[Kit4hk]

My textbook said,
''If the change of free energy is >0, the reaction occurs spontaneous''

However, I disagree with this statement because we don't know if the size of this free energy can oversome the activation energy that needs to process the reaction. Moreover, is there any scientific evidence that show ''entropy'' is exist?

[Yggdrasil]

For a reaction to be thermodynamically spontaneous and kinetically spontaneous is two different things.  If delta(G) < 0, then the reaction is thermodynamically spontaneous (i.e. it can occur as written without coupling to other reactions).  However, this does not mean that the reaction will occur quickly.  The conversion from diamond to graphite is thermodynamically spontaneous because graphite is the most stable form of carbon.  However, the reaction is not kinetically spontaneous because the activation energy is much larger than the thermal energy available at room temperature.

As for how can we show that entropy exists, consider this question:  why can we dissolve some salts in water and have the temperature of the water decrease?  But a better way to look at entropy is as the most likely (probable) outcome.  For example, consider a box full of quarters.  At first, all the quarters are facing heads up.  However, you shake the box.  Do you expect a low entropy (ordered) or high entropy (disordered) state when you look in the box after shaking it?  You expect to see about half of the quarters head up and the other half to be tails down, corresponding to an increase in entropy.  This is an example of entropy at work.

[Borek]

Moreover, is there any scientific evidence that show ''entropy'' is exist?

London bombing. TATP explosion is enthropy driven.