An inventor has approached you with a fantastic idea to collect all the effluent

Question

An inventor has approached you with a fantastic idea to collect all the effluent gas from the local power plant and convert it to gas that can be used to heat homes. Reduced pollution and a useful byproduct. Win-win!! She proposes to use solar power to break down water into H2 and O2 and then use the reaction of the H2 produced with the CO2 to form CH4. The reaction: CO2 (g) + H2 (g) ? 2H2O (g) + CH4 (g)

consider a situation where there is only 70% conversion of the CO2. The CO2 enters the reactor at 800K, the H2 enters the reactor at 298K and the molar ratio of the reactants is 1:4 (CO2:H2). The products leave the reactor at 1000K. Calculate the heat required (or released) in this reaction

Explanation / Answer

2CO2 + 4H2 = 2H2O + CH4

Since this reaction causes the temperature to increases 200K, the energy equivalent to 200K is RT, 200*8.314 = 1.67 kJ/mol. This reaction is only 70% efficient and therefore, the heat required is 1.67/0.7 = 2.38 kJ per mole of CH4 production.

For a detailed thermochemcial calculations, data of heat of formation, heat capacity and its temperature dependence are required.

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