# Entropy & spontaneity

A spontaneous reaction is a reaction that, given the necessary activation energy (${E}_{\text{a}}$), proceeds without continuous outside assistance (e.g., the reaction between sodium and water). A non-spontaneous reaction requires energy to be continually supplied to it (e.g., the decomposition of water).

Entropy ($S$) is a measure of randomness or disorder. One analogy for this is a deck of cards: when they are stacked in a pile, there is only a certain number of ways they can be arranged. When the cards are thrown into the air, entropy increases greatly because there is nearly infinitely more ways that they can be arranged when they land. You can see this visually because they appear much more chaotic and disorganized when they land compared to when they were stacked neatly.

We can determine the entropy change associated with a reaction using standard entropy, which is defined as the entropy of one mole of a substance at SATP, measured in joules per mole kelvin (J/mol⋅K). The equation is very similar to Hess’s law type 2:

$ΔS=∑nSproducts−∑nSreactants.$

These physical changes increase entropy:

• increase in volume (of a gaseous system)
• increase in temperature
• state change from solid to liquid, liquid to gas, or solid to gas

These chemical changes also increase entropy:

• fewer moles of reactants molecules, more moles of product molecules
• complex molecules break down into simpler ones
• solid/liquid reactants become liquid/gaseous products

Enthalpy change and entropy change together determine whether a reaction is spontaneous:

• $\mathrm{\Delta }H<0,\mathrm{\Delta }S>0\phantom{\rule{0.2778em}{0ex}}⟹\phantom{\rule{0.2778em}{0ex}}$ spontaneous
• $\mathrm{\Delta }H>0,\mathrm{\Delta }S<0\phantom{\rule{0.2778em}{0ex}}⟹\phantom{\rule{0.2778em}{0ex}}$ non-spontaneous
• same sign $\phantom{\rule{0.2778em}{0ex}}⟹\phantom{\rule{0.2778em}{0ex}}$ depends on temperature