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Magazine Chapter 12: Q34 E (page 706)
Use the data provided in a graphical method to determine the order and rate constant of the following reaction:\({\bf{2P}} \to {\bf{Q}} + {\bf{W}}\)
Time (s) | 9.0 | 13.0 | 18.0 | 22.0 | 25.0 |
(P) (M) | 1.077 脳 10鈭�3 | 1.068 脳 10鈭�3 | 1.055 脳 10鈭�3 | 1.046 脳 10鈭�3 | 1.039 脳 10鈭�3 |
Short Answer
The order of the reaction is the first order. The rate constant of the reaction is \({\bf{2}}{\bf{.6}} \times {\bf{1}}{{\bf{0}}^{{\bf{ - 3}}}}{{\bf{s}}^{{\bf{ - 1}}}}\)
Step by step solution
Step 1: Plotting of graph
The plot of ln(P) vs time is linear. This indicates first-order reaction kinetics.
Calculation of rate constant
The constant rate of a first-order reaction is as follows:
\({\bf{K = }}\frac{{{\bf{In}}\frac{{{{{\bf{(P)}}}_{\bf{0}}}}}{{{\bf{(P)}}}}}}{{\bf{t}}}\)
Time | (P) | ln(P) |
9 | 1.077 脳 10鈭�3 | -6.833 |
13 | 1.068 脳 10鈭�3 | -6.841 |
18 | 1.055 脳 10鈭�3 | -6.854 |
22 | 1.046 脳 10鈭�3 | -6.862 |
25 | 1.039 脳 10鈭�3 | -6.869 |
Now, the slope of the plot is given as
\(Slope = \frac{{\Delta y}}{{\Delta x}}\)
Where \({\bf{\Delta y}}\) is the change in values of (ln P) at two different times t, and \({\bf{\Delta }}x\) is the corresponding difference in time.
\(Slope = \frac{{( - 6.8540) - ( - 6.841)}}{{18 - 13}} = - 2.6*{10^{ - 3}}{s^{ - 1}}\)
Calculation
Rate= -(slope)
\(\begin{align} &= - ( - 2.6*{10^{ - 3}}{s^{ - 1}}){s^{ - 1}}\\ &= 2.6*{10^{ - 3}}{s^{ - 1}}\end{align}\)
Thus, the order of the reaction is first order with a rate constant of \({\bf{2}}{\bf{.6}} \times {\bf{1}}{{\bf{0}}^{{\bf{ - 3}}}}{{\bf{s}}^{{\bf{ - 1}}}}\)
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