Problem 21 - Chemistry in Context

Question

Balance these equations in which ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) burns in oxygen. a. \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) b. \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) c. \(\mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\)

Step-by-Step Solution

Answer

a. \( \mathrm{C}_{2} \mathrm{H}_{4} + \mathrm{O}_{2} \rightarrow 2\mathrm{C} + 2\mathrm{H}_{2} \mathrm{O} \); b. \( \mathrm{C}_{2} \mathrm{H}_{4} + 3\mathrm{O}_{2} \rightarrow 2\mathrm{CO} + 2\mathrm{H}_{2} \mathrm{O} \); c. \( \mathrm{C}_{2} \mathrm{H}_{4} + 3\mathrm{O}_{2} \rightarrow 2\mathrm{CO}_{2} + 2\mathrm{H}_{2} \mathrm{O} \).

Step 1: Identify Atoms in the Reaction (a)

For the equation \( \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \), notice that we have ethene \( \mathrm{C_{2}H_{4}} \) producing carbon \(\mathrm{C}\) and water \(\mathrm{H_{2}O}\). Count the atoms: 2 carbon atoms and 4 hydrogen atoms on the left; we need the same number on the right. Oxygen atoms should also balance.

Step 2: Balancing Carbon in Reaction (a)

From \( \mathrm{C_{2}H_{4}} \), put a coefficient of 2 in front of \( \mathrm{C} \) (product side) to balance carbon, making the equation \( \mathrm{C_{2}H_{4} + O_{2} \longrightarrow 2\mathrm{C} + \mathrm{H_{2}O}} \).

Step 3: Balancing Hydrogen in Reaction (a)

From \( \mathrm{C_{2}H_{4}} \), there are 4 hydrogen atoms total, so place a coefficient of 2 in front of \( \mathrm{H_{2}O} \) to balance hydrogen: \( \mathrm{C_{2}H_{4} + O_{2} \longrightarrow 2\mathrm{C} + 2\mathrm{H_{2}O}} \).

Step 4: Balancing Oxygen in Reaction (a)

We have 2 oxygen atoms required for \( 2\mathrm{H_{2}O} \). Therefore, place a coefficient of 1 in front of \( \mathrm{O_{2}} \): \( \mathrm{C_{2}H_{4} + O_{2} \longrightarrow 2\mathrm{C} + 2\mathrm{H_{2}O}} \). No further adjustments are needed.

Step 5: Balanced Equation (a)

The balanced equation for (a) is \( \mathrm{C}_{2} \mathrm{H}_{4}(g)+ \mathrm{O}_{2}(g) \longrightarrow 2\mathrm{C}(s)+2 \mathrm{H}_{2} \mathrm{O}(g)\).

Step 6: Identify Atoms in Reaction (b) and Initial Carbon Balance

For \( \mathrm{C}_{2} \mathrm{H}_{4} + \mathrm{O}_{2} \longrightarrow \mathrm{CO} + \mathrm{H}_{2} \mathrm{O} \), balance carbon atoms first by placing a coefficient of 2 in front of \( \mathrm{CO} \): \( \mathrm{C}_{2} \mathrm{H}_{4} + \mathrm{O}_{2} \longrightarrow 2 \mathrm{CO} + \mathrm{H}_{2} \mathrm{O} \).

Step 7: Balancing Hydrogen in Reaction (b)

There are 4 hydrogen atoms, so place a coefficient of 2 in front of \( \mathrm{H_{2}O} \) to balance hydrogen: \( \mathrm{C}_{2} \mathrm{H}_{4} + \mathrm{O}_{2} \longrightarrow 2 \mathrm{CO} + 2 \mathrm{H_{2}O} \).

Step 8: Balancing Oxygen in Reaction (b)

Now there are 4 oxygen atoms from \( 2\mathrm{CO} \) and 2 oxygen atoms from \( 2\mathrm{H_{2}O} \), totaling 6 oxygen atoms needed. Thus, place a coefficient of 3 in front of \( \mathrm{O_{2}} \): \( \mathrm{C}_{2} \mathrm{H}_{4} + 3\mathrm{O_{2}} \longrightarrow 2 \mathrm{CO} + 2 \mathrm{H_{2}O} \).

Step 9: Balanced Equation (b)

The final balanced equation for (b) is \( \mathrm{C}_{2} \mathrm{H}_{4}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2\mathrm{CO}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\).

