Problem 45
Question
Air Pollutants Sulfur oxides are major air pollutants. The reaction between sulfur dioxide and oxygen can be written in two ways: $$ \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g) $$ and $$ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) $$
Step-by-Step Solution
Verified Answer
Question: Provide a step-by-step explanation on how to obtain the second equation from the given balanced chemical equation, $$\mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g)$$.
Answer: To obtain the second equation from the given balanced chemical equation, follow these steps:
1. Balance the coefficients: The given equation is already balanced.
2. Multiply the equation by 2: This will yield $$2(\mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g)) \rightleftharpoons 2 (\mathrm{SO}_{3}(g))$$.
3. Distribute the multiplied value: The new equation becomes $$2 \, \mathrm{SO}_{2}(g) + 2 \times \frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons 2 \, \mathrm{SO}_{3}(g)$$.
4. Simplify the equation: The final equation is $$2 \, \mathrm{SO}_{2}(g) + \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$$.
1Step 1: Balance the coefficients
The first equation ($$\mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g)$$) has a balanced relationship between the reactants and products. However, to make the coefficients in the whole numbers, let's multiply the entire equation by 2.
2Step 2: Multiply the equation by 2
By multiplying both sides of the equation with 2, we obtain:
$$2(\mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g)) \rightleftharpoons 2 (\mathrm{SO}_{3}(g))$$
3Step 3: Distribute the multiplied value
Now, distribute the multiplied value (2) across the reactants and products in the equation. This gives:
$$2 \, \mathrm{SO}_{2}(g) + 2 \times \frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons 2 \, \mathrm{SO}_{3}(g)$$
4Step 4: Simplify the equation
Simplify the equation by performing the multiplication for the oxygen term:
$$2 \, \mathrm{SO}_{2}(g) + \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$$
Now, we have obtained the second equation from the first one. The balanced chemical equation for the reaction between sulfur dioxide and oxygen is:
$$2 \, \mathrm{SO}_{2}(g) + \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$$
Key Concepts
Sulfur DioxideAir PollutantsStoichiometry
Sulfur Dioxide
Sulfur dioxide (SO₂) is a significant compound in chemistry and the environment. It's a chemical with a sharp, choking smell, often a byproduct of burning fossil fuels like coal and oil. This compound is particularly relevant when discussing air pollution because it's one of the many gases released during the combustion of these materials.
Sulfur dioxide naturally occurs from volcanic activity. However, human activities have vastly increased its presence in the atmosphere. Industrial processes, especially those involving coal-fired power plants, contribute extensively to SO₂ emissions. It's crucial to understand the role of sulfur dioxide since it reacts easily with other substances, forming compounds like sulfuric acid, a component of acid rain.
Sulfur dioxide naturally occurs from volcanic activity. However, human activities have vastly increased its presence in the atmosphere. Industrial processes, especially those involving coal-fired power plants, contribute extensively to SO₂ emissions. It's crucial to understand the role of sulfur dioxide since it reacts easily with other substances, forming compounds like sulfuric acid, a component of acid rain.
- Contributes to atmospheric pollution
- Results from both natural sources and human activities
- Transforms into other harmful compounds
Air Pollutants
Air pollutants are substances in the air that can have adverse effects on both health and the environment. Sulfur oxides, like sulfur dioxide (SO₂) and sulfur trioxide (SO₃), are key players when discussing air pollution. These oxides can combine with water vapor in the atmosphere to produce acid rain, which harms ecosystems, corrodes buildings, and poses risks to human health.
The process of balancing chemical equations for such reactions is essential as it helps predict the amounts of reactants and products. It's critical for chemists to control emissions and reduce the impacts of these pollutants. Understanding how to represent these reactions accurately with balanced equations can guide methods to decrease pollution through industrial regulation and innovation.
The process of balancing chemical equations for such reactions is essential as it helps predict the amounts of reactants and products. It's critical for chemists to control emissions and reduce the impacts of these pollutants. Understanding how to represent these reactions accurately with balanced equations can guide methods to decrease pollution through industrial regulation and innovation.
- Includes various harmful gaseous compounds
- Implicates in environmental and health issues
- Understanding equations helps manage emissions
Stoichiometry
Stoichiometry is a branch of chemistry dedicated to understanding the quantities of reactants and products in a chemical reaction. It's like a recipe, ensuring each ingredient is used in just the right amount to achieve the desired outcome. In the context of air pollutants like sulfur dioxide, stoichiometry allows scientists and engineers to calculate how much of each substance is needed to cause or mitigate a reaction.
Balancing chemical equations, as demonstrated in the original exercise, is a vital skill for applying stoichiometry. For the chemical equation involving sulfur dioxide and oxygen, the balanced version shows precise mole ratios: 2 moles of SO₂ react with 1 mole of O₂ to form 2 moles of SO₃.
Balancing chemical equations, as demonstrated in the original exercise, is a vital skill for applying stoichiometry. For the chemical equation involving sulfur dioxide and oxygen, the balanced version shows precise mole ratios: 2 moles of SO₂ react with 1 mole of O₂ to form 2 moles of SO₃.
- Ensures proper understanding of reactant and product quantities
- Essential for chemical precision
- Helps in predicting outcomes of chemical reactions
Other exercises in this chapter
Problem 42
The equilibrium constant \(K_{p}\) for the synthesis of ammonia, $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ is \(4.3 \t
View solution Problem 44
At a given temperature, the equilibrium constant \(K_{c}\) for the reaction $$ 2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+2 \math
View solution Problem 46
At a given temperature, \(K_{e}\) for the reaction $$ 2 \mathrm{NO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) $
View solution Problem 47
At a given temperature, \(K_{c}\) for the reaction \(2 \mathrm{SO}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{SO}_{3}(\mathrm{g})\)
View solution