In order to generate electricity, the heat produced by fuel combustion (dihydrogen, methanol, etc.) — Physical Chemistry — Thermodynamics Chemistry Question
Use of dihydrogen: fuel cells
In order to generate electricity, the heat produced by fuel combustion (dihydrogen, methanol, etc.) can be used to evaporate liquid water. The produced steam turns a turbine, which drives a generator. In such a process, the chemical energy is first converted...
Compound H2O(g) H2O(l)
C°P 33.6 75.3
Standard latent heat of water at 373 K :
∆vapH°(H2O) = 40.66 kJ mol‒1
Standard potentials at 25 °C related to the standard hydrogen electrode (SHE) :
E°(O2(g)/H2O(l)) = 1.23 V /SHE
E°(CO2(g)/CH3OH(l)) = 0.03 V /SHE
Liquid methanol density :
ρmethanol = 0.79 g cm‒3
Model Answer
At the anode: H2(g) = 2 H+(aq) + 2 e−
At the cathode: 1/2 O2(g) + 2 H+(aq) + 2 e− = H2O(l)
Global reaction: H2(g) + 1/2 O2(g) = H2O(l)
Model Answer
U = E°(O2(g)/H2O(l)) – E°(H+(aq)/H2(g)) = 1.23 V
Model Answer
The temperature and the pressure of the system are fixed. Hence, the maximum...
Electric cars consume between 10 and 20 kWh / 100 km. Compute the volume of dihydrogen necessary to produce an electrical energy of 20 kWh at 1.0 bar.
Calculate the standard enthalpy of the combustion reaction of gaseous dihydrogen ∆combH°298K(H2(g)) at 298 K. Deduce the thermodynamic efficiency of the dihydrogen fuel cell.
The thermodynamic efficiency is smaller than 1 because there is a variation of the entropy of the system.
Calculate the standard entropy of the dihydrogen combustion reaction
Determine if the sign of this standard entropy is consistent with the balanced chemical equation for the reaction (Yes/No). Justify it by a short calculation using the stoichiometric coefficients.
Model Answer
The difference between the stoichiometric coefficients of the gaseous compounds in the balanced chemical equation for the reaction is:
0 – (1 + 1/2) = ‒3/2 < 0
This is consistent with a decrease of the disorder.
Determine the oxidation state of the carbon atom in methanol and in carbon dioxide.
Model Answer
In methanol: OS(C) = ‒II
In CO2: OS(C) = IV
Write down the redox half-reactions occurring at the anode and the cathode. Write down the balanced chemical equation for the global reaction of the running cell for one equivalent of liquid methanol.
Model Answer
At the anode: CH3OH(l) + H2O(l) = CO2(g) + 6 H+(aq) + 6 e−
At the cathode: 3/2 O2(g) + 6 H+(aq) + 6 e− = 3 H2O(l)
Global reaction: CH3OH(l) + 3/2 O2(g) = CO2(g) + 2 H2O(l)
Calculate the associated thermodynamic efficiency. Compare it to the efficiency of the dihydrogen fuel cell.
Model Answer
∆combG°298K(CH3OH(l)) = ‒ nF [E°(O2(g)/H2O(l)) ‒ E°(CH3OH(l)/CO2(g))]
∆combG°298K(CH3OH(l)) = ‒6 × 96485 × (1.23 ‒ 0.03)
∆combG°298K(CH3OH(l)) = ‒695 kJ mol–1
∆combH°298K(CH3OH(l)) = ‒ ∆fH°298K(CH3OH(l)) + ∆fH°298K(CO2(g)) + 2∆fH°298K(H2O(l))
∆fH°298K(H2O(l)) = ∆combH°298K(H2(g)) = ‒286 kJ mol‒1 (question 5). Hence:
∆combH°298K(CH3OH(l)) = ‒ (‒239) + (‒394) + 2 × (‒286)
∆combH°298K(CH3OH(l)) = ‒727 kJ mol–1
Calculate the volume of liquid methanol required to produce 20 kWh. Compare this value to the previously calculated volume of gaseous dihydrogen.
Model Answer
E being the energy to be produced: