Question

Calculate the molar mass of each hydrated compound. Note that the water of hydration is included in the molar mass. (See Section 3.7.) (a) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) (b) \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O},\) Epsom salts

Short answer

(a) 126.06 g/mol, (b) 246.52 g/mol.

Step-by-step solution

Write Chemical Formula and Identify Components

First, identify the chemical formula of the compound and list its components. For (a), the compound is \( \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \) which includes oxalic acid dihydrate. For (b), the compound is \( \mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O} \) which is magnesium sulfate heptahydrate (Epsom salts).

Determine Individual Molar Masses

Find the molar mass of each element. Use the periodic table for this information. For (a): H: 1.01 g/mol, C: 12.01 g/mol, O: 16.00 g/mol. For water (H2O), it is 2(1.01) + 16.00 = 18.02 g/mol. For (b): Mg: 24.31 g/mol, S: 32.07 g/mol, O: 16.00 g/mol.

Calculate Compound's Molar Mass Without Hydration

Calculate the molar mass of the main compound excluding water of hydration. For (a), \( \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} = 2(1.01) + 2(12.01) + 4(16.00) = 90.02 \) g/mol. For (b), \( \mathrm{MgSO}_{4} = 24.31 + 32.07 + 4(16.00) = 120.38 \) g/mol.

Calculate Molar Mass of Water of Hydration

Multiply the molar mass of water (18.02 g/mol) by the number of water molecules (hydrate). For (a), \( 2 \times 18.02 = 36.04 \) g/mol. For (b), \( 7 \times 18.02 = 126.14 \) g/mol.

Sum Molar Mass of Entire Hydrated Compound

Add the molar mass of the anhydrous compound to the molar mass of water of hydration. For (a), \( 90.02 + 36.04 = 126.06 \) g/mol. For (b), \( 120.38 + 126.14 = 246.52 \) g/mol.

Key concepts

Hydrated Compounds

Hydrated compounds are fascinating substances where water molecules are part of their crystal structure. These are not just random mixtures of compounds and water; rather, the water molecules are chemically bonded within the structure. Let's take the oxalic acid dihydrate, \( \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \), as an example. Here, the 'dihydrate' indicates two water molecules are attached to each formula unit of oxalic acid.

Understanding hydrated compounds is crucial in chemistry because:

• The water of hydration can affect a compound's physical properties, such as solubility and stability.
• In calculations, you'll need to include this water when determining the molar mass, as seen in the original exercise.

Remember, when you encounter terms like 'dihydrate' or 'heptahydrate,' these indicate how many water molecules are included per formula unit of the substance.

Stoichiometry

Stoichiometry refers to the calculation of reactants and products in chemical reactions. It relies heavily on the principle of conservation of mass, meaning the mass of reactants equals the mass of products. It's about counting molecules, in essence.

In the context of hydrated compounds, stoichiometry helps us determine how many water molecules are associated with each unit of the compound. By understanding stoichiometry, we can accurately calculate the molar mass of substances, which is the focus of our original exercise.

Using stoichiometry, you can:

• Determine molar relationships based on an equation.
• Calculate masses, volumes, and concentrations based on these mole relationships.
• Predict yields and determine limiting reactants in a chemical reaction.

Stoichiometry is a fundamental tool in chemistry, helping to balance equations and quantify relationships in chemical reactions, just like calculating the molar mass of hydrated compounds.

Chemical Formulas

Chemical formulas are the shorthand notation for substances in chemistry. They show the types and numbers of atoms in a molecule. For hydrated compounds like \( \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} \), the formula not only includes the main compound but also explicitly states how many water molecules are attached.

These formulas are crucial because:

• They provide essential information for understanding the composition of the compound.
• They are used to perform calculations like determining molar mass.
• They help in visualizing and understanding chemical reactions.

In our exercise, knowing the chemical formula allows us to deconstruct the compound into its basic components and accurately calculate its molar mass. This is why understanding chemical formulas is key to performing precise stoichiometric calculations.

Periodic Table

The periodic table is an invaluable tool in chemistry that organizes all known elements by increasing atomic number. It's not just a list; it is structured in a way that showcases trends in the elements' properties. For instance, the table helps us quickly find the atomic masses needed to calculate molar masses, which is a core element of the original exercise.

Here's why the periodic table is essential:

• It provides atomic masses which are essential for molar mass calculations.
• It allows you to understand the elemental composition and predict interactions.
• It helps identify an element’s properties, such as electronegativity and atomic radius.

When calculating the molar mass of hydrated compounds, you refer to the periodic table to get the mass of each element. For example, knowing that hydrogen has an atomic mass of 1.01 g/mol enables precise calculations for hydronium ions. Therefore, familiarity with the periodic table directly supports successful stoichiometric and chemical formula calculations.