Problem 142 - Chemistry The Science in Context

Question

With respect to the previous question, one way to reduce the formation of acid rain involves trapping the \(\mathrm{SO}_{2}\) by passing smokestack gases through a spray of calcium oxide and \(\mathrm{O}_{2} .\) The product of this reaction is calcium sulfate. a. Write a balanced chemical equation describing this reaction. b. How many metric tons of calcium sulfate would be produced from each ton of \(\mathrm{SO}_{2}\) that is trapped?

Step-by-Step Solution

Answer

Answer: 2.1271 metric tons of calcium sulfate are produced from 1 ton of sulfur dioxide.

Step 1: Write a balanced chemical equation

The reaction between Calcium oxide (CaO), Oxygen (O\(_2\)), and Sulfur dioxide (SO\(_2\)) can be written as follows: CaO + SO\(_2\) + 1/2 O\(_2\) \(\rightarrow\) CaSO\(_4\) This equation is now balanced since there are equal numbers of atoms of every element on both sides.

Step 2: Calculate the mass of calcium sulfate produced from 1 ton of sulfur dioxide

To determine the amount of calcium sulfate formed from each ton of \(\mathrm{SO}_{2}\) trapped, we'll use stoichiometry. We are given that there is 1 ton of sulfur dioxide, and we need to find out how many tons of calcium sulfate will be produced. First, we need the molar mass (in grams per mole) of sulfur dioxide and calcium sulfate, which can be found by adding up the atomic weights of all atoms in each compound: Molar mass of SO\(_2\) = S + (2 × O) = 32.06 + (2 × 16.00) = 64.06 g/mol Molar mass of CaSO\(_4\) = Ca + S + (4 × O) = 40.08 + 32.06 + (4 × 16.00) = 136.14 g/mol Now we will use stoichiometry to convert from tons of SO\(_2\) to tons of CaSO\(_4\). For simplicity, the conversion between grams and metric tons will be used: 1 metric ton = 1,000,000 grams. 1 metric ton of SO\(_2\) × (1,000,000 g/1 metric ton) × (1 mol SO\(_2\)/64.06 g) × (1 mol CaSO\(_4\)/1 mol SO\(_2\)) x (136.14 g/mol CaSO\(_4\)) × (1 metric ton/1,000,000 g) By doing the calculations, we get: (1 × 1,000,000) / 64.06 × 136.14 / 1,000,000 = 2.1271 metric tons of CaSO\(_4\) So, 2.1271 metric tons of calcium sulfate would be produced from each ton of \(\mathrm{SO}_{2}\) that is trapped.

Key Concepts

Chemical Equation Balancing

Balancing a chemical equation is like solving a puzzle. Every piece, or atom, must be used perfectly so that both sides of the equation are equal.
In the reaction to reduce acid rain formation, sulfur dioxide (SO \( _2 \) ), calcium oxide (CaO), and oxygen (O \( _2 \)) come together to form calcium sulfate (CaSO \( _4 \) ). Each molecule has a specific number of atoms, and these must be balanced on both sides.
The balanced chemical equation looks like this:

• CaO + SO \( _2 \) + 1/2 O \( _2 \) → CaSO \( _4 \)

In this equation, there's one calcium (Ca), one sulfur (S), and four oxygens (O) on both sides. Balancing equations ensures that everything follows the law of conservation of mass, meaning that no atoms are lost or gained during a reaction.
This balance is vital for accurately predicting the products of any chemical reaction.

Stoichiometry

Stoichiometry is the bridge connecting chemical reactions to real-world substances, allowing us to calculate precise amounts of products produced from reactants.
In this exercise, stoichiometry helps determine how much calcium sulfate (CaSO \( _4 \) ) forms from sulfur dioxide (SO \( _2 \) ).

Understanding the Calculation

Here, we start with 1 metric ton of SO \( _2 \) . First, convert that into grams (1 metric ton equals 1,000,000 grams). Next, use molar masses to convert these grams into moles.
The molar mass is like a recipe, telling us how many grams per mole we are dealing with:

• Molar mass of SO \( _2 \) = 64.06 g/mol
• Molar mass of CaSO \( _4 \) = 136.14 g/mol

Convert grams of SO \( _2 \) to moles, then use the balanced equation to convert moles of SO \( _2 \) to moles of CaSO \( _4 \), and finally convert those back to grams, yielding metric tons.
The detailed calculations show that 1 ton of SO \( _2 \) will produce approximately 2.1271 metric tons of calcium sulfate. This precision is key to applications such as controlling pollutant emissions.

Sulfur Dioxide

Sulfur dioxide (SO \( _2 \) ) is an important compound in the discussion of acid rain. It’s a colorless gas with a sharp, irritating smell, which is notorious for its role in pollution.

Where Sulfur Dioxide Comes From

SO \( _2 \) is primarily released during the burning of fossil fuels, like coal and oil, which naturally contain sulfur. Industrial processes such as metal smelting also release sulfur dioxide.

• Contributes significantly to air pollution
• Main precursor to acid rain formation

Environmental Impact

Once in the atmosphere, SO \( _2 \) can react with water vapor to form sulfuric acid (H \( _2 \)SO \( _4 \) ), one of the primary components of acid rain. This acid rain hurts ecosystems, damaging lakes and streams, forests, and even man-made structures.
Regulating SO \( _2 \) emissions is crucial for reducing these negative impacts and protecting both the natural environment and human health. Understanding its chemical behavior helps in forming strategies, like trapping with calcium oxide, to mitigate its effects.