Step 10: Identify Atoms in Reaction (c) and Initial Carbon Balance

For \( \mathrm{C}_{2} \mathrm{H}_{4} + \mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2} + \mathrm{H}_{2} \mathrm{O} \), put a coefficient of 2 in front of \( \mathrm{CO}_{2} \) to balance carbon atoms: \( \mathrm{C}_{2} \mathrm{H}_{4} + \mathrm{O}_{2} \longrightarrow 2 \mathrm{CO}_{2} + \mathrm{H}_{2} \mathrm{O} \).

Step 11: Balancing Hydrogen in Reaction (c)

As before, balance hydrogen by placing a coefficient of 2 in front of \( \mathrm{H_{2}O} \): \( \mathrm{C}_{2} \mathrm{H}_{4} + \mathrm{O}_{2} \longrightarrow 2 \mathrm{CO}_{2} + 2 \mathrm{H_{2}O} \).

Step 12: Balancing Oxygen in Reaction (c)

This configuration requires 4 oxygen atoms from \( 2\mathrm{CO}_{2} \) and 2 oxygen from \( 2\mathrm{H}_{2}O \), totaling 6. Place a coefficient of 3 in front of \( \mathrm{O}_{2} \): \( \mathrm{C}_{2} \mathrm{H}_{4} + 3\mathrm{O}_{2} \longrightarrow 2 \mathrm{CO}_{2} + 2 \mathrm{H_{2}O} \).

Step 13: Balanced Equation (c)

The final balanced equation for (c) is \( \mathrm{C}_{2} \mathrm{H}_{4}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\).

Key Concepts

Combustion Reactions

Combustion reactions are a category of chemical reactions that occur when a substance combines with oxygen and releases energy in the form of light or heat. A classic example is the burning of hydrocarbons, like ethane, in oxygen.
During a combustion reaction, hydrocarbons typically react with oxygen to produce carbon dioxide, water, and energy, though incomplete combustion can also yield carbon monoxide or carbon as products.
These reactions are critical in numerous applications, including energy production in car engines and power plants.

• Involves oxygen as a reactant.
• Produces energy, evident from heat or light.
• Results in carbon-based products.

Understanding the nuances of combustion reactions is crucial, as it's key to balancing chemical equations and optimizing industrial processes.

Stoichiometry

Stoichiometry is the mathematical aspect of chemistry that deals with the relationships between reactants and products in a chemical reaction. It's like a recipe that tells you how much of each ingredient (reactant) you need to make a certain number of cakes (products).
When balancing equations, stoichiometry ensures that the number of atoms for each element is the same on both sides of the equation. This is founded on the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction.

• Helps determine the quantities of reactants needed.
• Ensures balanced chemical equations.
• Relies on ratios to predict the outcome of reactions.

By mastering stoichiometry, you can accurately predict the amount of products formed from given reactants, essential for fields like chemistry, biology, and engineering.

Oxygen as a Reactant

In chemistry, oxygen is known for its role as a vital reactant, especially in combustion reactions. When oxygen reacts with a substance, it typically leads to an exothermic reaction, meaning that it releases heat.

In the case of ethane combustion, oxygen facilitates the conversion of ethane into various carbon-containing products like carbon dioxide and carbon monoxide.
Uncontrolled reactions with oxygen can be dangerous due to their highly exothermic nature, which is why understanding oxygen's role and behavior in such reactions is crucial for safety and efficiency.

• Consumes oxygen from the atmosphere.
• Essential for oxidation processes.
• Contributes to energy release in combustion.

Using this knowledge, process engineers can design systems that optimize these reactions for industrial and environmental efficiency.

Carbon as a Product

In combustion reactions, carbon is one of the primary products formed when hydrocarbons are burned. Depending on the amount of oxygen present, carbon can be released in different forms: carbon dioxide in complete combustion, carbon monoxide or solid carbon in incomplete combustion.

Carbon dioxide is a greenhouse gas that is a major focus of attention due to its role in climate change. Carbon monoxide, on the other hand, is a toxic gas with serious health implications when inhaled.

• Forms carbon-based products like CO, CO₂, or C.
• Affects environmental and health factors.
• Understanding its formation helps in pollution control.

Knowledge of carbon's different forms and their environmental impacts is essential for developing strategies to reduce emissions and improve air quality.