Day 17

the signs of ∆Suniverse

all spontaneous processes produce an increase in the entropy of the universe ∆Suniverse > 0, spontaneous in forward direction ∆Suniverse < 0, spontaneous in reverse direction ∆Suniverse = 0, equilibrium this law allows us to predict the direction of spontaneity or will a reaction proceed in the forward or reverse direction

measuring spontaneity in water

at 1 atm when T > 0°C, ice melts when T < 0°, water freezes ∆Ssystem is positive as positional entropy for the phase change ∆Ssurroudnings determined primarily by the flow of energy into or out of the system as heat ∆Hfusion of water is positive ∆Ssurroundings is negative components are in opposition and the sign is determined by temperature magnitude of ∆Ssurroundings depends on the temperature at which the heat is transferred

∆Suniverse in H2O (s) to H2O (l)

at lower temperatures (< 0°C), ∆Suniverse is negative as (∆Hsystem/T) > ∆Ssystem and the process is non-spontaneous at higher temperatures (> 0°C), ∆Suniverse is positive as (∆Hsystem/T) < ∆Ssystem and the process is spontaneous at 0°C, ∆Ssystem is zero as (∆Hsystem/T) = ∆Ssystem and the system is at equilibrium melting and solidification occurs at equal rates both entropy and enthalpy must be taken into account to determine spontaneity

proof of the ∆S equation 2

changes in entropy when a system changes from an initial state to a final state can be calculated for N molecules, W1 and W2 are related to the volumes V1 and V2 kBNA = R

∆Suniverse and enthalpy

qsurr = -qsystem qsystem = ∆H in constant-pressure conditions

natural world and entropy

smaller S → larger S ordered to disordered less probable to more probable

standard free energy, ∆G°

standard free energy of reaction (∆G°rxn) is the free energy change for a reaction when it occurs under standard state conditions, when reactants in their standard states are changed to products in their standard states the standard free energy of formation (∆G°f) is the free energy change that occurs when 1 mole of the compound is formed from its elements in their standard states

proof of the ∆S equation

thermodynamic definition of entropy (S) heat is absorbed by an ideal gas in an isothermal, reversible expansion ∆U = q + w = 0

exothermity favors (but not guarantees) spontaneity

∆Suniverse = (-∆Hsystem/T) + ∆Ssystem if ∆Hsystem is negative, higher chance for ∆Suniverse to be positive

ideal gas assumption

1. gas particles have point mass (no volume) 2. no intermolecular forces only temperature changes the internal energy

Gibbs free energy, G

* ∆G = ∆H - T∆S < for spontaneity

proof of the ∆S equation 1

consider a reversible isothermal expansion work (ie. constant T, change in P & V carried in a reversible path) in ideal gases, constant temperature means ∆U = 0 the recess can be seen as taking place in a series of small steps at each step, the external pressure is adjusted to match the internal pressure at each stage of the expansion the total work when the system expands from V1 to V2 is the sum (integral) of all the nfinitesimal changes between the limits V1 and V2

criteria for spontaneity: the second law of thermodynamics

driving force of spontaneous change is the tendency of matter and energy to disperse chaotically smaller S → larger S need to take into account the entropy changes of the system and surroundings for non-isolated systems to find total ∆S (ie. ∆Suniverse) the criterion for spontaneous change is ∆Suniverse = ∆Ssystem + ∆Ssurroundings > 0 all spontaneous processes produce an increase in the entropy of the universe