For a particular isomer of C8H18, the following reaction produces 5099.5 kJ of heat per mole of C8H18(g) consumed, under standard conditions.
What is the standard enthalpy of formation of this isomer of C8H18(g)?
What is the reaction you have in mind?
To determine the standard enthalpy of formation (ΔHf°) for a specific isomer of C8H18, we can use Hess's Law, which states that the overall enthalpy change of a reaction is equal to the sum of the enthalpy changes of its individual steps. In this case, we can use the given reaction's enthalpy change along with the enthalpy changes of known formation reactions to calculate ΔHf° for the isomer.
The given reaction produces 5099.5 kJ of heat per mole of C8H18(g) consumed. Since it is not specified what the products of this reaction are, we cannot directly associate it with a known formation reaction.
To proceed, we need to compare the given reaction with known formation reactions for other compounds that have a similar molecular formula. Since the isomer of C8H18 is not specified, we'll consider one possible isomer, which is octane (n-octane).
The standard enthalpy change of formation (ΔHf°) for a compound is the enthalpy change when one mole of the compound is formed from its elements in their standard states (usually 25°C and 1 atm).
The known formation reaction for n-octane is:
2 CH4(g) + 13/2 O2(g) → C8H18(g) + 9 H2O(g)
The standard enthalpy change of formation for n-octane can be calculated using known enthalpies of formation for methane (CH4), oxygen (O2), and water (H2O).
ΔHf°(C8H18) = [2 ΔHf°(CH4) + (13/2) ΔHf°(O2)] - [ΔHf°(H2O) * 9]
Substituting the known values for the standard enthalpies of formation:
ΔHf°(C8H18) = [2 * (-74.8 kJ/mol) + (13/2) * 0 kJ/mol] - [(-285.8 kJ/mol) * 9]
ΔHf°(C8H18) = [-149.6 kJ/mol] - [-2572.2 kJ/mol]
ΔHf°(C8H18) = -149.6 kJ/mol + 2572.2 kJ/mol
ΔHf°(C8H18) ≈ 2422.6 kJ/mol
Therefore, the standard enthalpy of formation for this particular isomer of C8H18(g) is approximately 2422.6 kJ/mol.