Hmm can u explain it in your OWN words cuz I feel this is really complicating -.-
The need for input of energy symbolizes the fact that the reaction is
kinetically stable; meaning that the reaction must have some sort of energy input before it can proceed, otherwise, the reactants cannot reach the
activation energy threshold.
This is how the quote 'Methane does NOT burn Unless Lit.' is related to kinetic stability, i.e activation energy is required and provided by the source of energy when we light it up.
Thermodynamics is either (1) the energy released during a reaction, in which case ^G will be negative and the reaction exothermic, or (2) the energy consumed during a reaction, in which case ^G will be positive and the reaction endothermic.
Since we found that ^H
f is negative, it implies that energy is released and the reaction is exothermic.
Now we come to the difference between kinetic and thermodynamic stabilities.A reaction is said to be kinetically stable when it requires a large activation energy. In this case we've been told that reaction does not occur unless we light it up, meaning that the reaction is kinetically stable.
Something that is thermodynamically stable will not need an input of energy to be converted from reactants to products, because its most stable and preferred state is that of being composed of products. Instead, a thermodynamically-stable reaction will require energy to be converted from products back to reactants.
It's almost as if a kinetically-stable reaction is stubborn and does not want to be converted into products-- it's too lazy. You have to induce it to become products by giving it kinetic energy, which MOVES the reaction forward (kinetics = movement). The same is for thermodynamically-stable reactions, except you'd be inducing the reaction to go back into reactants from a state of products.