomic mass units (amu). This is calculated based on the relative abundance of isotopes of the element. Each isotope has a different mass number, reflecting the number of protons and neutrons in the nucleus. The atomic mass allows us to compare the mass of different atoms on a relative scale and also serves as a crucial bridge between the atomic scale and the macroscopic scale.

For example, in the solved exercise, the atomic mass of iridium is given as 192.22 g/mol, which means that one mole of iridium atoms weighs 192.22 grams. It's important to understand that this value is an average across all isotopes of iridium as they occur naturally.

Molar Mass

Molar mass is defined as the mass of one mole of a given substance (chemical element or chemical compound) expressed in grams per mole (g/mol). It correlates the mass of a substance to its amount in moles and is a fundamental concept in chemistry for stoichiometry calculations. The molar mass of an element is the atomic mass taken from the periodic table and expressed in units of g/mol.

When dealing with compounds like lead(II) sulfide (PbS), one would sum the molar masses of lead and sulfur, based on their given atomic masses, to find the compound's molar mass. As shown in the solution, this addition results in PbS having a molar mass of 239.27 g/mol. Understanding how to calculate molar mass is vital for converting between the mass of a substance and the amount in moles.

Mole Concept

The mole is a fundamental unit in chemistry that provides a bridge between the atomic world and the practical world of measuring substances. One mole is defined as the amount of substance that contains as many entities (atoms, ions, molecules, etc.) as there are atoms in 12 grams of pure carbon-12 (i.e., Avogadro's number, which is approximately 6.022 x 10^23). This concept allows chemists to count particles by weighing them.

For instance, when the exercise asks for the number of moles of iron (Fe), given a mass of 1.43 kg, the calculation uses the mole concept to convert this mass into moles, considering the molar mass of iron. The result of the calculation confirms the number of moles present in the given sample. Knowing the mole concept is crucial for understanding chemical reactions and for the determination of chemical composition.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions in chemistry. It is based on the law of conservation of mass where the total mass of the reactants equals the total mass of the products. Stoichiometry uses the mole concept to allow for balanced equations and thus, to predict how much product will form from a certain amount of reactants (and vice versa). It's essentially the math behind chemistry.

Stoichiometric calculations require balanced chemical equations, molar masses of the substances involved, and the mole ratios from the balanced equation. This allows chemists to calculate the masses of different reactants needed to produce a desired amount of product. The problems from the exercise demonstrate this by relating the mass of given substances to their moles.

Chemical Composition

Chemical composition refers to the identity and relative number of the elements that make up any particular compound. This composition can be represented using chemical formulas, which convey the proportions of elements present in a compound. By knowing the chemical formula and the molar masses of its elements, one can determine the molar mass of the compound and perform a variety of calculations, such as finding the number of moles of the compound present in a given mass.

Moreover, chemical composition is at the heart of chemical reactions. For example, copper(II) oxide (CuO) contains one copper atom and one oxygen atom per molecule. In stoichiometric calculations, the knowledge of its chemical composition leads to correctly finding its molar mass and applying it to find the number of moles from a given mass, as illustrated in the exercise's solution.