# How do I find the order for each reactant?

##### 1 Answer

It must be done for two trials where one of the reactants' concentrations are held constant. (Otherwise there are too many unknowns.)

A general **rate law** is:

#r(t) = k[A]^m[B]^n# where

#[" "]# is the concentration in#"mol/L"# or#"M"# ,#r(t)# is the initial rate of reaction in#"M/s"# , and#m# and#n# are reaction orders (the weights of each reactant on the overall reaction order).

For any reaction, we need its kinetics data. Bare minimum we need:

#[A]# for three trials#[B]# for three trials#r(t)# for three trials

If we consider

#r_1(t) = k[A]_1^m[B]_1^n#

#r_2(t) = k[A]_2^m[B]_2^n#

#r_3(t) = k[A]_3^m[B]_3^n# where the rate constant

#k# is the same for the same reaction at the same temperature.

To find the orders, it tends to be easiest to **choose trials in which** **or**

In the case that no trial data are sufficiently nice, then for trials

#color(blue)((r_i(t))/(r_j(t))) = ([A]_i^m[B]_i^n)/([A]_j^m[B]_j^m)#

#= color(blue)((([A]_i)/([A]_j))^m(([B]_i)/([B]_j))^n)#

For example, if we had trials such that

#(r_i(t))/(r_j(t)) = (([B]_i)/([B]_j))^n#

Assuming the data are not sufficiently nice, take the

#ln((r_i(t))/(r_j(t))) = ln(([B]_i)/([B]_j))^n#

Using the property that

#=> nln(([B]_i)/([B]_j))# .

Therefore, **as long as trials were chosen that held** **constant**:

#color(blue)(n = ln((r_i(t))/(r_j(t)))/(ln(([B]_i)/([B]_j))))#

Or, **as long as trials were chosen that held** **constant**:

#color(blue)(m = ln((r_i(t))/(r_j(t)))/(ln(([A]_i)/([A]_j))))#