Rate constant of the first-order reaction when initial...

Rate constant of the first-order reaction when initial concentration $C_{0}$ and concentration $C_{t}$ at time $t$ is given by equation: $k_{t}=\log C_{0}-\log C_{t}$ Graph is a straight line if we plot (a) $\mathrm{t} \operatorname{vs} \log \mathrm{C}_{\mathrm{o}}$ (b) $\mathrm{t} \mathrm{vs} \log \mathrm{C}_{\mathrm{t}}$ (c) $\mathrm{t}^{-1} \operatorname{vs} \log \mathrm{C}_{\mathrm{t}}$ (d) $\log C_{o} \operatorname{vs} \log C_{t}$

Rate constant of the first-order reaction when initial concentration $C_{0}$ and concentration $C_{t}$ at time $t$ is given by equation:
$k_{t}=\log C_{0}-\log C_{t}$
Graph is a straight line if we plot
(a) $\mathrm{t} \operatorname{vs} \log \mathrm{C}_{\mathrm{o}}$
(b) $\mathrm{t} \mathrm{vs} \log \mathrm{C}_{\mathrm{t}}$
(c) $\mathrm{t}^{-1} \operatorname{vs} \log \mathrm{C}_{\mathrm{t}}$
(d) $\log C_{o} \operatorname{vs} \log C_{t}$

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Key Concepts

Rate Constant

The rate constant is a numerical value that characterizes the speed of a chemical reaction. In the context of a first-order reaction, it is obtained from the slope of the linear plot derived from the integrated rate law, thus reflecting how quickly the reactant concentration decreases over time.

Graphical Analysis in Kinetics

Graphical analysis in reaction kinetics involves plotting transformed concentration data against time to obtain a straight line, from which kinetic parameters like the rate constant can be deduced. For first-order reactions, plotting log C? versus time gives a linear trend with a slope equal to -k.

First-Order Reaction

A first-order reaction is one in which the rate of reaction is directly proportional to the concentration of one reactant. In such reactions, a change in concentration leads to a corresponding change in the rate, and the mathematical treatment of its kinetics results in a linear relationship when appropriately transformed.

Integrated Rate Law

The integrated rate law provides a relationship between the concentration of a reactant and time for a specific order of reaction. For a first-order reaction, it is commonly expressed as log C? = log C? - kt, allowing the determination of the rate constant from the slope of a plot of log concentration versus time.

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