Write the balanced equation, then outline the steps necessary to determine the information requested in each of the following: (a) The number of moles and the mass of Mg required to react with \(5.00 \mathrm{g}\) of \(\mathrm{HCl}\) and produce \(\mathrm{MgCl}_{2}\) and \(\mathrm{H}_{2}\). (b) The number of moles and the mass of oxygen formed by the decomposition of \(1.252 \mathrm{g}\) of silver(I) oxide. (c) The number of moles and the mass of magnesium carbonate, \(\mathrm{MgCO}_{3}\), required to produce \(283 \mathrm{g}\) of carbon dioxide. (MgO is the other product.) (d) The number of moles and the mass of water formed by the combustion of \(20.0 \mathrm{kg}\) of acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\), in an excess of oxygen. (e) The number of moles and the mass of barium peroxide, \(\mathrm{BaO}_{2}\), needed to produce \(2.500 \mathrm{kg}\) of barium oxide, \(\mathrm{BaO}\) \(\left(\mathrm{O}_{2}\right.\) is the other product.)

Understanding balanced chemical equations is essential for the study of chemical reactions, as they show the conservation of mass. In a balanced chemical equation, the number of atoms on the reactant side must equal the number on the product side.

For example, the equation for the reaction between magnesium and hydrochloric acid is written as Mg + 2HCl → MgCl₂ + H₂. Here, we have one magnesium atom, two chlorine atoms, and two hydrogen atoms on both sides of the equation.

Importance in Stoichiometry

Balanced equations are instrumental in stoichiometry, as they provide the mole ratios needed to solve for quantities in a chemical reaction. By using the mole ratio from the balanced equation, students can calculate the moles of another substance reacting or produced. Therefore, ensuring the chemical equation is balanced before proceeding with calculations is a crucial step.

The mole concept is a bridge between the micro-world of atoms and molecules and the macro-world that we can measure. One mole is defined as exactly 6.022 x 10²³ (Avogadro's number) of particles (atoms, molecules, ions, or electrons).

In chemical stoichiometry, moles provide a consistent method to convert between atoms/molecules and grams. For example, if we have 0.137 moles of HCl, we're referring to 0.137 x 6.022 x 10²³ molecules of hydrochloric acid.

Role in Calculations

By knowing the number of moles, we can use the molar mass of a substance to calculate the mass needed in a reaction. Molar mass is the weight of one mole of a substance and can be found on the periodic table. The concept simplifies complex chemical calculations and allows chemists to predict the outcomes of reactions quantitatively.

Molar mass calculations are vital for converting between moles and grams, enabling chemists to accurately measure substances for reactions. The molar mass is the mass of one mole of a substance and is usually expressed in grams per mole (g/mol).

Each element's molar mass is found on the periodic table and is equivalent to its atomic weight. For compounds, the molar mass is the sum of the molar masses of all atoms in the molecule. For instance, the molar mass of H₂O is 18.02 g/mol since it has two hydrogen atoms (1.01 g/mol each) and one oxygen atom (16.00 g/mol).

Applying Molar Mass in Calculations

Calculating the mass of a substance requires multiplying its number of moles by its molar mass. In one of our exercise examples, the mass of magnesium carbonate (MgCO₃) required to produce carbon dioxide is found by multiplying the moles of MgCO₃ by its molar mass (84.31 g/mol). Such calculations are the cornerstone of predicting the amounts of reactants needed and products formed in a chemical reaction.