It would be great if someone could explain why entropy is a driving force for a reaction in simple terms as my online research has come to no avail
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entropy is the distribution of energy across a system
No, that is not correct. Entropy has nothing to do with energy.
Entropy is an abstract quantity S defined for equilibrium states. The law of entropy (2nd law of thermodynamics) says that
In an isolated system, the entropy cannot decrease.
Usually when some processes go on, like chemical reaction, the entropy is not even defined. However, when you compare the entropy ##S_1## at the beginning and entropy ##S_2## at the end, when the system is again in equilibrium, if the system was isolated during the whole time then ##S_2 \geq S_1##.
However, for the case of chemical reaction, the system is presumably not isolated because usually the beginning and the end of the chemical reaction occur at the same temperature and the same pressure. The restoration of the original temperature can occur because the reacting mixture is in thermal contact with the surroundings.
In such case the entropy law does not apply for the system, since the mixture ##m## is not isolated. The entropy of the mixture can decrease.
However, the entropy law does apply again if we include the surroundings (laboratory) to the system. Quantities ##S_1##, ##S_2## then refer to entropy of such large system.
However, working with such entropies of the enlarged system is not practicable, as we do not know entropy of room etc. For this reason the entropy law is reformulated using Gibbs energy G = U - TS + PV (here S and other quantities are those of the mixture only).
The idea is as follows:
From the law of entropy, the heat absorbed by the mixture
$$
\Delta Q \geq T\Delta S,
$$
since the process is most probably not reversible.
Since ##\Delta U = \Delta Q - P\Delta V##, we obtain the equation
$$
\Delta U + p\Delta V - T\Delta S \leq 0.
$$
This is the same as
$$
\Delta (U - TS + PV) \leq 0,
$$
because the temperature and pressure do not change - they are given by the atmosphere. The quantity in the brackets is the Gibbs energy ##G##.
So, the entropy law leads to another law:
In a process which has the same T and P at the beginning and at the end, the Gibbs energy cannot increase.
If the reaction is spontaneous, G will decrease. Now from the above formula you can see that if final state has greater entropy, G decreases. Also, if the final state has lower volume, G decreases.
If the reaction occurs, ##\Delta G## is negative.
If ##\Delta G < 0## because the enthalpy ## U + PV## decreased enough, we say the reaction is driven enthalpically - it is an exothermic reaction; the system gives off heat (e.g. hydrogen + oxygen => boom + water + heat).
If ##\Delta G < 0## because of increase in entropy, one says the reaction is driven entropically; the system can also absorb some heat. For example, dissolving salt in some alcohol solutions makes them cool down. As it gets to the original temperature, it receives heat and in the end its entropy increases.
