Question

Calculate the molar mass of each of the following: (a) \(\mathrm{SnO}\) (b) \(\mathrm{BaF}_{2}\) (c) \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) (d) \(\mathrm{MnCl}_{2}\)

Short answer

(a) 134.71 g/mol, (b) 175.33 g/mol, (c) 342.17 g/mol, (d) 125.84 g/mol

Step-by-step solution

Understanding the Problem

Determine the molar mass of each given compound: (a) \(\text{SnO}\) (b) \(\text{BaF}_{2}\) (c) \(\text{Al}_{2}\text{(SO}_{4}\text{)}_{3}\) (d) \(\text{MnCl}_{2}\)

Find Atomic Masses

Consult the periodic table to find the atomic masses: \(\text{Sn}: 118.71\) g/mol, \(\text{O}: 16.00\) g/mol, \(\text{Ba}: 137.33\) g/mol, \(\text{F}: 19.00\) g/mol, \(\text{Al}: 26.98\) g/mol, \(\text{S}: 32.07\) g/mol, \(\text{O}: 16.00\) g/mol, \(\text{Mn}: 54.94\) g/mol, \(\text{Cl}: 35.45\) g/mol.

Calculate Molar Mass of \(\text{SnO}\)

Add the atomic masses of Sn and O: Atomic masses: Sn = 118.71 g/mol, O = 16.00 g/mol \(\text{Molar Mass of SnO} = 118.71 + 16.00 = 134.71 \) g/mol

Calculate Molar Mass of \(\text{BaF}_{2}\)

Add the atomic masses of Ba and 2 F: Atomic masses: Ba = 137.33 g/mol, F = 19.00 g/mol \(\text{Molar Mass of BaF}_{2} = 137.33 + 2\times19.00 = 137.33 + 38.00 = 175.33 \) g/mol

Calculate Molar Mass of \(\text{Al}_{2}\text{(SO}_{4}\text{)}_{3}\)

Add the atomic masses: Atomic masses: Al = 26.98 g/mol, S = 32.07 g/mol, O = 16.00 g/mol \(\text{Molar Mass of Al}_{2}\text{(SO}_{4}\text{)}_{3} = 2\times26.98 + 3\times(32.07 + 4\times16.00) = 2\times26.98 + 3\times(32.07 + 64) = 53.96 + 3\times96.07 = 53.96 + 288.21 = 342.17 \) g/mol

Calculate Molar Mass of \(\text{MnCl}_{2}\)

Add the atomic masses of Mn and 2 Cl: Atomic masses: Mn = 54.94 g/mol, Cl = 35.45 g/mol \(\text{Molar Mass of MnCl}_{2} = 54.94 + 2\times35.45 = 54.94 + 70.90 = 125.84 \) g/mol

Key concepts

atomic mass

Atomic mass is fundamental when it comes to molar mass calculations. Atomic mass refers to the mass of an individual atom, often expressed in atomic mass units (amu) or grams per mole (g/mol). You can find these values listed on the periodic table. For example, the atomic mass of oxygen is 16.00 g/mol, while the atomic mass of tin (Sn) is 118.71 g/mol. By understanding atomic masses, you can easily calculate the molar mass of compounds by adding together the atomic masses of the constituent elements. This is the first step to mastering stoichiometry.

periodic table

The periodic table is an indispensable tool in chemistry. It organizes all the known elements in a structured manner based on their atomic number, electron configurations, and recurring chemical properties. The periodic table also provides essential information like atomic masses, which are crucial for finding the molar mass of compounds. When you're given a chemical formula, like \(\mathrm{BaF}_{2}\) or \(\mathrm{MnCl}_{2}\), you can turn to the periodic table to find the atomic masses of Ba, F, Mn, and Cl. This layout facilitates easy reference and allows chemists to rapidly gather data needed for their calculations.

chemical compounds

Chemical compounds are substances formed by the chemical combination of two or more different elements. The properties of a compound are distinct from the properties of its constituent elements. Chemical formulas, such as \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\), indicate the types and numbers of atoms in a molecule. Understanding these formulas is essential for molar mass calculations. For instance, in \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\), the formula indicates that the compound consists of 2 aluminum atoms, 3 sulfur atoms, and 12 oxygen atoms. By multiplying the quantity of each type of atom by its atomic mass and summing these values, you can find the molar mass of the compound.

stoichiometry

Stoichiometry involves the quantitative relationships between the reactants and products in a chemical reaction. A solid understanding of stoichiometry enables you to calculate how much of a substance is needed or produced. This often involves calculating molar masses and using them in proportionate relationships. For example, when calculating the molar mass of \(\mathrm{SnO}\), you add the molar mass of Sn (118.71 g/mol) and O (16.00 g/mol) to get 134.71 g/mol. Such calculations are the building blocks of stoichiometric equations, allowing chemists to scale reactions accurately and determine the amounts of reactants and products involved.