Question

Determine the molar mass for the following compounds. (Chapter 10) a. \(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) b. \(\mathrm{Fe}(\mathrm{OH})_{3}\) d. the name of the compound is tetraphosphorus decoxide.

Short answer

The molar masses for the given compounds are as follows: a. \(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2} \cdot 6 \mathrm{H}_{2}\mathrm{O}\): 291.07 g/mol b. \(\mathrm{Fe}(\mathrm{OH})_{3}\): 106.88 g/mol d. Tetraphosphorus decoxide (P4O10): 283.88 g/mol

Step-by-step solution

Identify elements and their molar masses from the periodic table

First, we need to determine the molar masses for each element in the compound. Using the periodic table, we have: - Co (Cobalt): 58.93 g/mol - N (Nitrogen): 14.01 g/mol - O (Oxygen): 16.00 g/mol - H (Hydrogen): 1.01 g/mol

Calculate the molar mass for each part of the compound

Now, we will determine the molar masses for each part of the compound: 1. Co: 1 x 58.93 g/mol = 58.93 g/mol 2. NO3: 1 N (14.01 g/mol) + 3 O (16.00 g/mol) = 14.01 + 48.00 = 62.01 g/mol 3. H2O: 2 H (1.01 g/mol) + 1 O (16.00 g/mol) = 2.02 + 16.00 = 18.02 g/mol

Calculate the overall molar mass of the compound

Now, we combine the molar masses from each part while taking into account the stoichiometry and hydration: Overall molar mass = 1 Co (58.93 g/mol) + 2 (NO3) (62.01 g/mol) + 6 (H2O) (18.02 g/mol) = 58.93 + 124.02 + 108.12 = 291.07 g/mol So, the molar mass of \(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2} \cdot 6 \mathrm{H}_{2}\mathrm{O}\) is 291.07 g/mol. #b. Fe(OH)3#:

Identify elements and their molar masses from the periodic table

First, we need to determine the molar masses for each element in the compound. Using the periodic table, we have: - Fe (Iron): 55.85 g/mol - O (Oxygen): 16.00 g/mol - H (Hydrogen): 1.01 g/mol

Calculate the molar mass for each part of the compound

Now, we will determine the molar masses for each part of the compound: 1. Fe: 1 x 55.85 g/mol = 55.85 g/mol 2. OH: 1 O (16.00 g/mol) + 1 H (1.01 g/mol) = 16.00 + 1.01 = 17.01 g/mol

Calculate the overall molar mass of the compound

Now, we combine the molar masses from each part while taking into account the stoichiometry: Overall molar mass = 1 Fe (55.85 g/mol) + 3 (OH) (17.01 g/mol) = 55.85 + 51.03 = 106.88 g/mol So, the molar mass of \(\mathrm{Fe}(\mathrm{OH})_{3}\) is 106.88 g/mol. #d. Tetraphosphorus decoxide (P4O10)#:

Identify elements and their molar masses from the periodic table

First, we need to determine the molar masses for each element in the compound. Using the periodic table, we have: - P (Phosphorus): 30.97 g/mol - O (Oxygen): 16.00 g/mol

Calculate the overall molar mass of the compound

Now, we combine the molar masses from each part while taking into account the stoichiometry: Overall molar mass = 4 P (30.97 g/mol) + 10 O (16.00 g/mol) = 123.88 + 160.00 = 283.88 g/mol So, the molar mass of tetraphosphorus decoxide (P4O10) is 283.88 g/mol.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships that govern the combination of elements in chemical reactions. To successfully engage in stoichiometry, one must understand the principles behind chemical equations, as these equations provide the necessary information regarding the proportions of reactants and products involved in a reaction.

In stoichiometric calculations, the conservation of mass is a crucial concept. This means that the mass of the reactants in a reaction equals the mass of the products. For the calculation of the molar mass of a compound, such as Co(NO3)2 • 6 H2O or Fe(OH)3, stoichiometry takes into account the amount (in moles) of each element that combines to form a given compound. Molar masses obtained from the periodic table are pivotal for these calculations, as they provide the weight of one mole of an atom or a molecule.

Understanding how to apply stoichiometry to determine molar masses involves balancing the number of moles of each element based on the compound's chemical formula. For example, in the case of Fe(OH)3, the stoichiometric coefficients indicate that there are three hydroxide (OH) groups for every one iron (Fe) atom. This relationship is critical for accurately calculating the molar mass of the compound.

Periodic Table

The periodic table is an organized chart of chemical elements, arranged in order of increasing atomic number. It is a fundamental tool in chemistry as it systematically displays the elements' properties, allowing chemists to quickly retrieve information such as atomic mass, electronic configurations, and valence electrons.

For molar mass calculations, the periodic table is indispensable as it provides the atomic masses of elements, which are averages of isotopic masses standardized to carbon-12. When calculating the molar mass of a compound, like tetraphosphorus decoxide (P4O10), you start by looking up the atomic masses of phosphorus (P) and oxygen (O) on the periodic table. By understanding how to read this crucial chart, students learn to transform atomic masses into molar masses, multiplying by the corresponding stoichiometric factor from the molecule's formula to find the compound's total molar mass.

Molecular Composition

The molecular composition of a compound refers to the types and numbers of atoms that combine to form a molecule, as represented by its chemical formula. This composition is integral to determining the physical and chemical properties of a molecule, including its molar mass.

Calculating molar mass based on molecular composition involves identifying each distinct atom within the molecule and the number of times each atom appears. For instance, in the compound Co(NO3)2 • 6H2O, the composition includes cobalt (Co), nitrate (NO3), and water (H2O) molecules. By acknowledging the number of times each group appears, known as the subscript in the chemical formula, and considering any hydrates (as in the six water molecules), chemists can accurately calculate the total molar mass.

Understanding molecular composition also means recognizing polyatomic ions, like the nitrate in cobalt(II) nitrate hexahydrate, and individual components of a molecule, which is essential for performing molar mass and stoichiometric calculations correctly.