Problem 30 - Chemistry: An Atoms-Focused Approach

Question

Catalytic Converters and Combustion Catalytic converters in automobiles combat air pollution by converting \(\mathrm{NO}\) and \(\mathrm{CO}\) into \(\mathrm{N}_{2}\) and \(\mathrm{CO}_{2}\) : $$2 \mathrm{CO}(g)+2 \mathrm{NO}(g) \rightarrow \mathrm{N}_{2}(g)+2 \mathrm{CO}_{2}(g)$$ a. How is the rate of formation of \(\mathrm{N}_{2}\) related to the rate of consumption of CO? b. How is the rate of formation of \(\mathrm{CO}_{2}\) related to the rate of consumption of NO? c. How is the rate of consumption of CO related to the rate of consumption of NO?

Step-by-Step Solution

Answer

Based on the given balanced chemical equation, we found the following relationships: a. The rate of formation of N2 is half the rate of consumption of CO. b. The rate of formation of CO2 is equal to the rate of consumption of NO. c. The rate of consumption of CO is equal to the rate of consumption of NO.

Step 1: Understand the Balanced Chemical Equation

The given balanced chemical equation is: $$2 \mathrm{CO}(g)+2 \mathrm{NO}(g) \rightarrow \mathrm{N}_{2}(g)+2\mathrm{CO}_{2}(g)$$ From this equation, we can observe that for every 2 moles of CO consumed, 1 mole of N2 is formed, and for every 2 moles of NO consumed, 2 moles of CO2 are formed. ##Step 2: Find the Relationship between the Rate of Formation of N2 and the Rate of Consumption of CO##

Step 2: Relationship between the Rate of Formation of N2 and the Rate of Consumption of CO

Since for every 2 moles of CO consumed, 1 mole of N2 is formed, the rate of formation of N2 is half the rate of consumption of CO. Mathematically, we can write this as: $$\text{Rate of formation of N}_{2} = \frac{1}{2}\times \text{Rate of consumption of CO}$$ ##Step 3: Find the Relationship between the Rate of Formation of CO2 and the Rate of Consumption of NO##

Step 3: Relationship between the Rate of Formation of CO2 and the Rate of Consumption of NO

For every 2 moles of NO consumed, 2 moles of CO2 are formed. Hence, the rate of formation of CO2 is equal to the rate of consumption of NO. Mathematically, we can write this as: $$\text{Rate of formation of CO}_{2} = \text{Rate of consumption of NO}$$ ##Step 4: Find the Relationship between the Rate of Consumption of CO and the Rate of Consumption of NO##

Step 4: Relationship between the Rate of Consumption of CO and the Rate of Consumption of NO

In the balanced chemical equation, for every 2 moles of CO consumed, 2 moles of NO are also consumed. This means the rate of consumption of CO is equal to the rate of consumption of NO. Mathematically, we can write this as: $$\text{Rate of consumption of CO} = \text{Rate of consumption of NO}$$ So, the relationships between the rates of formation and consumption of the reactants and products are: a. The rate of formation of N2 is half the rate of consumption of CO. b. The rate of formation of CO2 is equal to the rate of consumption of NO. c. The rate of consumption of CO is equal to the rate of consumption of NO.

Key Concepts

Balanced Chemical Equation

A balanced chemical equation is essential for understanding the stoichiometric relationship between reactants and products in a chemical reaction. In the given equation for a catalytic converter,\[2 \mathrm{CO}(g) + 2 \mathrm{NO}(g) \rightarrow \mathrm{N}_{2}(g) + 2\mathrm{CO}_{2}(g)\]we see that every molecule and particle involved in the reaction is accounted for. Balancing is crucial because it follows the Law of Conservation of Mass, ensuring that the number of each type of atom on the reactant side equals the number on the product side.
By understanding this balancing act, we can scale the reaction precisely, which is critical for calculating the required amounts of reactants and predicting product yields. In our equation, every 2 molecules of CO and NO contribute to the formation of 1 molecule of \(\mathrm{N}_{2}\) and 2 molecules of \(\mathrm{CO}_{2}\). This equation provides a clear "recipe" for how these substances convert and change phases during the reaction process managed by catalytic converters.

Rate of Reaction

The rate of reaction tells us how fast a chemical reaction occurs, and in the context of catalytic converters, it helps understand how efficiently these devices can reduce pollutants. **Rate** is typically defined as the change in concentration of a reactant or product over time.

In the balanced equation provided, we see the relationships:

• The rate at which \(\mathrm{N}_{2}\) is produced is half the rate at which CO is consumed.
• The rate at which \(\mathrm{CO}_{2}\) is produced is equal to the rate at which NO is consumed.
• The rates of consumption of CO and NO are equal to each other.

Understanding these relationships helps vehicles engineers optimize catalytic converters to promote faster reaction rates, effectively reducing the emission of harmful gases. Catalysts help by providing an alternative pathway with lower activation energy, thereby increasing the rate without being consumed in the reaction.

Air Pollution Reduction

Catalytic converters play a crucial role in the battle against air pollution by reducing harmful emissions from vehicular exhausts. They convert three main pollutants:

• Carbon monoxide (CO), a poisonous gas.
• Nitrogen oxides (NO and NO2), which contribute to smog and acid rain.
• Hydrocarbons, which can be harmful to health.

Inside a catalytic converter, these substances are converted into less harmful emissions:

• \(\mathrm{CO}\) is oxidized to form \(\mathrm{CO}_{2}\), a greenhouse gas but less toxic than CO.
• \(\mathrm{NO}_x\) is reduced to form \(\mathrm{N}_{2}\), a natural constituent of the atmosphere.
• Unburned hydrocarbons are oxidized into \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\mathrm{O}\).

By decreasing these pollutants, catalytic converters help to improve air quality, making urban areas healthier places to live.

Combustion

Combustion is the chemical process of burning, where a substance reacts quickly with oxygen to release energy. This process is central to many forms of energy production and propulsion, including the internal combustion engines used in most vehicles. In a typical combustion reaction, hydrocarbons in fuel react with oxygen, producing carbon dioxide and water, along with energy.### Incomplete vs. Complete CombustionIncomplete combustion occurs when there isn't enough oxygen to allow the fuel to react completely to form \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2}\mathrm{O}\). Instead, incomplete combustion produces \(\mathrm{CO}\) (carbon monoxide) and soot or other pollutants.Vehicles often undergo incomplete combustion, which leads to air pollution. Catalytic converters help in achieving more complete combustion by converting more of these hazardous byproducts into safer emissions. Through the process of catalysis, they enable additional reactions that convert the incomplete combustion products into purely oxidized products, reducing toxic emissions that enter the atmosphere.