Step 1: Understanding the Question:
The question asks us to identify the false statement regarding a chemical reaction that possesses the experimental rate law equation $r = k [\text{H}_2][\text{I}_2]$.
Step 2: Key Formula or Approach:
For a general rate law expression $r = k [A]^x [B]^y$, the exponent $x$ denotes the order with respect to reactant $A$, the exponent $y$ denotes the order with respect to reactant $B$, and the sum of the exponents ($x + y$) defines the overall reaction order.
Step 3: Detailed Explanation:
Given the rate law:
$$r = k [\text{H}_2]^1 [\text{I}_2]^1$$
The exponent of $[\text{H}_2]$ is 1, which means the reaction is of the first order with respect to $\text{H}_2$ (Statement A is correct).
The exponent of $[\text{I}_2]$ is 1, which means the reaction is of the first order with respect to $\text{I}_2$ (Statement C is correct).
The overall order of the reaction is calculated by summing these individual exponents: $\text{Overall Order} = 1 + 1 = 2$ (Statement D is correct).
Therefore, statement (B), which claims that the overall order of the reaction is 1, is completely false.
Step 4: Final Answer:
The statement that is NOT true is option (B).