Question

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

Short answer

a. Fe₂O₃ is an ionic compound and there are \(1.5667 \times 10^{1}\) moles of it in 2.50 kg. b. PbCl₄ is an ionic compound and there are \(7.2756 \times 10^{-5}\) moles of it in 25.4 mg.

Step-by-step solution

Identify the type of compound

Fe₂O₃ is composed of a metal (iron, Fe) and a nonmetal (oxygen, O). When a metal combines with a nonmetal, the bond is generally ionic. Thus, Fe₂O₃ is an ionic compound.

Calculate the molar mass of the compound

To find the molar mass of Fe₂O₃, we add the molar masses of 2 Fe atoms and 3 O atoms: Molar mass of Fe = 55.845 g/mol Molar mass of O = 16.00 g/mol Molar mass of Fe₂O₃ = (2 × 55.845 g/mol) + (3 × 16.00 g/mol) = 159.69 g/mol

Convert the given mass to moles

We are given 2.50 kg of Fe₂O₃. First, we'll convert kilograms to grams: 2.50 kg × (1000 g/kg) = 2500 g Now, we can use the molar mass to convert grams to moles: moles of Fe₂O₃ = (2500 g) / (159.69 g/mol) = 15.667 moles

Express the moles in scientific notation

To express the moles in scientific notation, we'll rewrite the number as a decimal between 1 and 10, multiplied by the appropriate power of 10: 15.667 moles = \(1.5667 \times 10^{1}\) moles #Part b#

Identify the type of compound

PbCl₄ is composed of a metal (lead, Pb) and a nonmetal (chlorine, Cl). As in part a, the bond is generally ionic when a metal combines with a nonmetal. Thus, PbCl₄ is an ionic compound.

Calculate the molar mass of the compound

To find the molar mass of PbCl₄, we add the molar masses of 1 Pb atom and 4 Cl atoms: Molar mass of Pb = 207.2 g/mol Molar mass of Cl = 35.45 g/mol Molar mass of PbCl₄ = (1 × 207.2 g/mol) + (4 × 35.45 g/mol) = 349.0 g/mol

Convert the given mass to moles

We are given 25.4 mg of PbCl₄. First, we'll convert milligrams to grams: 25.4 mg × (1 g/1000 mg) = 0.0254 g Now, we can use the molar mass to convert grams to moles: moles of PbCl₄ = (0.0254 g) / (349.0 g/mol) = 0.000072756 moles

Express the moles in scientific notation

To express the moles in scientific notation, we'll rewrite the number as a decimal between 1 and 10, multiplied by the appropriate power of 10: 0.000072756 moles = \(7.2756 \times 10^{-5}\) moles To summarize, the solutions are: a. Fe₂O₃ is an ionic compound and there are \(1.5667 \times 10^{1}\) moles of it in 2.50 kg. b. PbCl₄ is an ionic compound and there are \(7.2756 \times 10^{-5}\) moles of it in 25.4 mg.

Key concepts

Molar Mass Calculation

Understanding the concept of molar mass is fundamental in chemistry for converting between mass and moles of a substance. The molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol).

To calculate the molar mass, we add together the atomic masses of all atoms in a molecule of the substance. Atomic masses can be found on the periodic table, and these values represent the average mass of all naturally occurring isotopes of an element.

For example, when calculating the molar mass of water (H₂O), we sum the molar masses of 2 hydrogen (H) atoms and 1 oxygen (O) atom. With H having a molar mass of about 1.01 g/mol and O having a molar mass of about 16.00 g/mol, the molar mass of water would be approximately (2 * 1.01 g/mol) + (1 * 16.00 g/mol) = 18.02 g/mol.

This concept allows us to convert from grams to moles using the formula:
\[\text{number of moles} = \frac{\text{given mass in grams}}{\text{molar mass}}\]
It’s crucial to accurately determine the number of each type of atom in a compound's formula to apply this correctly.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is especially useful in chemistry and physics, where measurements can span a huge range of values.

In scientific notation, a number is written as the product of two factors: a coefficient that is at least 1 but less than 10, and a power of 10. This format is \[a \times 10^{n}\], where 'a' is the coefficient and 'n' is the exponent indicating the number of decimal places the decimal point has been moved.

For instance, to convert 0.000507 to scientific notation, we move the decimal point three places to the right, which gives us 5.07 and the exponent will be -3, because we moved to the right. So, 0.000507 in scientific notation is \(5.07 \times 10^{-3}\).

This notation simplifies calculations and makes it easier to understand and compare very large or very small numbers. When working with moles and mass, it's common to express results in scientific notation to maintain precision without using cumbersome long numbers.

Ionic and Molecular Compounds

Chemical compounds are classified as either ionic or molecular based on the types of bonds holding the atoms together. Ionic compounds form when metals transfer electrons to nonmetals, resulting in a lattice of positively and negatively charged ions held together by ionic bonds, a type of electrostatic attraction. Common table salt (NaCl) is a classic example of an ionic compound.

Molecular compounds, on the other hand, form when two or more nonmetals share electrons, creating covalent bonds. Such compounds are characterized by the distinct molecules that result from these bonds, like water (H₂O) or carbon dioxide (CO₂).

To determine whether a compound is ionic or molecular, we look at the components; metals indicate an ionic compound, while nonmetals indicate a molecular compound. Knowing the nature of the compound is critical for predicting its properties and behaviors, such as melting point, boiling point, solubility, and conductivity. For example, ionic compounds typically have higher melting and boiling points and conduct electricity when molten, unlike molecular compounds which generally have lower melting and boiling points and do not conduct electricity.