What is the minimum amount of \(6.0 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) necessary to produce \(15.0 \mathrm{~g}\) of \(\mathrm{H}_{2}(g)\) according to the reaction: $$ 2 \mathrm{Al}(\mathrm{s})+3 \mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q)+3 \mathrm{H}_{2}(g) $$

Molar mass is a fundamental concept in chemistry, representing the mass of one mole of a substance. One mole is defined as the amount of substance containing as many particles, such as atoms or molecules, as there are atoms in 12 grams of carbon-12. This is approximately 6.022 x 10²³ particles, a value known as Avogadro's number.

The molar mass is typically expressed in grams per mole (g/mol) and can be found by summing the atomic masses of all the atoms in a molecule. For example, water (H₂O) has a molar mass of approximately 18.02 g/mol, calculated from two hydrogen atoms (each about 1.01 g/mol) plus one oxygen atom (about 16.00 g/mol).

To determine the number of moles from a given mass, the formula is ( n = \frac{m}{M} ), where \(m\) is the mass of the substance and \(M\) is its molar mass. Understanding molar mass is crucial for stoichiometry calculations, as it allows us to convert between mass and moles, linking the macroscopic world we can measure to the microscopic world of atoms and molecules.

In a chemical reaction, stoichiometry is used to describe the quantitative relationship between reactants and products. It's like a recipe in cooking that specifies how much of each ingredient you need for a dish; stoichiometry tells you how much of each reactant you need to produce a certain amount of product. The coefficients in a balanced chemical equation provide the ratios of moles of reactants and products.

For instance, in the reaction \(2\text{Al}(s) + 3\text{H}_2\text{SO}_4(aq) \longrightarrow \text{Al}_2(\text{SO}_4)_3(aq) + 3\text{H}_2(g)\), the stoichiometric coefficients 2, 3, and 3 tell us that two moles of aluminum react with three moles of sulfuric acid to produce three moles of hydrogen gas.

When solving stoichiometry problems, you compare the ratio of reactants used in the equation to the amount of product desired. It's the key for predicting the outcomes of reactions and is necessary for scaling up from lab-scale experiments to industrial production.

Molarity is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution (mol/L or M). It's an essential concept for preparing solutions in the lab and for performing calculations involving reactions in solution.

To find the volume of a solution with a given molarity that's required for a reaction, you use the formula \(V = \frac{n}{C}\), where \(V\) is the volume in liters, \(n\) is the number of moles of solute, and \(C\) is the concentration of the solution in molarity (M). For example, if you need 1 mole of solute and you have a 1 M solution, you would need 1 liter of the solution.

Understanding molarity helps you dilute concentrated solutions to a desired concentration, calculate how much solute is needed to make a specific solution, and determine the amount of reactant in a given volume of solution for a reaction. It's especially important for quantitative aspects of chemical reactions that occur in solution.