Question

For the following reaction at a particular temperature which takes place as- follows \(2 \mathrm{~N}_{2} \mathrm{O}_{5} \rightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2}\) \(2 \mathrm{NO}_{2}+1 / 2 \mathrm{O} 2 \rightarrow \mathrm{N}_{2} \mathrm{O}_{5}\) The value of activation energies are \(E_{1}\) and \(E_{2}\) respectively then a. \(\mathrm{E}_{1}>\mathrm{E}_{2}\) b. \(\mathrm{E}_{1}=2 \mathrm{E}_{2}\) c. \(2 \mathrm{E}_{1}=\mathrm{E}_{2}\) d. \(\mathrm{E}_{1}<\mathrm{E}_{2}\)

Short answer

d. \(E_1 < E_2\)

Step-by-step solution

Understand the Reactions

The given reactions are: 1) Forward Reaction: \(2 \mathrm{N}_{2} \mathrm{O}_{5} \rightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2}\) and 2) Reverse Reaction: \(2 \mathrm{NO}_{2}+1/2 \mathrm{O}_{2} \rightarrow \mathrm{N}_{2} \mathrm{O}_{5}\). We are comparing the activation energies for these reactions, denoted as \(E_1\) for the forward reaction and \(E_2\) for the reverse reaction.

Analyze Reaction Direction

In chemical reactions, the forward reaction of breaking down a compound (\(\mathrm{N}_{2} \mathrm{O}_{5}\) decomposing into \(\mathrm{NO}_{2}\) and \(\mathrm{O}_{2}\)) typically has a smaller activation energy compared to the reverse reaction where products recombine to form the original compound. Generally, building a more complex compound (as in the reverse reaction) requires more energy.

Compare Activation Energies

Since forming \(\mathrm{N}_{2} \mathrm{O}_{5}\) from \(\mathrm{NO}_{2}\) and \(\mathrm{O}_{2}\) is more energy-intensive than decomposing \(\mathrm{N}_{2} \mathrm{O}_{5}\) to \(\mathrm{NO}_{2}\) and \(\mathrm{O}_{2}\), \(E_2\) (reverse reaction) is greater than \(E_1\) (forward reaction). Thus, we conclude that \(E_1 < E_2\).

Key concepts

Chemical Reactions

Chemical reactions are processes where substances called reactants transform into different substances known as products. In the given exercise, the reactants are substances like \(\mathrm{N}_2\mathrm{O}_5\) and the products result after decomposition, such as \(\mathrm{NO}_2\) and \(\mathrm{O}_2\).

During a chemical reaction, bonds between atoms are broken and new bonds are formed, leading to a change in the molecular structure of the involved chemicals.

Some key points about chemical reactions are:

• They can be fast, like explosion-type reactions, or slow, like rust formation.
• Catalysts are often used to speed up reactions without being consumed in the process.
• Temperature, pressure, concentration, and the presence of catalysts can influence the rate and outcome of a reaction.

Understanding these factors helps in predicting how a reaction will proceed and what conditions are optimal for it.

Forward and Reverse Reactions

Forward and reverse reactions refer to the direction in which chemical reactions proceed. A forward reaction is when reactants are converted to products, as in the decomposition of \(\mathrm{N}_2\mathrm{O}_5\) into \(\mathrm{NO}_2\) and \(\mathrm{O}_2\). The reverse reaction, conversely, takes the products and converts them back into the original reactants, as when \(\mathrm{NO}_2\) and \(\mathrm{O}_2\) recombine to form \(\mathrm{N}_2\mathrm{O}_5\).

Some critical points about these reactions:

• In a closed system, forward and reverse reactions can reach a state of equilibrium where the rate of the forward reaction equals the rate of the reverse reaction.
• The dynamic balance in equilibrium doesn’t mean that the concentrations of reactants and products are equal, but rather that their ratios remain constant.
• The concept of equilibrium is essential in understanding how reactions occur in real-world scenarios, such as in industrial chemical processes.

Energy Comparison in Reactions

The activation energy of a reaction is the minimum energy required for the reactants to undergo a transformation into products. This energy barrier must be overcome for a reaction to proceed. In the given reactions, we compare the activation energies \(E_1\) for the forward reaction and \(E_2\) for the reverse reaction.

Key aspects regarding the energy comparison include:

• The forward reaction \(2\mathrm{N}_2\mathrm{O}_5 \rightarrow 4\mathrm{NO}_2+\mathrm{O}_2\) generally has a lower activation energy \(E_1\) compared to the reverse reaction \(2\mathrm{NO}_2+1/2\mathrm{O}_2 \rightarrow \mathrm{N}_2\mathrm{O}_5\) where \(E_2\) is higher.
• Typically, decomposition reactions (breaking complex molecules into simpler ones) have lower activation energies than synthesis reactions (forming complex molecules from simpler ones).
• The relationship \(E_1

Understanding these energy requirements helps in designing processes that optimize energy use in industrial applications.