Question

Find the ∆Hrxn for the reaction: 3C(s)+4H2(g) →C3H8(g) Using these reactions with known ∆H’s: C3H8(g) + 5O2(g) → 3CO2(g) + 4H2O(g) ∆H = −2043 kJ C(s) + O2(g) → CO2(g) ∆H = −393.5 kJ 2H2(g) + O2(g) → 2H2O(g) ∆H = −483.6 kJ Express your answer in kJ.

Answer 1

Answer : The $\Delta H^o_{rxn}$ for the reaction is -104.7 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 chemical equation for the formation of propane follows:

$3C(s)+4H_2(g)\rightarrow C_3H_8(g)$;   $\Delta H^o_{rxn}=?$

The intermediate balanced chemical reaction are:

(1) $C_3H_8(g)+5O_2(g)\rightarrow 3CO_2(g)+4H_2O(g)$;    $\Delta H_1=-2043kJ$

(2) $C(s)+O_2(g)\rightarrow CO_2(g)$;    $\Delta H_2=-393.5kJ$

(3) $2H_2(g)+O_2(g)\rightarrow 2H_2O(g)$;    $\Delta H_3=-483.6kJ$

Now we are reversing the reaction 1, multiplying reaction 2 by 3 and multiplying reaction 3 by 2 and then adding all the reaction, we get:

(1) $3CO_2(g)+4H_2O(g)\rightarrow C_3H_8(g)+5O_2(g)$;    $\Delta H_1=2043kJ$

(2) $C(s)+O_2(g)\rightarrow CO_2(g)$;    $\Delta H_2=3\times -393.5kJ=-1180.5kJ$

(3) $2H_2(g)+O_2(g)\rightarrow 2H_2O(g)$;    $\Delta H_3=2\times -483.6kJ=-967.2kJ$

The expression for enthalpy of the reaction follows:

$\Delta H^o_{rxn}=\Delta H_1+\Delta H_2+\Delta H_3$

Putting values in above equation, we get:

$\Delta H^o_{rxn}=(2043)+(-1180.5)+(-967.2)=-104.7kJ$

Hence, the $\Delta H^o_{rxn}$ for the reaction is -104.7 kJ.