Question

Coal gasification can be represented by the equation: 2 C(s) + 2 H2O(g) → CH4(g) + CO2(g) ΔH = ? Use the following information to find ΔH for the reaction above. CO(g) + H2(g) → C(s) + H2O(g) ΔH = -131 kJ CO(g) + H2O(g) → CO2(g) + H2(g) ΔH = -41 kJ CO(g) + 3 H2(g) → CH4(g) + H2O(g) ΔH = -206 kJ

Answer 1

Answer: The $\Delta H^o_{rxn}$ for the reaction is 15 kJ.

Explanation:

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 given chemical reaction follows:

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

The intermediate balanced chemical reaction are:

(1) $CO(g)+H_2(g)\rightarrow C(s)+H_2O(g)$    $\Delta H_1=-131kJ$   ( × 2)

(2) $CO(g)+H_2O(g)\rightarrow CO_2(g)+H_2(g)$     $\Delta H_2=-41kJ$

(3) $CO(g)+3H_2(g)\rightarrow CH_4(g)+H_2O(g)$     $\Delta H_3=-206kJ$

The expression for enthalpy of the reaction follows:

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

Putting values in above equation, we get:

$\Delta H^o_{rxn}=[(2\times -(-131))+(1\times (-41))+(1\times (-206))]=15kJ$

Hence, the $\Delta H^o_{rxn}$ for the reaction is 15 kJ.