The combination of coke and steam produces a mixture called coal gas, which can be used as a fuel or as a starting material for other reactions. If we assume coke can be represented by graphite, the equation for the production of coal gas is

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

Determine the standard enthalpy change for this reactionf rom the following standard enthalpies of reactions:

C(s)+H2O(g)--->CO(g)+H2(g) delta H=131.3 kJ

CO(g)+H2O(g)--->CO2(g)+H2(g) delta H=-41.2 kJ

CH4(g)+H2O(g)--->3H2(g)+CO(g) delta H=206.1 kJ

Hess’s law of constant heat summation states that the amount of heat absorbed or evolved in a given chemical equation remains the same whether the process occurs in one step or several steps.

According to this law, the chemical equation is treated as ordinary algebraic expressions and can be added or subtracted to yield the required equation. This means that the enthalpy change of the overall reaction is equal to the sum of the enthalpy changes of the intermediate reactions.

The chemical equation for the reaction of carbon and water follows:

[tex]2C(s)+2H_2O(g)\rightarrow CH_4(g)+CO_2(g)[/tex] [tex]\Delta H^o_{rxn}=?[/tex]

The intermediate balanced chemical reaction are:

(1) [tex]C(s)+H_2O(g)\rightarrow CO(g)+H_2(g)[/tex] [tex]\Delta H_1=131.3kJ[/tex] ( × 2)

(2) [tex]CO(g)+H_2O(g)\rightarrow CO_2(g)+H_2(g)[/tex] [tex]\Delta H_2=-41.2kJ[/tex]

(3) [tex]CH_4(g)+H_2O(g)\rightarrow 3H_2(g)+CO(g)[/tex] [tex]\Delta H_3=206.1kJ[/tex]

The expression for enthalpy of the reaction follows:

[tex]\Delta H^o_{rxn}=[2\times \Delta H_1]+[1\times \Delta H_2]+[1\times (-\Delta H_3)][/tex]

Putting values in above equation, we get:

[tex]\Delta H^o_{rxn}=[(2\times (131.3))+(1\times (-41.2))+(1\times (-206.1))]=15.3kJ[/tex]

Hence, the [tex]\Delta H^o_{rxn}[/tex] for the reaction is 15.3 kJ.