Question

Calculate the number of moles of the indicated substance present in each of the following samples. a. \(47.2 \mathrm{~g}\) of aluminum oxide b. \(1.34 \mathrm{~kg}\) of potassium bromide c. \(521 \mathrm{mg}\) of germanium d. \(56.2 \mu \mathrm{g}\) of uranium e. \(29.7 \mathrm{~g}\) of sodium acetate f. 1.03 g of sulfur trioxide

Short answer

The moles for each substance are as follows: a. \(0.463 \: \text{moles of Al}₂\text{O}₃\) b. \(11.26 \: \text{moles of KBr}\) c. \(7.2 \times 10^{-3} \: \text{moles of Ge}\) d. \(2.363 \times 10^{-7} \: \text{moles of U}\) e. \(0.362 \: \text{moles of NaC}₂\text{H}₃\text{O}₂\) f. \(0.0129 \: \text{moles of SO}₃\)

Step-by-step solution

a. Calculating moles of aluminum oxide

1. Determine the molar mass of aluminum oxide (Al₂O₃): M(Al₂O₃) = 2 * M(Al) + 3 * M(O) 2. Look up the atomic mass of aluminum (Al) and oxygen (O) from the periodic table: M(Al) = 26.98 g/mol, M(O) = 16.00 g/mol 3. Calculate molar mass: M(Al₂O₃) = 2 * 26.98 + 3 * 16.00 = 53.96 + 48.00 = 101.96 g/mol 4. Calculate the number of moles: \(n = \frac{m}{M} = \frac{47.2}{101.96} = 0.463 \: \text{moles of Al}₂\text{O}₃\)

b. Calculating moles of potassium bromide

1. Determine the molar mass of potassium bromide (KBr): M(KBr) = M(K) + M(Br) 2. Look up the atomic mass of potassium (K) and bromine (Br) from the periodic table: M(K) = 39.10 g/mol, M(Br) = 79.90 g/mol 3. Calculate molar mass: M(KBr) = 39.10 + 79.90 = 119.00 g/mol 4. Convert the mass to grams: \(m = 1.34 \: \text{kg} * 1000 = 1340 \: \text{g}\) 5. Calculate the number of moles: \(n = \frac{m}{M} = \frac{1340}{119.00} = 11.26 \: \text{moles of KBr}\)

c. Calculating moles of germanium

1. Look up the atomic mass of germanium (Ge) from the periodic table: M(Ge) = 72.63 g/mol 2. Convert the mass to grams: \(m = 521 \: \text{mg} * \frac{1 \: \text{g}}{1000 \: \text{mg}} = 0.521 \: \text{g}\) 3. Calculate the number of moles: \(n = \frac{m}{M} = \frac{0.521}{72.63} = 7.2 \times 10^{-3} \: \text{moles of Ge}\)

d. Calculating moles of uranium

1. Look up the atomic mass of uranium (U) from the periodic table: M(U) = 238.03 g/mol 2. Convert the mass to grams: \(m = 56.2 \times 10^{-6} \: \text{g}\) 3. Calculate the number of moles: \(n = \frac{m}{M} = \frac{56.2 \times 10^{-6}}{238.03} = 2.363 \times 10^{-7} \: \text{moles of U}\)

e. Calculating moles of sodium acetate

1. Determine the molar mass of sodium acetate (NaC₂H₃O₂): M(NaC₂H₃O₂) = M(Na) + M(C) * 2 + M(H) * 3 + M(O) * 2 2. Look up the atomic mass of sodium (Na), carbon (C), hydrogen (H), and oxygen (O) from the periodic table: M(Na) = 22.99 g/mol, M(C) = 12.01 g/mol, M(H) = 1.01 g/mol, M(O) = 16.00 g/mol 3. Calculate molar mass: M(NaC₂H₃O₂) = 22.99 + 2 * 12.01 + 3 * 1.01 + 2 * 16.00 = 82.03 g/mol 4. Calculate the number of moles: \(n = \frac{m}{M} = \frac{29.7}{82.03} = 0.362 \: \text{moles of NaC}₂\text{H}₃\text{O}₂\)

f. Calculating moles of sulfur trioxide

1. Determine the molar mass of sulfur trioxide (SO₃): M(SO₃) = M(S) + 3 * M(O) 2. Look up the atomic mass of sulfur (S) and oxygen (O) from the periodic table: M(S) = 32.07 g/mol, M(O) = 16.00 g/mol 3. Calculate molar mass: M(SO₃) = 32.07 + 3 * 16.00 = 80.07 g/mol 4. Calculate the number of moles: \(n = \frac{m}{M} = \frac{1.03}{80.07} = 0.0129 \: \text{moles of SO}₃\)

Key concepts

Molar Mass

Molar mass, often denoted by capital M, is a fundamental concept in chemistry that relates the mass of a substance to its amount in moles. It is defined as the mass of one mole of a given substance and is usually expressed in units of grams per mole (g/mol). The molar mass of a compound can be calculated by summing the atomic masses of its constituent atoms, multiplied by their respective quantities in the formula.

For instance, in the provided exercise for aluminum oxide (Al₂O₃), its molar mass was calculated by adding two times the atomic mass of aluminum to three times the atomic mass of oxygen. In the periodic table, the atomic mass of aluminum is listed as 26.98 g/mol, and that of oxygen is 16.00 g/mol. Hence, the molar mass M(Al₂O₃) equals to 2 * 26.98 g/mol + 3 * 16.00 g/mol, which equals 101.96 g/mol.

Atomic Mass

Atomic mass, sometimes referred to as atomic weight, is the mass of a single atom of a chemical element. It is usually expressed in atomic mass units (amu), with one atomic mass unit defined as one-twelfth the mass of a carbon-12 atom. In practice, the atomic masses of elements are averaged weights, accounting for the various isotopes and their abundances.

In our exercise, we use the atomic masses of multiple elements to calculate molar masses of different compounds. For example, the atomic mass of germanium is given as 72.63 g/mol. When converting mass from milligrams to grams (since molar mass units are in grams), it's crucial to use correct conversion factors, as was done when determining the moles of germanium. For 521 mg of germanium, the mass is first converted into grams (0.521 g), which is then divided by the atomic mass (72.63 g/mol) to find the number of moles.

Stoichiometry

Stoichiometry is an area of chemistry that involves the calculation of the quantities of reactants and products in chemical reactions. It is based on the principle that matter is neither created nor destroyed during a chemical reaction, which is known as the Law of Conservation of Mass. In simple terms, stoichiometry ensures that atoms are balanced on both sides of a chemical equation, reflecting the reality that the same number of each type of atom must appear in the reactants and products.

The stoichiometric calculations often start by determining the number of moles, because moles provide a way to 'count' atoms and molecules by relating their quantities to their weights. The previous examples, such as calculating the moles of sodium acetate or sulfur trioxide, are all exercises in stoichiometry. These calculations are foundational for reactions, allowing chemists to predict the outcomes of reactions and the amounts needed to achieve them.