Second Order Rate Constant Calculator
Compute second order rate constant using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
1/[A]t = 1/[A]0 + kt
The second-order integrated rate law relates the reciprocal of concentration to time linearly. 1/[A]t is the reciprocal concentration at time t, 1/[A]0 is the reciprocal initial concentration, k is the rate constant, and t is time. The half-life is t1/2 = 1/(k[A]0).
Frequently Asked Questions
What is a second-order reaction?
A second-order reaction has a rate that depends on the square of one reactant concentration or the product of two first-order concentrations. The integrated rate law for a second-order reaction in one reactant is 1/[A]t = 1/[A]0 + kt, where [A]t is concentration at time t, [A]0 is initial concentration, and k is the rate constant. A plot of 1/[A] versus time gives a straight line with slope k. Common examples include the dimerization of nitrogen dioxide and the reaction of iodide with persulfate.
How does the half-life of a second-order reaction differ from first-order?
For a second-order reaction, the half-life depends on the initial concentration: t1/2 = 1/(k[A]0). This means each successive half-life is longer than the previous one, as the concentration decreases. In contrast, a first-order reaction has a constant half-life of ln(2)/k regardless of concentration. This concentration-dependent half-life is a key experimental signature of second-order kinetics and explains why these reactions slow down more dramatically over time.
What are the units of a second-order rate constant?
The second-order rate constant k has units of M^-1 s^-1 (or equivalently L mol^-1 s^-1). These units ensure that the rate law rate = k[A]^2 gives a rate in M/s (mol per liter per second). For comparison, first-order rate constants have units of s^-1 and zero-order rate constants have units of M/s. The units of k can be used as a quick check of reaction order when analyzing experimental data. In the integrated rate law, k multiplied by time must have units of M^-1.
How do you identify a second-order reaction experimentally?
To identify second-order kinetics, plot 1/[A] versus time. If the plot is linear, the reaction is second order with respect to A, and the slope equals k. Alternatively, use the method of initial rates: if doubling the concentration quadruples the rate, the reaction is second order. You can also check if the half-life is inversely proportional to initial concentration. Another approach is to compare the fit of zeroth-order, first-order, and second-order integrated rate laws to the experimental data.
What is the difference between overall second-order and second-order in one reactant?
A reaction can be overall second order in two ways. First, it can be second order in a single reactant, where rate = k[A]^2. Second, it can be first order in each of two reactants, where rate = k[A][B]. The integrated rate laws differ: for rate = k[A]^2, use 1/[A]t = 1/[A]0 + kt. For rate = k[A][B] with unequal initial concentrations, a more complex logarithmic expression is needed. Second Order Rate Constant Calculator handles the single-reactant case, which is the most commonly encountered form.
Is Second Order Rate Constant Calculator free to use?
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