Interpretation: Given the decomposition of
Concept Introduction:
The integrated rate law equation explains how the concentrations of reactants change with time.
Consider a first order
The concentration of the reactant A at time t is given by the below equation
Where,
The integrated rate law for this first order reaction is obtained by taking the natural logarithm of both sides of
That is,
Using Dalton's law, the partial pressure of formic acid is given by
Where,
The order of the reaction can be determined from a plot of concentration against time.
If we plot concentration against time, and if the curve is linear, the reaction is a zero order reaction.
If we plot log of concentration against time and if the curve is linear, the reaction is a first order reaction.
If we plot concentration inverse against time and if the curve is linear, the reaction is a second order reaction.
Answer to Problem 11.50PAE
Solution: The rate constant is
Explanation of Solution
Given Information: The table containing the total pressures in the reaction vessel during the decomposition of
Decomposition of
The initial partial pressure of
Calculate the partial pressure of
Partial pressure of
Partial pressure of
Partial pressure of
Therefore, the total pressure at any given time t is given as
Time(t) | Total pressure |
|
0 | 491.7 | 491.7 |
185.3 | 549.6 | 434.0 |
242.8 | 566.6 | 417.0 |
304.5 | 584.1 | 399.5 |
362.7 | 599.9 | 383.7 |
429.5 | 617.2 | 366.4 |
509.7 | 637.0 | 346.6 |
606.3 | 659.5 | 324.1 |
We need to plot these values of partial pressure with time to see if the reaction is zero order or not
As some points do not lie on the straight line, the curve is not linear. Thus, it is not a zero order reaction.
Time(t) | |
|
0 | 491.7 | 6.1978687744 |
185.3 | 434.0 | 6.0730445341 |
242.8 | 417.0 | 6.0330862218 |
304.5 | 399.5 | 5.9902137652 |
362.7 | 383.7 | 5.9498609973 |
429.5 | 366.4 | 5.9037256328 |
509.7 | 346.6 | 5.8481713773 |
606.3 | 324.1 | 5.7810521101 |
Here we see the curve is linear and thus the reaction is a first order reaction.
To calculate the rate constant, we need the negative slope of the line in the plot
Hence, the rate constant is the negative of the slope obtained. It is equal to
The concept of integrated rate law and the manipulation the data into a plot helps in determining the order of the decomposition of
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Chapter 11 Solutions
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