A student attempted to calculate the enthalpy change for the combustion of gaseous methanol according to the target equation
CH₃OH(g) + 23 O₂(g) → CO₂(g) + 2 H₂O(l)
The student used the three thermochemical equations shown below and recorded a running tally of species to verify cancellation. The work is reproduced exactly as written.
(1) CH₃OH(l) + 23 O₂(g) → CO₂(g) + 2 H₂O(l) ΔH=−726kJ
(2) CH₃OH(g) → CH₃OH(l) ΔH=−38kJ
(3) H₂O(l) → H₂O(g) ΔH=+44kJ
Running Tally Written by Student (after adding the three equations as shown):
Reactants remaining: CH₃OH(g) + 23 O₂(g)
Products remaining: CO₂(g) + 2 H₂O(l) + H₂O(g)
Reported overall ΔH=−720kJ.
Assume all tabulated ΔH values are correct for the equations shown. The student’s goal is to obtain only the species in the target equation and an accurate ΔH.
(1) Part 1: (a) Identify each distinct error made in the student’s procedure or bookkeeping. For each error, cite the specific evidence in the student’s work that reveals the mistake.
(2) Part 2: (b) Rewrite the sequence of thermochemical equations, stating clearly any reversal or stoichiometric scaling you apply to individual equations so that all unwanted species cancel and the net equation exactly matches the target reaction.
(3) Part 3: (c) Calculate the corrected value of ΔH for the combustion of gaseous methanol based on your revised sequence in part (b). Show all steps clearly, including intermediate arithmetic.
(4) Part 4: (d) Explain, in terms of the law of conservation of energy, why an incorrect cancellation of H₂O(g) in the running tally necessarily leads to an erroneous overall ΔH.