Problem 41 - Chemistry Matter and Change

Question

Identify each as an ionic or molecular compound and convert the given mass to moles. Express your answers in scientific notation. \begin{equation}a. 2.50 \mathrm{kg} \quad \mathrm{Fe}_{2} \mathrm{O}_{3} \quad \text { b. } 25.4 \mathrm{mg} \quad \mathrm{PbCl}_{4}\end{equation}

Step-by-Step Solution

Answer

Both compounds are ionic. \( \text{Fe}_2\text{O}_3: 1.565 \times 10^{1} \text{ moles}; \text{PbCl}_4: 7.28 \times 10^{-5} \text{ moles}.\)

Step 1: Determine Type of Compound

An ionic compound consists of metals and non-metals, while a molecular compound typically consists of non-metals only. For \( \text{Fe}_2\text{O}_3 \), iron (Fe) is a metal and oxygen (O) is a non-metal, so it is an ionic compound. For \( \text{PbCl}_4 \), lead (Pb) is a metal and chlorine (Cl) is a non-metal, so it is also an ionic compound.

Step 2: Convert Mass to Grams

1 kilogram (kg) equals 1000 grams (g), so convert \( 2.50 \text{ kg} \) of \( \text{Fe}_2\text{O}_3 \) to grams: \( 2.50 \times 1000 = 2500 \text{ g} \). For \( 25.4 \text{ mg} \) of \( \text{PbCl}_4 \), convert milligrams to grams: 1 milligram (mg) equals 0.001 grams (g), so \( 25.4 \times 0.001 = 0.0254 \text{ g} \).

Step 3: Calculate Moles of Fe2O3

The molar mass of \( \text{Fe}_2\text{O}_3 \) is obtained by adding the atomic masses of its components: \( 2 \times 55.85 \text{ (Fe)} + 3 \times 16.00 \text{ (O)} = 159.7 \text{ g/mol} \). Convert the mass to moles by dividing: \( \frac{2500 \text{ g}}{159.7 \text{ g/mol}} = 15.65 \text{ moles} \), which is \( 1.565 \times 10^{1} \text{ moles} \) in scientific notation.

Step 4: Calculate Moles of PbCl4

The molar mass of \( \text{PbCl}_4 \) is found by adding the atomic masses of its components: \( 1 \times 207.2 \text{ (Pb)} + 4 \times 35.45 \text{ (Cl)} = 349.0 \text{ g/mol} \). Convert the mass to moles by dividing: \( \frac{0.0254 \text{ g}}{349.0 \text{ g/mol}} = 7.28 \times 10^{-5} \text{ moles} \).

Key Concepts

Molar Mass Calculation

Molar mass is a crucial concept in chemistry that helps identify the mass of one mole of a substance. It is expressed in grams per mole (g/mol). To determine the molar mass of a compound, one must add up the atomic masses of each element in the compound.
For example, when calculating the molar mass of iron (III) oxide, Fe extsubscript{2}O extsubscript{3}, you take into account the atomic masses of iron and oxygen. Fe has an atomic mass of approximately 55.85 g/mol, while O is about 16.00 g/mol. Adding them together, you get:

• 2 Fe: 2 × 55.85 = 111.70 g/mol
• 3 O: 3 × 16.00 = 48.00 g/mol

Thus, the total molar mass is 159.7 g/mol.
Mastering molar mass calculation is essential, as it is often the first step in many chemical equations and conversions.

Conversion from Mass to Moles

Conversion from mass to moles is a fundamental chemical calculation that connects the mass of a substance to the amount in moles. Moles are a convenient unit in chemistry because they relate the large quantities of particles in a substance to its mass.
To perform this conversion, use the formula:

• Number of moles = Mass of substance (g) / Molar mass (g/mol)

For instance, if you have 2500 grams of Fe extsubscript{2}O extsubscript{3}, knowing its molar mass is 159.7 g/mol, you can calculate the moles:

• 2500 g ÷ 159.7 g/mol = 15.65 moles

This concept is equally crucial in reactions and equations, as understanding the mole relationship helps determine how much of a substance is needed or produced.

Scientific Notation in Chemistry

Scientific notation is a method used to express very large or very small numbers conveniently. In chemistry, it simplifies working with quantities such as masses of atoms and molecules.
The format for scientific notation is:

• A number between 1 and 10 multiplied by a power of ten, like:
  7.28 × 10⁻⁵

Scientific notation makes it easier to handle numbers in calculations by reducing the number of zeroes you have to write out.
For instance, expressing the number of moles of PbCl extsubscript{4} (0.0000728 moles) in scientific notation becomes 7.28 × 10⁻⁵ moles. This practice aids in precision and clarity, making it an invaluable tool in chemistry.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It allows chemists to predict the quantities of different substances involved in reactions, ensuring correct proportions are used.
Key aspects of stoichiometry include:

• Mole Ratios: Derived from the coefficients of a balanced equation; they show the proportions of reactants and products.
• Converting Units: Involves using molar mass and Avogadro's number to switch between mass, volume, particles, and moles.

For example, if a reaction produces water from hydrogen and oxygen, knowing the stoichiometry ensures the right amounts of hydrogen and oxygen are combined.
Without precise stoichiometry, it's difficult to achieve the desired outcomes in chemical processes, making this concept essential not just for academics but also for industrial applications.