A quantity of \(13.5 \mathrm{~g}\) of aluminium when changes to \(\mathrm{Al}^{3+}\) ion in solution, will lose \((\mathrm{Al}=27)\) (a) \(18.0 \times 10^{23}\) electrons (b) \(6.02 \times 10^{23}\) electrons (c) \(3.01 \times 10^{23}\) electrons (d) \(9.1 \times 10^{23}\) electrons

Crucial to understanding the mole concept in chemistry is Avogadro's number, a constant that defines the number of particles found in one mole of any substance. To be precise, Avogadro's number is approximately \(6.02 \times 10^{23}\). It's the bridge that connects the macroscopic world we can observe and measure with the microscopic world of atoms and molecules.

Imagine if you had a dozen eggs — that’d be 12 eggs. Similarly, if chemists say they have a mole of aluminum atoms, they have \(6.02 \times 10^{23}\) aluminum atoms. This is immensely useful because with Avogadro's number, we can count out atoms much like eggs, only on a much, much smaller scale. This allows for precise calculations in chemical reactions and formulations.

The molar mass is an essential piece of the puzzle when converting between mass and moles. It represents the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For an element, the molar mass is numerically equivalent to the atomic mass found on the periodic table but with the unit g/mol attached.

For instance, aluminum has a molar mass of \(27 \text{g/mol}\), which is a way of saying that one mole of aluminum atoms weighs 27 grams. When given a mass of a substance, like \(13.5 \text{g}\) of aluminum, determining the number of moles involves dividing the mass by the molar mass, a step that sets the stage for deeper chemical calculations.

Unraveling Chemical Recipes

Stoichiometry could be likened to the recipe for chemical reactions, detailing the proportions in which substances react and form products. Chemists use stoichiometry to calculate reactant and product quantities during chemical reactions.

It requires a balanced chemical equation and the conversion of masses to moles or vice versa. Stoichiometry is the quantitative foundation upon which chemical equations and reactions rest. It ensures that the law of conservation of mass is respected, the principle that matter is neither created nor destroyed in a chemical reaction.

Math Meets Chemistry

Chemical calculations are the bread and butter of laboratory work and industrial applications. These calculations often involve the mole concept, Avogadro's number, and molar masses as critical components. By skillfully combining these concepts, chemists can predict how much product will form in a reaction, the amount of a reactant needed, or even the number of ions and electrons involved in a chemical change.

The steps for calculating electrons lost when aluminum forms ions is an example of chemical calculations in action. We start with a known mass, convert to moles, use Avogadro's number to find the number of atoms, and then determine the number of electrons each atom will lose or gain. Every step is pivotal to obtaining an accurate final answer.