The reaction; \(2 \mathrm{~N}_{2} \mathrm{O}_{5} \longrightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2}\), shows an increase in concentration of \(\mathrm{NO}_{2}\) by \(20 \times 10^{-3}\) mol litre \(^{-1}\) in 5 second. Calculate (a) rate of appearance of \(\mathrm{NO}_{2}\), (b) rate of reaction and (c) rate of disappearance of \(\mathrm{N}_{2} \mathrm{O}_{5}\).

Understanding chemical kinetics is crucial for explaining how reactions occur and determining the rate at which they take place. Chemical kinetics focuses on reaction rates, the factors affecting these rates, and the mechanisms by which reactions proceed.

In the given exercise, we examine the kinetics of the decomposition of dinitrogen pentoxide ((N_2O_5)) into nitrogen dioxide ((NO_2)) and oxygen ((O_2)). The increase in (NO_2) concentration within a specific timeframe allows us to explore the kinetic principles that govern this chemical change.

To delve deeper, imagine you're observing a crowded market; some people enter (reactants forming products), some leave (products getting formed). Chemical kinetics would be the study of how fast people are coming and going out of the market (rate of reaction). It's the difference in the 'crowd' over time that tells us the rate at which these changes occur in a reaction.

The reaction rate refers to the speed at which reactants turn into products. In the exercise, we calculate the reaction rate based on the change in concentration of (NO_2) over time. This is akin to timing how quickly a juggler throws balls into the air (products forming from reactants).

The rate of appearance of (NO_2) is calculated by measuring the increase in its concentration over a span of 5 seconds. This involves a simple formula: \(\text{Rate of appearance} = \frac{\Delta[\text{product}]}{\Delta t}\), where '\(\Delta[\text{product}]\)' is the change in concentration of the product and '\(\Delta t\)' is the duration of time in seconds. With the given data, we can find that new ', 'molecules of (NO_2) are essentially 'thrown into the air' at a certain rate, which is precisely quantifiable.

The concept of stoichiometry is embedded within the laws of conservation of mass and the defined proportions of chemical reactions. It quantitatively describes the relationships between reactants and products in a chemical reaction based on their mole ratios. In simpler terms, stoichiometry is like a detailed recipe that accounts for how much of each ingredient (reactant) you need to end up with the desired amount of cake (product).

In the given exercise, stoichiometry is applied to connect the dots between the rates of appearance and disappearance of substances. For every 4 moles of (NO_2) produced, 2 moles of (N_2O_5) are used up. The stoichiometry of the reaction tells us the rate at which (N_2O_5) disappears is related to the rate at which (NO_2) appears. Calculating the rate of disappearance of (N_2O_5) becomes possible by considering this mole ratio, giving a clear depiction of how this 'recipe' proceeds over time.