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The two most common forms of second-order reactions will be discussed in detail in this section. To describe how the rate of a second-order reaction changes with concentration of reactants or products, the differential (derivative) rate equation is used as well as the integrated rate equation.
For the units of the reaction rate to be moles per liter per second (M/s), the units of a second-order rate constant must be the inverse (M −1 ·s −1). Because the units of molarity are expressed as mol/L, the unit of the rate constant can also be written as L(mol·s).
Because the units of the reaction rate are always moles per liter per second, the units of a first-order rate constant are reciprocal seconds (s −1). The integrated rate law for a first-order reaction can be written in two different ways: one using exponents and one using logarithms.
What is a second-order reaction. Learn the differential & integrated forms of the second-order formula, along with units. What is the half-life. Check out a few examples.
k Units of a Second-Order Reaction. Let’s assume it is a second-order reaction in molecule A: rate = k[A] 2 \[k\; = \;\frac{{{\rm{rate}}}}{{{{\left[ {\rm{A}} \right]}^2}}}\] And now, add the units for the rate and concentration:
Second order reactions can be defined as chemical reactions wherein the sum of the exponents in the corresponding rate law of the chemical reaction is equal to two. The rate of such a reaction can be written either as r = k [A]2, or as r = k [A] [B].
A second order reaction is a reaction where x + y = 2. This can happen if one reactant is consumed at a rate proportional to the square of the reactant's concentration (rate = k [A] 2) or both reactants are consumed linearly over time (rate = k [A] [B]). The units of the rate constant, k, of a second-order reaction are M -1 ·s -1.
There is also a formula that you can use as a shortcut to determine the units of a rate constant: k units = M1-n · t-1. where n is the reaction order. If we needed to determine the units of k for a second-order reaction, we would use 1 for the n: k units = M1-2 · t-1 = M -1 · t-1.
The integrated rate law for our second-order reactions has the form of the equation of a straight line: $$\frac{1}{[A]_t}=kt+\frac{1}{[A]_0}\\y=mx+b$$ A plot of $\frac{1}{[A]_t}$ versus t for a second-order reaction is a straight line with a slope of k and an intercept of $\frac{1}{[A]_0}$.
The unit of the rate constant for the second-order reaction described in Example 12.4 was determined to be L mol −1 s −1. L mol −1 s −1 . For the third-order reaction described in Example 12.5 , the unit for k was derived to be L 2 mol −2 s −1 .