Consider the following data for the given reaction $$2HI_{(g)} \rightarrow H_{2(g)} + I_{2(g)}$$. $$[HI] \text{ (mol L}^{-1}\text{)}$$: $$0.005, \; 0.01, \; 0.02$$. Rate $$\text{(mol L}^{-1} \text{ s}^{-1}\text{)}$$: $$7.5 \times 10^{-4}, \; 3.0 \times 10^{-3}, \; 1.2 \times 10^{-2}$$. The order of the reaction is _______.

Given data for $$2HI_{(g)} \to H_{2(g)} + I_{2(g)}$$:

Let rate = $$k[HI]^n$$.

Using experiments 1 and 2:

$$\frac{3.0 \times 10^{-3}}{7.5 \times 10^{-4}} = \left(\frac{0.01}{0.005}\right)^n$$

$$4 = 2^n$$

$$n = 2$$

Verification with experiments 2 and 3:

$$\frac{1.2 \times 10^{-2}}{3.0 \times 10^{-3}} = \left(\frac{0.02}{0.01}\right)^n$$

$$4 = 2^n$$

$$n = 2$$ ✓

The order of the reaction is $$\boxed{2}$$.