Problem 72 - Chemistry Matter and Change

Question

Apply The molar mass of a compound is twice that of its empirical formula. How are the compound’s molecular and empirical formulas related?

Step-by-Step Solution

Answer

The molecular and empirical formulas of a compound are related when the molar mass of the compound is twice that of its empirical formula. In such a case, the molecular formula is exactly twice the empirical formula, meaning that the molecular formula has two times the number of atoms for each element compared to its empirical formula. If the empirical formula is represented by E and the molecular formula by M, the relationship can be expressed as M = 2 × E.

Step 1: Define molecular and empirical formulas

A molecular formula shows the exact number of atoms of each element present in one molecule of a compound. Empirical formula is the simplest whole-number ratio of atoms in a compound. For example, the molecular formula of glucose is C₆H₁₂O₆, but its empirical formula is CH₂O (reduced to the simplest whole-number ratio)

Step 2: Relationship between molar mass and empirical formula

Molar mass is the mass of one mole of a substance, usually expressed in grams. The molar mass of a substance can be found by summing the masses of its constituent elements according to their molecular formula. When the molar mass of a compound is twice that of its empirical formula, it means the mass of the molecular formula (actual compound) is twice the mass of the simplest ratio (empirical formula).

Step 3: Establish the relationship between molecular and empirical formulas

If the molar mass of the compound is twice that of its empirical formula, the molecular formula will be twice the empirical formula. In other words, the molecular formula will have two times the number of atoms for each element compared to its empirical formula. Let's denote the empirical formula as E and the molecular formula as M. Then: M = 2 × E This means that the molecular formula is twice the empirical formula. For example, if the empirical formula of a compound is CH₂O and its molar mass is twice that of its empirical formula, then the molecular formula of the compound would be C₂H₄O₂ (two times CH₂O).

Key Concepts

Empirical Formula

An empirical formula represents the simplest whole-number ratio of the atoms of each element in a compound. It does not provide insight into the exact number of atoms, but it gives the basic blueprint of how many of each type of atom are in the compound relative to each other. Thus, it can be thought of as the baseline formula for a compound.

To determine an empirical formula, one must:

• First, find the amount in moles of each element in a sample of a compound, typically starting from the percentage by mass of each element.
• Next, express the ratio of the amount of these elements in the simplest whole numbers.

Empirical formulas are crucial in chemistry, especially in stoichiometry, as they provide foundational information about the relationships between elements in compounds. For instance, while glucose has a molecular formula of C₆H₁₂O₆, its empirical formula is CH₂O.

Molar Mass

The concept of molar mass is pivotal in understanding compounds. Molar mass is akin to a bridge between the microscopic world of molecules and the macroscopic world of grams and kilograms. It's expressed in units of grams per mole (g/mol) and signifies the mass of one mole of a given substance, which equates to roughly 6.022 x 10²³ particles (Avogadro's number).

To calculate molar mass:

• Determine the atomic mass of each element in the compound from the periodic table.
• Multiply each element’s atomic mass by the number of atoms of that element, as given in the molecular formula.
• Add up all these values to obtain the molar mass of the compound.

Understanding the molar mass is essential for converting between grams and moles, designing reactions with proper stoichiometry, and for formulas that relate to the molecular and empirical relationships of compounds. For example, if a compound's molar mass is twice that of its empirical formula, its molecular formula will have twice as many atoms of each element compared to its empirical formula.

Compound Chemistry

Understanding the chemistry of compounds involves knowing how elements combine to form substances with new properties. This knowledge is rooted in grasping the nature of chemical bonds and how compounds are represented through chemical formulas.

The study of compounds explores:

• How elements bond together to form molecules or lattice structures through ionic or covalent bonds.
• The role of valency in dictating how elements combine and the ratios in which they do so.

A deep understanding of compound chemistry aids in predicting how substances will interact in chemical reactions, determining the products of reactions, and ensuring reactions are engineered efficiently. It also involves working with empirical and molecular formulas to comprehend how different elements in a compound contribute to its overall properties. This holistic understanding of compounds, from their formation to their interaction, shapes much of the work in chemistry from basic studies to advanced applications.