The given data represents the initial concentrations of reactants, NO and Cl2, and the corresponding rates of formation of NOCl at a temperature of 10 degrees Celsius. By analyzing this data, we can determine the order of the reaction and calculate the rate constant.

To determine the order of the reaction, we need to analyze the relationship between the concentrations of the reactants and the rate of the reaction.

1. Initial concentrations of reactants and corresponding rates:
- [NO] = 0.10 mol dm-3, [Cl2] = 0.10 mol dm-3, rate = 0.18 mol dm-3 min-1
- [NO] = 0.10 mol dm-3, [Cl2] = 0.20 mol dm-3, rate = 0.36 mol dm-3 min-1
- [NO] = 0.10 mol dm-3, [Cl2] = 0.10 mol dm-3, rate = 0.20 mol dm-3 min-1
- [NO] = 0.20 mol dm-3, [Cl2] = 0.20 mol dm-3, rate = 1.44 mol dm-3 min-1

2. Relationship between reactant concentrations and rate:
- When the concentration of NO is kept constant at 0.10 mol dm-3 and the concentration of Cl2 is doubled from 0.10 mol dm-3 to 0.20 mol dm-3, the rate of the reaction doubles from 0.18 mol dm-3 min-1 to 0.36 mol dm-3 min-1.
- When the concentration of Cl2 is kept constant at 0.10 mol dm-3 and the concentration of NO is doubled from 0.10 mol dm-3 to 0.20 mol dm-3, the rate of the reaction increases by a factor of 10 from 0.18 mol dm-3 min-1 to 1.44 mol dm-3 min-1.

Based on this analysis, we can conclude that the rate of the reaction is dependent on the concentration of Cl2 and the concentration of NO. Therefore, the reaction is not a zero-order or first-order reaction, but a second-order reaction.

To calculate the rate constant (k), we can use the rate equation for a second-order reaction, which is given by:
rate = k * [NO] * [Cl2]

Using the first set of data, we can substitute the values to obtain:
0.18 = k * 0.10 * 0.10

Solving for k, we get:
k = 0.18 / (0.10 * 0.10) = 18 dm3 mol-1 min-1

Therefore, the order of the reaction is second order and the rate constant is 18 dm3 mol-1 min-1.