Question
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The favourable conditions for a spontaneous reaction are;
(A) $T\Delta S > \Delta H,\Delta H = + ve,\Delta S = + ve$
(B) $T\Delta S > \Delta H,\Delta H = + ve,\Delta S = - ve$
(C) $T\Delta S = \Delta H,\Delta H = + ve,\Delta s = - ve$
(D) $T\Delta S = \Delta H,\Delta H = + ve,\Delta s = + ve$

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Hint: Spontaneous reactions are reactions, that once started, continues by itself without further input of energy from the outside.
These spontaneous reactions are mainly accompanied by the high entropy mean high disorder in the system.

Step by step solution:
The free energy change for the spontaneous reactions is as follows.
$\Delta G = \Delta H - T\Delta S$
For spontaneous reactions the free energy change is always negative.
The reaction is spontaneous if $\Delta G < 0$.
\[\Delta H - T\Delta S < 0\]
\[T\Delta S > \Delta H\]
$T\Delta S > \Delta H,\Delta H = + ve,\Delta S = + ve$
In option – “A”
$\Delta H$ is +ve and $\Delta S$is +ve and \[T\Delta S > \Delta H\].
$0 > \Delta H - T\Delta S$
$0 > \Delta G$
Hence, the process is spontaneous.

Therefore, the correct option –“A”.

Additional information: A spontaneous reaction is a change that has a natural tendency to happen under certain conditions. Example : Oxidation of iron
Most of the exothermic reactions tend to proceed spontaneously and endothermic reactions tend to be non – spontaneous.
The spontaneity of any reaction can be predicted by calculating Gibbs free energy .
The Gibbs free energy is indicated by the following equation.
$\Delta G = \Delta H - T\Delta S$
$\Delta G$ = Standard Gibbs free energy
$\Delta H$ = Standard enthalpy change
T = Temperature
\[\Delta S\] = Standard entropy change

If \[\Delta G < 0\] the change is spontaneous
If \[\Delta G < 0\] ,the change is non spontaneous.

Note:
- If \[\Delta H = - ve\] and \[\Delta S = + ve\] the reaction is spontaneous in forward direction.
- If \[\Delta H = + ve\] and \[\Delta S = - ve\] the reaction is spontaneous in the reverse direction.
- If \[\Delta G < 0\], the reaction is spontaneous in the forward direction.
- If \[\Delta G > 0\] , the reaction is nonspontaneous in the forward direction
- If \[\Delta G = 0\], the system will be present in equilibrium state and this reaction does not prefer any direction i.e., either back ward or forward reaction.