Why is 1/t used as a measure of rate of reaction?
The Correct Answer and Explanation is :
The use of ( \frac{1}{t} ) as a measure of the rate of reaction is rooted in the concept of reaction kinetics. In chemical reactions, the rate is typically defined as the change in concentration of a reactant or product over time. Mathematically, the rate can be expressed as:
[
\text{Rate} = -\frac{d[\text{Reactant}]}{dt} \quad \text{or} \quad \text{Rate} = \frac{d[\text{Product}]}{dt}
]
where ( [\text{Reactant}] ) and ( [\text{Product}] ) are the concentrations of the reactant and product, respectively, and ( t ) is time.
When considering simple reactions, especially those that proceed to completion, the rate of reaction often decreases as the reactants are consumed. As a result, measuring the rate directly can be challenging, especially in cases where the concentration changes are not uniform. To simplify the analysis, one can relate the rate to time by using the reciprocal of time, ( \frac{1}{t} ).
This approach is particularly useful in the context of pseudo-first-order reactions, where one reactant is in large excess compared to another. In such cases, the overall reaction can appear to be first-order with respect to the limiting reactant, and the rate can be approximated as being inversely proportional to time.
Additionally, expressing reaction rates as ( \frac{1}{t} ) allows for easier comparison across different reactions and conditions. It highlights how quickly a reaction occurs: a larger value of ( \frac{1}{t} ) indicates a faster reaction, while a smaller value suggests a slower reaction.
In summary, using ( \frac{1}{t} ) as a measure of the rate of reaction provides a convenient and effective way to quantify and compare reaction kinetics, particularly when dealing with varying concentrations and reaction orders. This method enhances our understanding of reaction dynamics in both experimental and theoretical frameworks.