Question

The reaction, \[MgO(s)+C(s)\to Mg(s)+CO(g)\], for which ${{\Delta }_{r}}{{H}^{0}}=+491.1kJmo{{l}^{-1}}$ and ${{\Delta }_{r}}{{S}^{0}}=198.0J{{K}^{-1}}mo{{l}^{-1}}$ is not feasible at 298K. Temperature above which reaction will be feasible is:
(A) 1890.0 K
(B) 2480.3 K
(C) 2040.5 K
(D) 2380.5 K

Answer 1

Hint: The reaction is feasible or not depending on the sign of $\Delta G$. If the value of $\Delta G$ is positive then the reaction is not feasible which means that the reaction does not happen and similarly if the value of $\Delta G$ is negative then the reaction is feasible which means that the reaction will happen.

Complete step by step solution:
Reaction given in the question:
\[MgO(s)+C(s)\to Mg(s)+CO(g)\]
Other given data from the question:
Enthalpy of the reaction i.e. ${{\Delta }_{r}}{{H}^{0}}=+491.1kJmo{{l}^{-1}}$
And the value of ${{\Delta }_{r}}{{S}^{0}}=198.0J{{K}^{-1}}mo{{l}^{-1}}$
Given that the reaction is not feasible at 298K
Temperature above which reaction will be feasible can be calculated by the ratio of delta H to delta S.
We will convert the value of enthalpy from KJ to J and the conversion from kJ to J is done by multiplying the number with 1000.
The temperature above which reaction will be feasible = $\dfrac{\Delta H}{\Delta S}=\dfrac{(491.1)(1000)}{198}$
The temperature above which reaction will be feasible= 2480.3 K

Hence the correct answer is option (C)

Additional information:
Enthalpy is an equivalent quantity which is equal to the total heat content of the system or we can say that the enthalpy is equal to the internal energy of the system plus the product of volume and pressure.


Note: To be a feasible reaction the reaction must occur spontaneously, which means that no extra energy is applied for the reaction to take place. A redox reaction is feasible only when a species having higher potential gets reduced which means that it accepts the electrons and the species having low potential get oxidized which means that it loses electrons.