50% of a reaction is completed in 16 min under similar conditions 75% ...
The Order of the Reaction
In chemical kinetics, the order of a reaction refers to the mathematical relationship between the concentration of reactants and the rate of the reaction. It helps us determine how the rate of the reaction changes as the concentration of reactants changes. The order of a reaction can be determined experimentally by studying the reaction rate under different conditions.
Reaction Completion Percentages
In this given problem, we are provided with two key pieces of information regarding the completion of the reaction:
- 50% of the reaction is completed in 16 minutes
- 75% of the reaction is completed in 48 minutes
Determining the Order of the Reaction
To determine the order of the reaction, we need to analyze the relationship between the completion percentage and the time taken for each percentage.
Let's denote the completion percentage as P and the time taken as t. We can write the following equations based on the given information:
Equation 1: P = k1 * t
Equation 2: P = k2 * t
Here, k1 and k2 are rate constants for the reaction.
If we take the ratio of Equation 1 to Equation 2, we get:
P / P = (k1 * t) / (k2 * t)
Simplifying the equation, we get:
k1 / k2 = P / P
Since P / P = 75% / 50% = 1.5, we can conclude that:
k1 / k2 = 1.5
Interpreting the Result
The ratio of the rate constants (k1 / k2) is equal to the ratio of the completion percentages (1.5). This indicates that the rate of the reaction increases by a factor of 1.5 as the completion percentage increases by a factor of 1.5.
Based on this information, we can determine the order of the reaction:
Order of the reaction = 1.5
Therefore, the order of the reaction is 1.5.
It is important to note that the order of a reaction can be a fractional value, indicating a complex reaction mechanism. The order of a reaction helps us understand the kinetics of a reaction and provides insights into the mechanism and rate-determining step of the reaction.