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the derivation of second order reaction rate constant expression when there are two different reactants are reacting.

8 years ago

Answers : (2)

Ashwin Sinha
520 Points

Dear Neeta Gupta,

second-order reaction depends on the concentrations of one second-order reactant, or two first-order reactants.

For a second order reaction, its reaction rate is given by:

\ -\frac{d[A]}{dt} = 2k[A]^2 or \ -\frac{d[A]}{dt} = k[A][B] or \ -\frac{d[A]}{dt} = 2k[B]^2

In several popular kinetics books, the definition of the rate law for second-order reactions is -\frac{d[A]}{dt} = k[A]^2. Conflating the 2 inside the constant for the first, derivative, form will only make it required in the second, integrated form (presented below). The option of keeping the 2 out of the constant in the derivative form is considered more correct, as it is almost always used in peer-reviewed literature, tables of rate constants, and simulation software.[8]

The integrated second-order rate laws are respectively

\frac{1}{[A]} = \frac{1}{[A]_0} + kt


\frac{[A]}{[B]} = \frac{[A]_0}{[B]_0} e^{([A]_0 - [B]_0)kt}

[A]0 and [B]0 must be different to obtain that integrated equation.

The half-life equation for a second-order reaction dependent on one second-order reactant is \ t_ \frac{1}{2} = \frac{1}{k[A]_0}. For a second-order reaction half-lives progressively double.

Another way to present the above rate laws is to take the log of both sides: \ln{}r = \ln{}k + 2\ln\left[A\right]

Examples of a Second-order reaction
  • 2\mbox{NO}_2(g) \rightarrow \; 2\mbox{NO}(g) + \mbox{O}_2(g)




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8 years ago
E.Nandhini ketha
115 Points
Chemical kinetics, also known as reaction kinetics, Chemical kinetics is the study of rates of chemical processes.
2 years ago
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