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Homework Statement
Find the integrated rate law for a first order reaction
The Attempt at a Solution
We have r = -d[A]/dt = k[A]
Integration with respect to [A] gives
[A] = (1/2)k*[A]^2
Is this it?
An integrated rate law is a mathematical expression that relates the concentration of a reactant to time during a chemical reaction. It is used to determine the rate constant and reaction order of a reaction.
An integrated rate law can be derived by integrating the rate law expression with respect to time and applying any necessary mathematical manipulations. The specific method of derivation depends on the reaction order and rate law of the given reaction.
A zero-order integrated rate law has a constant rate and the concentration of the reactant decreases linearly over time. A first-order integrated rate law has a rate that is directly proportional to the concentration of the reactant, resulting in an exponential decrease in concentration over time. A second-order integrated rate law has a rate that is proportional to the square of the concentration of the reactant, resulting in a more rapid exponential decrease in concentration over time.
To use an integrated rate law to determine the rate constant and reaction order, you must plot experimental data of concentration versus time and determine the slope of the resulting line. The slope of the line will correspond to the rate constant, and the reaction order can be determined by comparing the integrated rate law equation to the given rate law for the reaction.
Yes, an integrated rate law can be used to determine the rate of a reaction at any given time by substituting the value of time into the integrated rate law equation and solving for the concentration of the reactant at that time. This can be useful for predicting the progress of a reaction or determining the best time to measure the concentration of a reactant for accurate rate constant determination.