The given reaction was studied at \[ - {10^ \circ }C\] and the following data was obtained.
\[2NO(g) + C{l_2}(g) \to 2NOCl(s)\]
\[{\left[ {NO} \right]_0}\]and \[{\left[ {C{l_2}} \right]_0}\] are the initial concentrations and r₀ is the initial reaction rate. The overall order of the reaction is: (Round off to the nearest integer).

Hint: 1. The Order of Reaction describes the power dependence of the rate on the concentration of each reactant.
2. The overall order of the reaction for all three experiments should be the same.

Complete Step by Step Solution:
1. Order of reaction: The addition of the concentration of the reactants in the rate law formula is known as the order of the reaction.
2. The expression of the order of the reaction is as follows:
\[Rate = k{\left[ A \right]^x}{\left[ B \right]^y}\]
Where, A=concentration of species A
B=concentration of species B
x=order of reaction with respect to A
y=order of reaction with respect to B
k=rate constant
3. The overall order of the reaction is the sum of the order of reaction to each ingredient.
4. The given reaction was performed by three experiments that have different initial concentrations and rate of reaction values.
5. Apply the first experiment values of the initial concentration of the reactants and rate of reaction in the general formula:
\[0.18 = k{\left[ {0.10} \right]^x}{\left[ {0.10} \right]^y}(1)\]
6. Apply the second experiment values in the general formula:
\[0.36 = k{\left[ {0.10} \right]^x}{\left[ {0.20} \right]^y}(2)\]
7. Put all the third experiment values in the rate of reaction formula:
\[1.44 = k{\left[ {0.20} \right]^x}{\left[ {0.20} \right]^y}(3)\]
8. Divide the equation (3) by (2)
\[\dfrac{{0.36}}{{1.44}} = \dfrac{{k{{\left[ {0.10} \right]}^x}{{\left[ {0.20} \right]}^y}}}{{k{{\left[ {0.20} \right]}^x}{{\left[ {0.20} \right]}^y}}}\]
\[\dfrac{1}{4} = {\left( {\dfrac{1}{2}} \right)^x} \Rightarrow x = 2\]
9. Divide the equation (2) by (1)
\[\dfrac{{0.18}}{{0.36}} = \dfrac{{k{{\left[ {0.10} \right]}^x}{{\left[ {0.10} \right]}^y}}}{{k{{\left[ {0.10} \right]}^x}{{\left[ {0.20} \right]}^y}}}\]
\[\dfrac{1}{2} = {\left( {\dfrac{1}{2}} \right)^y} \Rightarrow y = 1\]
10. The order of the reaction with respect to the \[NO\]is two and the order of the reaction with respect to the \[C{l_2}\]is one. So, the overall order of the reaction is three which is the sum of the order of the reaction of reactants.
The overall order of reaction is 3.

Additional information:
1. The order of reaction shows the chemical kinetics of the reaction.
2. The order of reaction shows how the concentration of each species affects the reaction rate.

Note: The order of the reaction is determined by the concentration of the species that determine the rate-determining. Many reactions go through several transition states. Therefore, for many reactions, the reaction orders are not necessarily equal to the stoichiometric coefficients.