Given the energy diagram above, what is ΔH when 0.5 mol of methane is combusted, forming H2O(g)?

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Restating the problem and options to set the stage:
Question: Given the energy diagram above, what is ΔH when 0.5 mol of methane is combusted, forming H2O(g)? Options: –404.5 kJ, +1618. kJ, –809.0 kJ, –1618 kJ, +404.5 kJ, +809.0 kJ.

Step-by-step analysis of each option:
Option 1: –404.5 kJ
This value represents half of the standard combustion enthalpy of CH4, assuming ΔHrxn for the full reaction (1.0 mol CH4 combusted) is about –809.0 kJ. Since the problem specifies 0.5 mol of CH4, the enthalpy change scales linearly with the amount of fuel. Therefore, ΔH = (0.5 mol / 1.0 mol) × (–809.0 kJ) = –404.5 kJ. This is consistent with the given ΔHrxn per mole and the amount used.

Option 2: +1618. kJ
Positive sign would imply an endothermic process, which contradicts the provided energy diagram where combustion of methane releases energy. Therefore this is incorrect.

Option 3: –809.0 kJ
This would be the enthalpy change for combusting 1.0 mol CH4 under the stated conditions. Since only 0.5 mol is reacting, using the full amount would overstate ΔH by a factor of two. Thus, this is not correct for 0.5 mol.

Option 4: –1618 kJ
This corresponds to combusting 2.0 mol CH4 (twice the standard 1.0 mol energy) or a doubled amount. With only 0.5 mol reacting, this would be four times too large in magnitude, so it is incorrect for the given quantity.

Option 5: +404.5 kJ
A positive value would indicate an endothermic process, which does not align with methane combustion being exothermic as shown in the diagram. This is incorrect.

Option 6: +809.0 kJ
Again, this implies endothermic behavior and is not consistent with the exothermic combustion of methane depicted. This is incorrect.

Summary rationale: The key idea is that the enthalpy change scales with the amount of reactant. The diagram provides ΔHrxn ≈ –809.0 kJ per 1.0 mol CH4 combusted. For 0.5 mol CH4, you divide by 2, yielding ΔH = –404.5 kJ. All other options either imply wrong sign, incorrect magnitude for the given amount, or misinterpret the stoichiometry.

CHEM 110 Section 3 (PM) SP25 Pre-Lecture Quiz 41 C16-1

Given the energy diagram above, what is ΔH when 0.5 mol of methane is combusted, forming H2O(g)?

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