Question

The United States chemical industry produces more sulfuric acid \(\left(\mathrm{H}_{2} \mathrm{SO}_{4}\right),\) in terms of mass, than any other chemical. What is the mass of 3.25 \(\mathrm{mol}\) of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) ?

Short answer

The mass of 3.25 mol of H₂SO₄ = 3.25 mol × (2 × 1.01 g/mol + 32.07 g/mol + 4 × 16.00 g/mol) = 3.25 mol × 98.09 g/mol = 318.29 g.

Step-by-step solution

Find the molar mass of each atom in H₂SO₄

To find the molar mass, we will use the following atomic masses: - Hydrogen (H) molar mass = 1.01 g/mol - Sulfur (S) molar mass = 32.07 g/mol - Oxygen (O) molar mass = 16.00 g/mol

Calculate the molar mass of H₂SO₄

To calculate the molar mass of H₂SO₄, we need to add the molar masses of all the atoms present in H₂SO₄. Since there are 2 Hydrogen atoms, 1 Sulfur atom, and 4 Oxygen atoms, the calculation will be: Molar mass of H₂SO₄ = 2 × Molar mass of H + Molar mass of S + 4 × Molar mass of O Molar mass of H₂SO₄ = 2 × 1.01 g/mol + 32.07 g/mol + 4 × 16.00 g/mol

Calculate the mass of 3.25 mol of H₂SO₄

Now that we have the molar mass of H₂SO₄, we can multiply it by the given number of moles (3.25 mol) to find the mass: Mass of H₂SO₄ = Number of moles × Molar mass Mass of H₂SO₄ = 3.25 mol × (2 × 1.01 g/mol + 32.07 g/mol + 4 × 16.00 g/mol) Now calculate the mass of H₂SO₄ and the problem will be solved.

Key concepts

Sulfuric Acid

Sulfuric acid, with the chemical formula \(\mathrm{H}_{2}\mathrm{SO}_{4}\), is one of the most important industrial chemicals. It's used in the production of fertilizers, cleaning agents, and in the lead-acid batteries found in cars.

Understanding its structure is key to solving problems involving sulfuric acid. It is composed of two hydrogen atoms (H), one sulfur atom (S), and four oxygen atoms (O). In stoichiometric calculations involving sulfuric acid, recognizing that it's a diprotic acid can make a difference. This means each molecule of sulfuric acid can donate two protons (or hydrogen ions), a fact that's essential in many chemical reactions and calculations.

In education, sulfuric acid often serves as an example to explain the concepts of molarity and reactivity due to its strong acidic nature. Moreover, its widespread use in various industries makes it a relevant substance for chemistry students to familiarize themselves with.

Stoichiometry

Stoichiometry is the section of chemistry that involves the quantification of reactants and products in chemical reactions. It is based on the conservation of mass where the total mass of reactants equals the total mass of products.

The stoichiometric coefficients that appear in a balanced chemical equation tell us in what ratio the molecules react and are formed. For example, in the decomposition of sulfuric acid into its elements, the coefficients indicate the mole ratio of all reactants and products.

Practical Application in Calculations

When a problem requires the calculation of the mass of a substance from a given number of moles, as in the sulfuric acid problem, stoichiometry is applied. By using the molar mass and the mole concept which relates the mass of a substance to the number of its molecules, stoichiometry aids in translating moles into grams, and vice versa, providing a fundamental tool for such calculations.

Chemical Molar Mass

The chemical molar mass is the mass of one mole of a substance. It is expressed in grams per mole (g/mol) and is calculated by summing the atomic masses of all the atoms in a molecule.

Calculating Molar Mass

To calculate the molar mass of a compound like sulfuric acid, we look at the periodic table for the atomic masses of hydrogen, sulfur, and oxygen. This mass must be multiplied by the number of each type of atom in the molecule. For \(\mathrm{H}_{2}\mathrm{SO}_{4}\), this involves adding the masses of 2 hydrogen atoms, 1 sulfur atom, and 4 oxygen atoms together.

Importance in Chemistry

Molar mass plays a crucial role in converting moles to grams, which is vital for laboratory work and understanding the quantities of substances involved in reactions. As a central concept in stoichiometry, it allows chemists to predict the outcomes of reactions quantitatively and to determine how much of each reactant is needed to produce a desired amount of product.