A) The decomposition reaction of Mg has a half-life of 50 minutes. Calculate the time it would take for 100g of Mg to decompose to 25g. b) For the reaction 3A + 2B --> C + 2D, 3.5 mol of A reacts with 2.0 mol of B to give 1.8 mol of C and 4.0 mol of D. Calculate the percent yield.

Energy of intermediate (valley after first peak) $\approx 20 \text{ kJ}$  
Energy of second transition state (second peak) $\approx 40 \text{ kJ}$

$$
E_a(\text{second step}) = \text{Energy of second transition state} - \text{Energy of intermediate}
$$
$$
E_a(\text{second step}) = 40 \text{ kJ} - 20 \text{ kJ} = \boxed{20 \text{ kJ}}
$$

Energy of reactants $\approx 10 \text{ kJ}$  
Energy of first transition state (first peak) $\approx 50 \text{ kJ}$
$$
E_a(\text{first step}) = \text{Energy of first transition state} - \text{Energy of reactants}
$$
$$
E_a(\text{first step}) = 50 \text{ kJ} - 10 \text{ kJ} = 40 \text{ kJ}
$$

The first step has an activation energy of $40 \text{ kJ}$, and the second step has an activation energy of $20 \text{ kJ}$.  
The **first step** is the rate-determining step because it has the **highest activation energy**.

Energy of products $\approx 0 \text{ kJ}$  
Energy of reactants $\approx 10 \text{ kJ}$
$$
\Delta H_{\text{overall}} = \text{Energy of products} - \text{Energy of reactants}
$$
$$
\Delta H_{\text{overall}} = 0 \text{ kJ} - 10 \text{ kJ} = -10 \text{ kJ}
$$
Since the overall change in enthalpy is negative, the overall reaction is **exothermic**.

Energy of intermediate $\approx 20 \text{ kJ}$  
Energy of reactants $\approx 10 \text{ kJ}$
$$
\Delta H_{\text{first step}} = \text{Energy of intermediate} - \text{Energy of reactants}
$$
$$
\Delta H_{\text{first step}} = 20 \text{ kJ} - 10 \text{ kJ} = \boxed{10 \text{ kJ}}
$$

Energy of products $\approx 0 \text{ kJ}$  
Energy of reactants $\approx 10 \text{ kJ}$
$$
\Delta H_{\text{overall}} = \text{Energy of products} - \text{Energy of reactants}
$$
$$
\Delta H_{\text{overall}} = 0 \text{ kJ} - 10 \text{ kJ} = \boxed{-10 \text{ kJ}}
$$