Question

In 2004 , about 48 million tons of sulfuric acid was produced in the United States. Calculate the amount of sulfur (in grams and moles) used to produce that amount of sulfuric acid.

Short answer

The U.S. used approximately \( 1.57 \times 10^{13} \) grams or \( 4.90 \times 10^{11} \) moles of sulfur to produce 48 million tons of sulfuric acid.

Step-by-step solution

Identify the Composition of Sulfuric Acid

Sulfuric acid has the chemical formula \( H_2SO_4 \). This means one molecule of sulfuric acid contains one sulfur atom, two hydrogen atoms, and four oxygen atoms.

Calculate the Molar Mass of Sulfuric Acid

The molar mass of sulfuric acid \( H_2SO_4 \) can be calculated by adding up the atomic masses: \( 2\times 1 \text{ (for hydrogen)} + 32 \text{ (for sulfur)} + 4 \times 16 \text{ (for oxygen)} = 98 \text{ g/mol} \).

Convert Tons of Sulfuric Acid to Grams

Since 1 ton equals 1,000,000 grams, 48 million tons of sulfuric acid would be \( 48,000,000 \times 1,000,000 = 48 \times 10^{12} \text{ grams} \) of sulfuric acid.

Calculate Moles of Sulfuric Acid

Using the molar mass from Step 2, calculate the moles of sulfuric acid: \[ \text{moles of } H_2SO_4 = \frac{48 \times 10^{12} \text{ grams}}{98 \text{ g/mol}} \approx 4.90 \times 10^{11} \text{ moles} \].

Calculate Moles of Sulfur

Since each molecule of sulfuric acid contains one atom of sulfur, the moles of sulfur are the same as the moles of sulfuric acid calculated in Step 4: \( 4.90 \times 10^{11} \text{ moles of sulfur} \).

Convert Moles of Sulfur to Grams

The atomic mass of sulfur is \( 32 \text{ g/mol} \). Therefore, the mass of sulfur is: \[ 4.90 \times 10^{11} \text{ moles} \times 32 \text{ g/mol} = 1.57 \times 10^{13} \text{ grams of sulfur} \].

Key concepts

Chemical Formula

A chemical formula is a representation of the elements within a compound and the ratio in which they combine. For sulfuric acid, the formula is \( H_2SO_4 \). This tells us that each molecule of sulfuric acid is made up of two hydrogen atoms (\( H \)), one sulfur atom (\( S \)), and four oxygen atoms (\( O \)).
Understanding chemical formulas is crucial because they provide important information about the composition and proportion of elements in compounds.
In sulfuric acid, the formula indicates that there's one sulfur atom per molecule, which becomes important when calculating the mass or moles of sulfur needed for manufacturing a certain quantity of sulfuric acid.

Molar Mass

The molar mass of a substance is the mass of one mole of that substance and is usually expressed in grams per mole (g/mol). It is calculated by adding up the atomic masses of all the atoms represented in the chemical formula.
For sulfuric acid \( H_2SO_4 \), the molar mass can be calculated by:

• Hydrogen: \( 2 \times 1 = 2 \) g/mol
• Sulfur: \( 1 \times 32 = 32 \) g/mol
• Oxygen: \( 4 \times 16 = 64 \) g/mol

Adding them together gives \( 98 \text{ g/mol} \).
This means that one mole of sulfuric acid weighs 98 grams. Knowing the molar mass allows us to convert between the mass of a substance and the amount in moles, facilitating chemical calculations.

Conversion of Units

Conversion of units is a fundamental skill in chemistry, as it allows us to express measurements in different units according to our needs. In the context of large-scale chemical production, like sulfuric acid manufacturing, converting tons to grams is necessary.
Since 1 ton is equivalent to 1,000,000 grams, calculating the total mass in grams for 48 million tons involves multiplication:

• 48 million tons \( = 48,000,000 \times 1,000,000 \) grams = \( 48 \times 10^{12} \) grams.
  

Such conversions are essential when dealing with industrial scales or laboratory work, where precise measurements are critical.

Stoichiometry

Stoichiometry is the branch of chemistry that involves the calculation of reactants and products in chemical reactions. It is based on the balanced chemical equation and the law of conservation of mass, which states that matter cannot be created or destroyed.
To determine the amount of sulfur needed for sulfuric acid production, we use stoichiometry. Since the chemical formula \( H_2SO_4 \) indicates one sulfur per molecule, the moles of sulfur will equal the moles of sulfuric acid. First, we calculate the moles of sulfuric acid using its molar mass:

• \( \text{moles of } H_2SO_4 = \frac{48 \times 10^{12} \text{ grams}}{98 \text{ g/mol}} \approx 4.90 \times 10^{11} \text{ moles} \)

As each molecule corresponds to one sulfur atom, this equals the moles of sulfur.
To find the mass of sulfur, multiply the moles by the atomic mass of sulfur (32 g/mol):

• \( 4.90 \times 10^{11} \times 32 \approx 1.57 \times 10^{13} \text{ grams of sulfur} \).

Stoichiometry ensures accurate chemical quantification, vital for industrial processes.