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प्रश्न
Describe the graphical representation of first order reaction.
Describe the graphical method for the determination of the order of a first order reaction.
How would you represent a first order reaction graphically?
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उत्तर १
The rate constant for first order reaction is,
kt = ln `([A_0])/([A])`
kt = In [A0] – In [A]
In [A] = In [A0] – kt
y = c + mx
If we follow the reaction by measuring the concentration of the reactants at regular time intervals ‘t’, a plot of ln [A] against ‘t’ yields a straight line with a negative slope. From this, the rate constant is calculated.
A plot of ln [A] vs t for a first-order reaction, \[\ce{A -> product}\] with initial concentration of [A] = 1.00 M and k = 2.5 × 10−2 min−1
उत्तर २
A first order reaction can be represented graphically in several ways. Some important graphical representations and their characteristics are as follows.
Reaction rate vs concentration plot: The rate law for a first-order reaction is given by
Rate = k[A]
A plot of reaction rate vs concentration of reactant for a first order reaction.
The equation y = mx indicates a straight line that passes through the origin. Plotting reaction rates against reactant concentration yields a straight line that passes through the origin, as illustrated in the picture above. The slope of the line corresponds to the rate constant of the reaction.
\[\ce{Slope of the line = \frac{CB}{AC} = k}\]
Concentration vs. time plot: We know that
[A] = [A]0 e−kt
Exponential decay of the conc. of reactant as a function of time for a first order reaction.
The equation shows that a first-order process is exponential, with the concentration of reactant decreasing exponentially over time. Graphing reactant concentrations over time yields an exponential decay curve, as illustrated in the image above.
log10 [A] vs time plot: We know that
\[\ce{k = \frac{2.303}{t} log_10 \frac{[A]_0}{[A]}}\]
This equation can be written as
\[\ce{log_10 [A] = - \frac{kt}{2.303} + log_10[A]_0}\]
The above equation is of the type y = mx + c and represents a straight line. Therefore, on plotting log10 [A] against t, a straight line (as shown in the figure above) is obtained. The slope of the line is equal to \[\ce{\frac{-k}{2.303}}\] while the intercept of the line on log10 [A] axis is equal to log10 [A]0. Thus,
\[\ce{Slope of the line = \frac{AC}{BC} = - \frac{k}{2.303}}\]
Intercept on log10 [A] axis = log10 [A]0
Thus, the value of k can be obtained from the slope of the line.
संबंधित प्रश्न
The rate constant of the first order reaction is 1.386 min–1. Calculate the time required for 80% reactant to decompose?
From the following data, show that the decomposition of hydrogen peroxide is a reaction of the first order:
| t (min) | 0 | 10 | 20 |
| V (ml) | 46.1 | 29.8 | 19.3 |
Where t is the time in minutes and V is the volume of standard KMnO4 solution required for titrating the same volume of the reaction mixture.
If time required to decrease concentration of reactant from 0.8 M to 0.2 M is 12 hours, the half life of this first order reaction is ____________.
For a zero order reaction, the plot of [A]t vs t is linear. The slope of the line is equal to ____________.
Which among the following is an example of zero order reaction?
A first order reaction is 50% completed in 16 minutes. The percentage of reactant that will react in 32 minutes is ____________.
Rate constant for zero order reaction is 2 × 10-2 mol L-1 s-1. If the concentration of the reactant after 25 sec. is 0.5 M, what is the initial concentration of reactant?
Which is the relation between half life and rate constant for a zero order?
A first order reaction takes 10 minute for 30% completion. Find rate constant of the reaction.
For a first order reaction, the plot of log k against 1/T is a straight line. The slope of the line is equal to ______.
