Determining reaction order is very simple. All you have to do is take the sum of the exponents of the chemicals in the rate law
Ex:
r=K[Ni]^2[Cl]
The nickel has a 2 as the exponent and the Cl has a 1 as its exponent. When you add the two numbers together you get 3. This means that the reaction is 3rd order
Ex:
r=K[Ni]^2[Cl]
The nickel has a 2 as the exponent and the Cl has a 1 as its exponent. When you add the two numbers together you get 3. This means that the reaction is 3rd order