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. \(12.7 \mathrm{g}\) of hydrogen gas, \(\mathrm{H}_{2}\) b. \(5.2 \mathrm{g}\) of calcium hydride, \(\mathrm{CaH}_{2}\) c. 41.6 mg of potassium hydroxide, KOH d. \(6.93 \mathrm{g}\) of hydrogen sulfide, \(\mathrm{H}_{2} \mathrm{S}\) e. \(94.7 \mathrm{g}\) of water, \(\mathrm{H}_{2} \mathrm{O}\) f. 321 mg of lead g. 8.79 g of silver nitrate, \(\mathrm{AgNO}_{3}\)

Short answer

a. \(n(H_2) = 6.29 \: \text{mol}\) b. \(n(CaH_2) = 0.123 \: \text{mol}\) c. \(n(KOH) = 7.41 \times 10^{-4} \: \text{mol}\) d. \(n(H_2S) = 0.203 \: \text{mol}\) e. \(n(H_2O) = 5.26 \: \text{mol}\) f. \(n(Pb) = 1.55 \times 10^{-3} \: \text{mol}\) g. \(n(AgNO_3) = 0.0517 \: \text{mol}\)

Step-by-step solution

a. Calculate number of moles of hydrogen gas H2

Firstly, calculate the molar mass of H2. M(H2) = 2 × atomic mass of H = 2 × 1.01 g/mol = 2.02 g/mol Now, we can calculate the number of moles using the formula: n(H2) = m(H2) / M(H2) = 12.7 g / 2.02 g/mol = 6.29 mol

b. Calculate number of moles of calcium hydride CaH2

Firstly, calculate the molar mass of CaH2. M(CaH2) = atomic mass of Ca + 2 × atomic mass of H = 40.08 g/mol + 2 × 1.01 g/mol = 42.10 g/mol Now, we can calculate the number of moles using the formula: n(CaH2) = m(CaH2) / M(CaH2) = 5.2 g / 42.10 g/mol = 0.123 mol

c. Calculate number of moles of potassium hydroxide KOH

Firstly, convert the mass from milligrams to grams. m(KOH) = 41.6 mg × (1 g / 1000 mg) = 0.0416 g Next, calculate the molar mass of KOH. M(KOH) = atomic mass of K + atomic mass of O + atomic mass of H = 39.10 g/mol + 16.00 g/mol + 1.01 g/mol = 56.11 g/mol Now, we can calculate the number of moles using the formula: n(KOH) = m(KOH) / M(KOH) = 0.0416 g / 56.11 g/mol = 7.41 × 10^-4 mol

d. Calculate number of moles of hydrogen sulfide H2S

Firstly, calculate the molar mass of H2S. M(H2S) = 2 × atomic mass of H + atomic mass of S = 2 × 1.01 g/mol + 32.07 g/mol = 34.09 g/mol Now, we can calculate the number of moles using the formula: n(H2S) = m(H2S) / M(H2S) = 6.93 g / 34.09 g/mol = 0.203 mol

e. Calculate number of moles of water H2O

Firstly, calculate the molar mass of H2O. M(H2O) = 2 × atomic mass of H + atomic mass of O = 2 × 1.01 g/mol + 16.00 g/mol = 18.02 g/mol Now, we can calculate the number of moles using the formula: n(H2O) = m(H2O) / M(H2O) = 94.7 g / 18.02 g/mol = 5.26 mol

f. Calculate number of moles of lead

Firstly, convert the mass from milligrams to grams. m(Pb) = 321 mg × (1 g / 1000 mg) = 0.321 g Next, find the atomic mass of lead, which is 207.2 g/mol. Now, we can calculate the number of moles using the formula: n(Pb) = m(Pb) / atomic mass of Pb = 0.321 g / 207.2 g/mol = 1.55 × 10^-3 mol

g. Calculate number of moles of silver nitrate AgNO3

Firstly, calculate the molar mass of AgNO3. M(AgNO3) = atomic mass of Ag + atomic mass of N + 3 × atomic mass of O = 107.87 g/mol + 14.01 g/mol + 3 × 16.00 g/mol = 169.87 g/mol Now, we can calculate the number of moles using the formula: n(AgNO3) = m(AgNO3) / M(AgNO3) = 8.79 g / 169.87 g/mol = 0.0517 mol

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with determining the quantities of reactants and products in chemical reactions. It is a fundamental concept for understanding how to calculate moles from mass, which is critical for both laboratory work and theoretical chemistry.

At the heart of stoichiometry is the balanced chemical equation, where the coefficients indicate the proportional amounts of each substance involved. These coefficients, combined with the molar masses of the substances, allow chemists to convert between grams, moles, and even particles like atoms or molecules. Stoichiometry relies on the principle that matter is neither created nor destroyed during a chemical reaction, which is known as the Law of Conservation of Mass.

Common stoichiometric calculations include mass-to-mass, mole-to-mole, mass-to-mole, and mole-to-volume conversions. In the context of a chemistry textbook exercise, students often use stoichiometry to calculate the number of moles of a substance when given its mass, by dividing the mass by the molar mass of the substance, a process clearly demonstrated in the step-by-step solutions of the textbook exercise above.

Molar Mass

The molar mass of a substance is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance (moles). It is usually expressed in units of grams per mole (g/mol) and is often used as a conversion factor in stoichiometry.

Molar mass is calculated by summing the average atomic masses of all the atoms in a molecule of the substance. Atomic masses can usually be found on the periodic table and, for compounds, you simply add up the atomic masses for each element according to its stoichiometric coefficient in the molecular formula. For an example, water (H₂O) has a molar mass of 18.02 g/mol because it is composed of two hydrogen atoms (2 x 1.01 g/mol) and one oxygen atom (16.00 g/mol).

In the provided textbook exercise, calculating molar mass is the first step required to determine the number of moles from a given mass. This is a crucial step because different substances have different molar masses, and therefore the same mass of two different substances will correspond to a different number of moles.

Chemical Compounds

Chemical compounds are substances composed of two or more different types of atoms bonded together in a specific ratio and structure. Understanding the composition and structure of chemical compounds is essential when working with stoichiometry and calculating moles from mass.

Each compound has a unique chemical formula that represents the type and number of atoms that make up the compound. For example, the formula CaH₂ indicates that each molecule of calcium hydride consists of one calcium atom and two hydrogen atoms. Such formulas are critical when calculating the molar mass as they tell you which atoms and how many of each are involved.

Compounds can be broken down into elements via chemical reactions and can be formed from elements or simpler compounds. The textbook exercise predominantly involves calculating moles for compounds, which necessitates an understanding of their molar mass based on the individual atomic masses of their constituent elements.