Problem 37 - Chemistry Matter and Change

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 \(\mathrm{H}_{2} \mathrm{SO}_{4}\) ?

Step-by-Step Solution

Answer

The mass of 3.25 moles of \( \mathrm{H}_{2} \mathrm{SO}_{4} \) is 318.5 grams.

Step 1: Understand the Problem

We are given the number of moles of sulfuric acid (3.25 moles) and need to find the mass of the sulfuric acid in these moles. This requires us to convert moles to grams using the molar mass of sulfuric acid, \( \mathrm{H}_{2} \mathrm{SO}_{4} \).

Step 2: Calculate the Molar Mass of \( \mathrm{H}_{2} \mathrm{SO}_{4} \)

To find the molar mass of \( \mathrm{H}_{2} \mathrm{SO}_{4} \), we need to sum the atomic masses of its constituent atoms. Hydrogen (H) has an atomic mass of about 1 g/mol, sulfur (S) about 32 g/mol, and oxygen (O) about 16 g/mol. Thus, the molar mass of \( \mathrm{H}_{2} \mathrm{SO}_{4} \) is calculated as follows:\[(2 \times 1) + (1 \times 32) + (4 \times 16) = 2 + 32 + 64 = 98 \text{ g/mol}\]

Step 3: Convert Moles to Grams

To find the mass of 3.25 moles of \( \mathrm{H}_{2} \mathrm{SO}_{4} \), use the molar mass we calculated. The mass \( m \) can be found using the formula:\[ m = \text{moles} \times \text{molar mass} \]Substitute the values we have:\[ m = 3.25 \text{ mol} \times 98 \text{ g/mol} = 318.5 \text{ g} \]

Step 4: Conclusion and Answer

The mass of 3.25 moles of \( \mathrm{H}_{2} \mathrm{SO}_{4} \) is 318.5 grams. Therefore, we have calculated the required mass using the given number of moles and the molecular weight.

Key Concepts

Moles to Grams Conversion

Converting moles to grams is a fundamental concept in chemistry that allows us to understand the mass of a substance when given its quantity in moles. In essence, moles measure the number of particles, such as atoms or molecules, in a particular substance. To convert moles to grams, you need to use the molar mass of the substance, which is the mass of one mole of that substance. The conversion process involves multiplying the number of moles by the molar mass. The formula to remember is:

• Mass (g) = Moles × Molar Mass (g/mol)

This process is crucial in many chemical calculations, as it bridges the gap between atomic-level interactions and macroscopic quantities we can measure.

Sulfuric Acid

Sulfuric acid, with the chemical formula \( \mathrm{H}_{2} \mathrm{SO}_{4} \), is one of the most widely produced and used industrial chemicals globally. It is a colorless and dense liquid that is highly corrosive and soluble in water, releasing heat upon mixing. This powerful acid plays a critical role in manufacturing fertilizers, refining oil, treating wastewater, and producing chemicals. Understanding the properties and applications of sulfuric acid is vital in chemistry, highlighting its versatility and significance in industrial processes.When dealing with sulfuric acid in calculations, always wear appropriate safety gear, as it can cause severe burns and releases fumes that should not be inhaled.

Atomic Mass

Atomic mass is a measure of the mass of an atom, typically expressed in atomic mass units (amu). It reflects the average mass of an element's isotopes, weighted by their natural abundance. Understanding atomic mass is crucial as it's a building block for calculating molar mass. Each element has its unique atomic mass, which you can find on the periodic table. For sulfuric acid, you need to know:

• Hydrogen (H): around 1 g/mol
• Sulfur (S): about 32 g/mol
• Oxygen (O): approximately 16 g/mol

These atomic masses are added together according to the numbers of each atom in a molecule to find its molar mass. This understanding bridges the gap between the microscopic world of atoms and macroscopic measurements like weight or mass.

Stoichiometry

Stoichiometry is the study of the relationships between the quantities of reactants and products in chemical reactions. This concept allows chemists to predict the outcomes of reactions quantitatively. By understanding stoichiometry:

• You can predict how much of a reactant is needed to completely react with a given amount of another reactant.
• It helps in calculating the yield of reactions and how much of a product will be formed.

In the context of calculating the mass of sulfuric acid, stoichiometry involves converting between the number of moles and the mass using the molar mass. This conversion is a practical application of stoichiometry, linking the theoretical aspects of chemical equations with real-world applications of measuring and predicting outcomes.