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

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

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2 Answers

Ashwin Sinha
520 Points
11 years ago

Dear Neeta Gupta,

A 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

or

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

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