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# 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

Last updated date: 22nd Jun 2024
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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)