Question

Calculate the molar mass of each hydrated compound. Note that the water of hydration is included in the molar mass. (See Section 2.11.) (a) \(\mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\)

Short answer

(a) 254.81 g/mol, (b) 249.72 g/mol.

Step-by-step solution

Identify the Components of Each Compound

For (a), the compound is \( \mathrm{Ni}(\mathrm{NO}_3)_2 \cdot 6 \mathrm{H_2O} \), which consists of nickel nitrate and 6 water molecules. For (b), the compound is \( \mathrm{CuSO}_4 \cdot 5 \mathrm{H_2O} \), which consists of copper sulfate and 5 water molecules.

Calculate the Molar Mass of the Anhydrous Compound

For \( \mathrm{Ni}(\mathrm{NO}_3)_2 \), the molar masses are: Ni (58.69 g/mol), N (2 \times 14.01 g/mol), O (6 \times 16.00 g/mol). So, the molar mass is: \( 58.69 + 2 \times (14.01 + 3 \times 16.00) = 146.69 \) g/mol.For \( \mathrm{CuSO}_4 \), the molar masses are: Cu (63.55 g/mol), S (32.07 g/mol), O (4 \times 16.00 g/mol). So, the molar mass is: \( 63.55 + 32.07 + 4 \times 16.00 = 159.62 \) g/mol.

Calculate the Molar Mass of Water of Hydration

Water (H2O) has a molar mass of approximately 18.02 g/mol. For (a), we multiply by 6: \( 6 \times 18.02 = 108.12 \) g/mol.For (b), we multiply by 5: \( 5 \times 18.02 = 90.10 \) g/mol.

Sum the Molar Masses

For (a): Add the molar mass of Ni(NO3)2 and water: \( 146.69 + 108.12 = 254.81 \) g/mol.For (b): Add the molar mass of CuSO4 and water: \( 159.62 + 90.10 = 249.72 \) g/mol.

Key concepts

Hydrated Compounds

Hydrated compounds are fascinating entities in the realm of chemistry. They are complex structures where specific numbers of water molecules are integrated into the compound's crystal structure. This inclusion of water, referred to as water of hydration, is crucial for many compounds, influencing their properties and reactions.

When we talk about hydrated compounds, we often use a dot to separate the compound's formula from the water molecules. For example, in the compound \( \mathrm{Ni}(\mathrm{NO}_3)_2 \cdot 6 \mathrm{H_2O} \), the dot signifies the association of six water molecules with each formula unit of nickel nitrate.

• The water molecules can significantly affect the physical properties of the compound, such as color, solubility, and melting point.
• In hydrated compounds, water can be driven off by heating, often resulting in a different substance known as the anhydrous form, which lacks water in its structure.

Understanding hydrated compounds is crucial in fields like chemistry and materials science, where water plays a pivotal role in the stability and reactivity of substances.

Chemical Formulas

A chemical formula is a shorthand notation that uses chemical element symbols and numbers to convey information about the types and proportions of atoms in a substance. It's like a recipe for molecules, providing vital information to chemists and scientists.

In a chemical formula, the subscripts denote the number of each type of atom within a molecule. For instance, \( \mathrm{CuSO}_4 \cdot 5 \mathrm{H_2O} \) indicates one copper (Cu), one sulfur (S), four oxygen (O), and five water (\( \mathrm{H_2O} \)) molecules associated with it.

• Subscripts apply only to the element they immediately follow. For example, in \( \mathrm{H_2O} \), the subscript "2" applies only to hydrogen (H), indicating two hydrogen atoms for every one oxygen (O) atom.
• Chemical formulas for hydrated compounds incorporate both the main compound and its water of hydration, separated by a dot.

Chemical formulas are foundational to understanding chemical reactions, as they allow scientists to balance equations and predict the outcomes of reactions by providing a clear depiction of the reactants involved.

Stoichiometry

Stoichiometry is an essential concept in chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is the backbone of predicting how substances will interact on a molecular level.

When calculating the molar mass of a compound, stoichiometry helps us understand the proportions of each element in the compound, as well as how these proportions change during chemical reactions. For example, when handling hydrated compounds like \( \mathrm{CuSO}_4 \cdot 5 \mathrm{H_2O} \), stoichiometry ensures that we correctly account for both the anhydrous compound and its water of hydration when calculating the total mass.

• Stoichiometry uses coefficients in balanced equations to relate the quantities of all reactants and products.
• It allows chemists to convert between mass, moles, and even the number of molecules using Avogadro's number.

Mastering stoichiometry is vital for making accurate predictions in chemical processes, determining yield, and scaling up reactions for industrial applications.

Water of Hydration

Water of hydration is the term used to describe water molecules that are chemically integrated within a substance's structure. These water molecules are not simply mixed with the compound; instead, they are part of its crystal lattice and contribute significantly to the properties of the compound.

In many cases, water of hydration plays a critical role in the stability, reactivity, and even color of the compound. For example, \( \mathrm{CuSO}_4 \cdot 5 \mathrm{H_2O} \), known as copper(II) sulfate pentahydrate, displays a bright blue color due to the presence of water in its structure. When this water is removed, typically by heating, the compound's appearance and properties change markedly.

• The water of hydration can be quantified when calculating a hydrated compound's molar mass, as it adds to the overall mass of the formula unit.
• Knowing the water of hydration is crucial for processes like dehydration and crystallization.

Understanding the role and calculation of water of hydration is fundamental for tasks like formula calculation and predicting how substances behave in various conditions.