Step-by-Step Solution:

1. Write the general rate law for the reaction. The reaction is $aG + bH \to Products$. The rate law can be expressed as: $R = k[G]^x[H]^y$ Where:

   • R is the rate of the reaction.
   • k is the rate constant.
   • [G] and [H] are the concentrations of reactants G and H, respectively.
   • x is the order of the reaction with respect to G.
   • y is the order of the reaction with respect to H. The overall order of the reaction is x + y.

2. Analyze the second condition to find the order with respect to G (x). The problem states that when the concentration of G is doubled while keeping the concentration of H fixed, the rate is doubled. Let the initial rate be $R_1$: $R_1 = k[G]^x[H]^y \quad \text{(Equation 1)}$ When [G] is doubled to 2[G], the new rate $R_2$ is $2R_1$: $R_2 = k(2[G])^x[H]^y = 2^x \cdot k[G]^x[H]^y \quad \text{(Equation 2)}$ Since $R_2 = 2R_1$, we can write: $2R_1 = 2^x \cdot (k[G]^x[H]^y)$ Substituting $R_1$ from Equation 1: $2(k[G]^x[H]^y) = 2^x (k[G]^x[H]^y)$ Dividing both sides by $k[G]^x[H]^y$ gives: $2 = 2^x$ Therefore, the order with respect to G is x = 1.

3. Analyze the first condition to find the order with respect to H (y). The problem states that when the concentrations of both G and H are doubled, the rate increases by eight times. Let the initial rate be $R_1$ (from Equation 1). When [G] becomes 2[G] and [H] becomes 2[H], the new rate $R_3$ is $8R_1$: $R_3 = k(2[G])^x(2[H])^y = 2^x \cdot 2^y \cdot k[G]^x[H]^y \quad \text{(Equation 3)}$ Since $R_3 = 8R_1$, we can write: $8R_1 = 2^x \cdot 2^y \cdot (k[G]^x[H]^y)$ Substituting $R_1$ from Equation 1: $8(k[G]^x[H]^y) = 2^x \cdot 2^y \cdot (k[G]^x[H]^y)$ Dividing both sides by $k[G]^x[H]^y$ gives: $8 = 2^x \cdot 2^y$ We already found that x = 1. Substituting this value: $8 = 2^1 \cdot 2^y$ $8 = 2 \cdot 2^y$ $4 = 2^y$ Since $4 = 2^2$, we have: $2^2 = 2^y$ Therefore, the order with respect to H is y = 2.

4. Calculate the overall order of the reaction. The overall order is the sum of the individual orders x and y. $\text{Overall Order} = x + y$ $\text{Overall Order} = 1 + 2 = 3$

Conclusion:

The overall order of the reaction is 3. This corresponds to option D.