Be sure to answer all parts. Coal gasification is a multistep process to convert coal into cleaner-burning fuels. In one step, a coal sample reacts with superheated steam: C (s) + H2O (g) → CO (g) + H2 (g) ΔH o rxn = 129.7 kJ (a) Combine the reaction above with the following two to write an overall reaction for the production of methane: CO (g) + H2O (g) → CO2 (g) + H2 (g) ΔH o rxn = - 41 kJ CO (g) + 3H2 (g) → CH4 (g) + H2O (g) ΔH o rxn = - 206 kJ In the overall reaction, include the physical states of each product and reactant. (b) Calculate ΔH o rxn for this overall change. 12.03 kJ (c) Using the value in (b) and calculating ΔH o rxn for the combustion of methane, find the total heat for gasifying 6.28 kg of coal and burning the methane formed. Assume water forms as a gas and the molar mass of coal is 12.00 g/mol.

A.

C (s) + H2O (g) - -> CO (g) + H2 (g) (x2)

CO (g) + H2O (g) - -> CO2 (g) + H2 (g)

CO (g) + 3 H2 (g) - -> CH4 (g) + H2O (g)

Adding the three equations up:

2C (s) + 2H2O (g) - -> 2CO (g) + 2H2 (g)

CO (g) + H2O (g) - -> CO2 (g) + H2 (g)

CO (g) + 3 H2 (g) - -> CH4 (g) + H2O (g)

Overall equation:

2C (s) + 2H2O (g) - -> CO2 (g) + CH4 (g)

B.

2C (s) + 2H2O (g) - -> 2CO (g) + 2H2 (g)

= 2x 129.7 kJ/mol = 259.4 kJ/mol

CO (g) + H2O (g) - -> CO2 (g) + H2 (g) ΔH°rxn = - 41.2 kJ/mol

Using their individual heat of formation;

ΔH°rxn = H products - H reactants

= (-393.5 + 0) - (-110.5 + - 241.8)

= - 41.2 kJ/mol

CO (g) + 3H2 (g) - -> CH4 (g) + H2O (g) ΔH°rxn = - 206.17 kJ/mol

Using their individual heat of formation;

ΔH°rxn = H products - H reactants

= (-74.87 + - 241.8) - (-110.5 + 0)

= - 206.17 kJ

ΔH°overall rxn = sum of energies for the 3 reactions above

ΔH°overall reaction = 259.4 + - 41.2 + - 206.17

= 12.03 kJ/mol

Overall equation for the reaction: 2C (coal) + 2H2O (g) - -> CO2 (g) + CH4 (g)

overall ΔH°rxn = 12.03 kJ/mol

C.

Number of moles of coal = mass/molar mass

= 6.28/12

= 0.523 mol

Total heat = number of moles * enthalpy change of the reaction

= 0.523 * 12.03

= 6.30 kJ