Sure, let's analyze the reaction step-by-step.
The given reaction is:
[tex]\[ \text{C (s)} + 2 \text{H}_2 (\text{g}) \rightarrow \text{CH}_4 (\text{g}) \][/tex]
The change in enthalpy ([tex]\(\Delta H\)[/tex]) for this reaction is:
[tex]\[ \Delta H = -74.9 \text{ kJ} \][/tex]
### Step-by-Step Analysis:
1. Understand the Sign of [tex]\(\Delta H\)[/tex]:
- The [tex]\(\Delta H\)[/tex] value is negative, which means that the reaction releases energy in the form of heat. Hence, it is an exothermic reaction.
2. Interpreting an Exothermic Reaction:
- In an exothermic reaction, energy is released to the surroundings. This means that the products of the reaction have lower energy compared to the reactants.
3. Energy Profile Diagram:
- In an energy profile diagram for an exothermic reaction, the energy level of the reactants is higher than that of the products. The difference in energy levels corresponds to the magnitude of [tex]\(\Delta H\)[/tex].
- Since the reaction releases 74.9 kJ of energy (as indicated by the negative sign), the energy of the reactants decreases by 74.9 kJ to form the products.
### Description of the Energy Profile:
- Reactants: C (s) and 2 H[tex]\(_2\)[/tex] (g) start at a higher energy level.
- Activation Energy: There is an initial rise in energy as the reactants absorb energy to reach the transition state, which is the peak of the diagram.
- Transition State: At the peak of the energy diagram, the energy is at its maximum, representing the activated complex.
- Products: CH[tex]\(_4\)[/tex] (g) forms at a lower energy level relative to the reactants.
- Energy Released: The difference in energy between the reactants' level and the products' level is 74.9 kJ, which is released to the surroundings.
So, the profile that best describes the reaction [tex]\(\text{C (s)} + 2 \text{H}_2 (\text{g}) \rightarrow \text{CH}_4 (\text{g})\)[/tex] with [tex]\(\Delta H = -74.9 \text{ kJ}\)[/tex] is an exothermic energy profile where the reactants are at a higher energy level than the products, and the energy released is 74.9 kJ.
