Question

Give the name and calculate the molar mass for each of the following substances. a. \(\mathrm{H}_{3} \mathrm{PO}_{4}\) b. \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) c. \(\mathrm{NaClO}_{4}\) d. \(\mathrm{PbCl}_{2}\) e. HBr f. \(\mathrm{Al}(\mathrm{OH})_{3}\)

Short answer

a. Phosphoric acid, \(\mathrm{H}_{3} \mathrm{PO}_{4}\): 98.0 g/mol b. Iron (III) oxide, \(\mathrm{Fe}_{2} \mathrm{O}_{3}\): 159.6 g/mol c. Sodium perchlorate, \(\mathrm{NaClO}_{4}\): 122.5 g/mol d. Lead (II) chloride, \(\mathrm{PbCl}_{2}\): 278.2 g/mol e. Hydrogen bromide, HBr: 80.9 g/mol f. Aluminum hydroxide, \(\mathrm{Al}(\mathrm{OH})_{3}\): 78.0 g/mol

Step-by-step solution

Identify the elements in the given substances

For each substance, list the elements present and the number of atoms of each element according to their formulas. a. \(\mathrm{H}_{3} \mathrm{PO}_{4}\): 3 Hydrogen (H), 1 Phosphorus (P), 4 Oxygen (O) b. \(\mathrm{Fe}_{2} \mathrm{O}_{3}\): 2 Iron (Fe), 3 Oxygen (O) c. \(\mathrm{NaClO}_{4}\): 1 Sodium (Na), 1 Chlorine (Cl), 4 Oxygen (O) d. \(\mathrm{PbCl}_{2}\): 1 Lead (Pb), 2 Chlorine (Cl) e. HBr: 1 Hydrogen (H), 1 Bromine (Br) f. \(\mathrm{Al}(\mathrm{OH})_{3}\): 1 Aluminum (Al), 3 Oxygen (O), 3 Hydrogen (H)

Find the molar masses of the involved elements

Refer to a periodic table to find the molar masses (also called atomic weights) of the elements present in each substance. Here are the molar masses for the involved elements, rounded to one decimal place: - Hydrogen (H): 1.0 g/mol - Phosphorus (P): 31.0 g/mol - Oxygen (O): 16.0 g/mol - Iron (Fe): 55.8 g/mol - Sodium (Na): 23.0 g/mol - Chlorine (Cl): 35.5 g/mol - Lead (Pb): 207.2 g/mol - Bromine (Br): 79.9 g/mol - Aluminum (Al): 26.98 g/mol

Calculate the molar mass of each substance

For each substance, multiply the molar mass of each element by the number of atoms of that element present in the substance's formula, and then sum the products to find the total molar mass. a. \(\mathrm{H}_{3} \mathrm{PO}_{4}\): (3 x 1.0) + (1 x 31.0) + (4 x 16.0) = 98.0 g/mol b. \(\mathrm{Fe}_{2} \mathrm{O}_{3}\): (2 x 55.8) + (3 x 16.0) = 159.6 g/mol c. \(\mathrm{NaClO}_{4}\): (1 x 23.0) + (1 x 35.5) + (4 x 16.0) = 122.5 g/mol d. \(\mathrm{PbCl}_{2}\): (1 x 207.2) + (2 x 35.5) = 278.2 g/mol e. HBr: (1 x 1.0) + (1 x 79.9) = 80.9 g/mol f. \(\mathrm{Al}(\mathrm{OH})_{3}\): (1 x 26.98) + (3 x 16.0) + (3 x 1.0) = 78.0 g/mol Here are the names and molar masses for each substance: a. Phosphoric acid, \(\mathrm{H}_{3} \mathrm{PO}_{4}\): 98.0 g/mol b. Iron (III) oxide, \(\mathrm{Fe}_{2} \mathrm{O}_{3}\): 159.6 g/mol c. Sodium perchlorate, \(\mathrm{NaClO}_{4}\): 122.5 g/mol d. Lead (II) chloride, \(\mathrm{PbCl}_{2}\): 278.2 g/mol e. Hydrogen bromide, HBr: 80.9 g/mol f. Aluminum hydroxide, \(\mathrm{Al}(\mathrm{OH})_{3}\): 78.0 g/mol

Key concepts

Chemical Formulas

Chemical formulas represent the composition of a compound using symbols for the elements and numbers to show the quantity of each element. These formulas are a shorthand way to describe the substances. For example, the formula \( \mathrm{H}_3\mathrm{PO}_4 \) tells us that in one molecule of this compound (phosphoric acid), there are 3 hydrogen atoms, 1 phosphorus atom, and 4 oxygen atoms.
By simply looking at a chemical formula, you can determine the elements present and how many atoms of each are in the molecule. This is crucial for chemical reactions and calculations, such as determining molar mass.
It's important to note that the numbers in a chemical formula (called subscripts) indicate the number of atoms of each element. For instance, \( \mathrm{Fe}_2\mathrm{O}_3 \) suggests 2 iron atoms and 3 oxygen atoms forming iron(III) oxide.

Periodic Table

The periodic table is an essential tool in chemistry that organizes all known chemical elements in an informative grid. Each element's box on the table shows crucial information, such as its atomic number, symbol, and atomic weight.
By referencing the periodic table, you can identify the molar mass of elements, which is the mass of one mole of an atom measured in grams per mole (g/mol). This is important when calculating the molar mass of compounds.
For instance, by looking at the periodic table, you can find that hydrogen has a molar mass of 1.0 g/mol, oxygen has 16.0 g/mol, and phosphorus has 31.0 g/mol. This information is instrumental in calculating the properties of chemical formulas and understanding their compositions.

Molecular Weight

Molecular weight, often referred to as molar mass in chemistry, is a measure of the total mass of a molecule. It's calculated by adding up the atomic masses of all atoms in a molecule's chemical formula, using the molar masses from the periodic table.
To calculate molar mass, follow these steps:

• Identify all elements in the formula.
• Find the molar mass of each element from the periodic table.
• Multiply the molar mass by the number of atoms of each element in the chemical formula.
• Sum all the values obtained for each element.

For example, the molar mass of \( \mathrm{H}_2\mathrm{O} \) (water) is 18.0 g/mol: 2 hydrogens (2 x 1.0) + 1 oxygen (1 x 16.0). Knowing molecular weight is essential for chemical reactions and for converting between grams and moles.

Element Identification

Element identification is the first step to solving any problem involving chemical formulas and molar mass calculations. Identifying the elements in a compound involves breaking down the chemical formula to list the elements involved.
For instance, in \( \mathrm{PbCl}_2 \) (lead(II) chloride), you identify that lead (Pb) and chlorine (Cl) are present. There’s one lead atom and two chlorine atoms in each formula unit of this compound.
This identification process helps you understand the compound's structure and is crucial for performing further calculations, such as finding molar mass. Knowing which elements are present and their quantities will also help in balancing equations and understanding chemical reactions.