Question

It is estimated that the day Mt. St. Helens erupted (May 18 , 1980 ), about \(4.0 \times 10^{5}\) tons of \(\mathrm{SO}_{2}\) were released into the atmosphere. If all the \(\mathrm{SO}_{2}\) were eventually converted to sulfuric acid, how many tons of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) were produced?

Short answer

Approximately \(6.1 \times 10^5\) tons of \(\mathrm{H}_2\mathrm{SO}_4\) were produced.

Step-by-step solution

Determine Molar Masses

First, we need to find the molar mass of both \( \text{SO}_2 \) and \( \text{H}_2\text{SO}_4 \). The molar mass of sulfur (S) is approximately 32.07 g/mol, oxygen (O) is approximately 16.00 g/mol, and hydrogen (H) is approximately 1.01 g/mol.

Calculate Molar Mass of \(\text{SO}_2\)

To find the molar mass of \( \text{SO}_2 \), add the mass of one sulfur atom to twice the mass of an oxygen atom: \[ \text{Molar mass of } \text{SO}_2 = 32.07 + 2 \times 16.00 = 64.07 \text{ g/mol} \]

Calculate Molar Mass of \(\text{H}_2\text{SO}_4\)

To find the molar mass of \( \text{H}_2\text{SO}_4 \), add twice the mass of a hydrogen atom, the mass of a sulfur atom, and four times the mass of an oxygen atom: \[ \text{Molar mass of } \text{H}_2\text{SO}_4 = 2 \times 1.01 + 32.07 + 4 \times 16.00 = 98.09 \text{ g/mol} \]

Use Stoichiometry

According to the chemical reaction \( \text{SO}_2 + \text{O}_2 \rightarrow \text{H}_2\text{SO}_4 \), one mole of \( \text{SO}_2 \) will produce one mole of \( \text{H}_2\text{SO}_4 \). This is a direct conversion.

Convert Tons of \(\text{SO}_2\) to Moles

We know there are \(4.0 \times 10^5 \) tons of \( \text{SO}_2 \). First, convert to grams (1 ton = 10^6 grams): \[ 4.0 \times 10^5 \text{ tons} \times 10^6 \text{ g/ton} = 4.0 \times 10^{11} \text{ g} \] Then, use the molar mass to find moles:\[ \text{Moles of } \text{SO}_2 = \frac{4.0 \times 10^{11} \text{ g}}{64.07 \text{ g/mol}} = 6.24 \times 10^9 \text{ moles} \]

Calculate Tons of \(\text{H}_2\text{SO}_4\)

Now, convert the moles of \( \text{H}_2\text{SO}_4 \) back into grams using its molar mass, then convert to tons:\[ \text{Grams of } \text{H}_2\text{SO}_4 = 6.24 \times 10^9 \text{ moles} \times 98.09 \text{ g/mol} = 6.12 \times 10^{11} \text{ g} \] Convert grams to tons:\[ \text{Tons of } \text{H}_2\text{SO}_4 = \frac{6.12 \times 10^{11} \text{ g}}{10^6 \text{ g/ton}} = 6.12 \times 10^5 \text{ tons} \]

Key concepts

Molar Mass Calculation

Understanding molar mass is essential for converting between grams and moles in stoichiometry. The molar mass of a compound is the sum of the molar masses of its constituent elements.

For example, to calculate the molar mass of sulfur dioxide (\( \text{SO}_2 \)), you add the molar mass of one sulfur atom (32.07 g/mol) with the molar mass of two oxygen atoms (2 x 16.00 g/mol):

• Total is 64.07 g/mol for \( \text{SO}_2 \).

Similarly, the molar mass of sulfuric acid (\( \text{H}_2\text{SO}_4 \)) requires you to add twice the molar mass of hydrogen (2 x 1.01 g/mol), the molar mass of sulfur (32.07 g/mol), and four times the molar mass of oxygen (4 x 16.00 g/mol):

• Total is 98.09 g/mol for \( \text{H}_2\text{SO}_4 \).

These calculations serve as the basis for converting between moles and grams.

Chemical Reaction Balancing

Balancing chemical equations ensures that the same number of each type of atom appears on both sides of the equation. For the reaction involving sulfur dioxide and oxygen to produce sulfuric acid, the balanced chemical equation is: \[ \text{SO}_2 + \text{O}_2 \rightarrow \text{H}_2\text{SO}_4 \]

This equation shows a 1:1 conversion from \( \text{SO}_2 \) to \( \text{H}_2\text{SO}_4 \).

• One mole of \( \text{SO}_2 \) produces one mole of \( \text{H}_2\text{SO}_4 \).

Balancing equations is crucial to accurately determine how much product is formed from given reactants. It ensures the law of conservation of mass is upheld, where mass is neither created nor destroyed in a chemical reaction.

Unit Conversion

Unit conversion is a key step in solving stoichiometry problems, as it allows quantities to be expressed in compatible units.

When dealing with large quantities, like tons, converting to smaller units, like grams, is often necessary. For instance:

• 1 ton = \( 10^6 \) grams.

In the exercise, \(4.0 \times 10^5\) tons of \( \text{SO}_2 \) is converted to grams:

• \(4.0 \times 10^5 \times 10^6 = 4.0 \times 10^{11} \) grams.

This conversion allows us to use the molar mass to determine moles, which is essential for further calculations.

Sulfuric Acid Production

Sulfuric acid production involves converting sulfur dioxide released from volcanic eruptions into sulfuric acid. This process is significant in both natural phenomena like volcanic activity and industrial production.

In this specific reaction, \( \text{SO}_2 \) emitted from a volcano reacts with oxygen in the atmosphere:

• Yields \( \text{H}_2\text{SO}_4 \), an important industrial chemical used in fertilizers, batteries, and cleaners.

Understanding this conversion highlights practical applications of stoichiometry and chemistry in everyday life.