C(s) + 2H₂(g) → CH₄(g); ∆H = –74.8 kJ mol^–1. Which of the following diagrams gives an accurate representation of the above reaction? [R → reactants; P → products]

The correct answer is the diagram where the reactants (R) are at a higher energy level than the products (P), and the vertical energy difference between their levels is labeled 74.8 kJ mol⁻¹ (as shown in the first image, image_0.webp).

To determine the correct energy profile diagram, we analyze the thermodynamic properties of the given chemical reaction:

$\text{C(s)}+2{\text{H}}_2\text{(g)}\to {\text{CH}}_4\text{(g)}$

The change in enthalpy ($\mathrm{\Delta H}$) for this reaction is given as:
$\mathrm{\Delta H}=-74.8\text{kJ}{\text{mol}}^{-1}$

1. Determine if the reaction is exothermic or endothermic:
A negative enthalpy change ($\mathrm{\Delta H}<0$) indicates that the reaction is exothermic, meaning energy is released to the surroundings. For an endothermic reaction, $\mathrm{\Delta H}$ would be positive.

2. Analyze the energy levels of reactants and products:
The enthalpy change is defined as the difference between the total enthalpy of the products ($H_{\text{P}}$) and the reactants ($H_{\text{R}}$):
$\mathrm{\Delta H}=H_{\text{P}}-H_{\text{R}}$
Since $\mathrm{\Delta H}=-74.8\text{kJ}{\text{mol}}^{-1}$, we have:
$H_{\text{P}}-H_{\text{R}}<0\Rightarrow H_{\text{R}}>H_{\text{P}}$
This means that the reactants (R) must be at a higher potential energy level than the products (P) on the energy diagram.

3. Identify the enthalpy difference in the diagram:
The magnitude of the energy difference between the reactants and products is $74.8\text{kJ}{\text{mol}}^{-1}$. In the correct diagram (image_0.webp):
• The vertical axis is labeled "Energy (kJ mol⁻¹)" and the horizontal axis is labeled "Reaction progress".
• The horizontal line representing the reactants (R) is higher than the horizontal line representing the products (P).
• A vertical double-headed arrow directly spanning the difference between the energy level of R and the energy level of P is labeled with the value "74.8".

Other options show incorrect relationships, such as representing an endothermic profile (where P is higher than R), or incorrectly labeling the activation energy (the peak of the curve relative to R) as the enthalpy change.