The mole is a useful unit for chemists because it relates the macroscopic properties of a substance (e.g., mass, volume) to the microscopic world of atoms, ions, and molecules.

Structure of Matter and the Mole:

• Atoms, ions, and molecules are incredibly small. It's impractical to count them individually.
• The mole provides a convenient way to count these particles. One mole contains a fixed number of particles (Avogadro's number).
• This allows chemists to relate the mass of a substance to the number of particles present. For example, knowing the molar mass of a compound (grams per mole) allows us to calculate the number of moles in a given mass of the compound, and vice versa.
• Many chemical reactions occur on a molecular or ionic level. Using moles allows us to accurately predict the amounts of reactants and products involved in a reaction based on the number of particles.

In essence, the mole bridges the gap between the macroscopic and microscopic worlds, making it a fundamental and essential unit in chemistry.

Given:

• Mass of MgCO₃ = 2.49 g
• Molar mass of MgCO₃ = 12.01 (Mg) + 12.01 (C) + 3 * 16.00 (O) = 39.01 g/mol

Calculation:

Number of moles (n) = $(mass/molar\; mass)$

n = 2.49 g / 39.01 g/mol = 0.0645 mol

Answer: The number of moles of magnesium carbonate is 0.0645 mol.

Solution:

1. Calculate the molar mass of the empirical formula (C₂H₆):

   M(C₂H₆) = (2 x 12) + (6 x 1) = 24 + 6 = 30 g/mol

2. Calculate the ratio of the molar mass of the compound to the molar mass of the empirical formula:

   Ratio = 58 g/mol / 30 g/mol = 1.93 (approximately)

3. Multiply the subscripts in the empirical formula by the ratio to obtain the molecular formula:

   Molecular Formula = C₂H₆ x 1.93 ≈ C_3.86H_7.68. Since we need whole numbers, we round to the nearest whole number.

4. Therefore, the molecular formula is C₄H₈.

Answer: C₄H₈