Energetics and Equilibria Flashcards
Boltzmann distribution
As energy of a level increases its population decreases
As temperature is raised, molecules move to higher energy levels
Classical view of entropy equation
dS in terms of dq and T
If system absorbs heat, dq will be positive (endo) - dS will be positive implying S increases
dS inversely related to temperature
First Law of Thermodynamics
Energy cannot be created or destroyed but is just transformed from one form into another
Internal energy - analogous to potential energy in mechanical systems - ‘stored up’ energy
+ve - done to system
q - heat absorbed by system
w - work done by system
w’ = -w
(w’ is reverse of work done on system)
State functions and path functions
State function: value depends only on state of substance under consideration; same value for a given state (U)
Path function: value which depends on path which system takes going from A to B (q and w)
Ideal gas equation
pV = nRT
Work done by gas expansion (equation) - dw’
Force which system moves against is that due to the external pressure
dw = -dw’
(dw - work done on the gas)
Expansion against constant external pressure (equation) - w’
Assumes that internal pressure is always greater than external pressure (remember that as the gas expands the internal pressure will fall)
If external pressure exceeds the internal pressure, gas will be compressed: Vf < Vi so w’ -ve
When is work done a maximum
Work done in a reversible process is a maximum
Reversible processes:
- infinitely slow
- at equilibrium
- do maximum work
- one whose direction can be changed by an infinitesimal change in some variable
Irreversible processes (spontaneous):
- go at finite rate
- not at equilibrium
- do less than the max work
Reversible isothermal expansion of an ideal gas (equation and derivation)
For an isothermal expansion of an ideal gas
dU = ?
dU = 0
First Law:
0 = q - w’
w’ = q
Entropy change in an isothermal expansion of an ideal gas (equation)
S - state function
Expression for dS is valid for any isothermal expansion of an ideal gas from Vi to Vf, whether or not the expansion is carried out reversibly
Differential forms of First Law with pV (equation)
Constant volume processes with dU
Heat capacities with heat supplied and temperature rise (equation)
Both c and Cm
Internal energy (U) linked to specific heat capacity (C) - equation
For process taking place at constant volume, heat is equal to change in internal energy
dU = q(const. vol)
Definition of enthalpy (equation)
H = U + pV
H - state function
Constant pressure linking enthalpy and heat (equation)
Heat capacity at constant pressure linking enthalpy and temperature (equation)
Variation of enthalpy with temperature (equation and derivation)
Can only measure changes in enthalpy rather than the absolute values of enthalpies of substances
Variation of entropy with temperature (equation and derivation)
Gibbs energy (equation)
G = H - TS
First Master Equation for dU
Second Master Equation for dG (equation and derivation)
Variation of Gibbs energy with pressure at constant temperature for an ideal gas (equation and derivation)
Variation of Gibbs energy with temperature at constant pressure - Gibbs-Helmholtz equation and derivation
Gibbs energy of the components of a mixture of ideal gases - variation with partial pressures (equation)
Gibbs energy of mixture is the sum of nG
Chemical potential of a gas (equation)
Chemical potential of a solution (equation)
Chemical potential of a solid or a liquid
Chemical potential is equal to standard chemical potential
Variation of drH with temperature (equation and derivation)
Variation of drS with temperature (equation and derivation)
Equilibrium constants for partial pressure and concentrations (equations)
Condition for chemical equilibrium in terms of chemical potentials (equation)
dG -ve: reaction proceeds from left to right (spontaneous)
dG +ve: reaction proceeds from right to left
dG = 0: equilibrium
Relation between dG and equilibrium constant (equation and derivation)
Interpretation of dG = -RT ln K
- dG -ve: K > 1 - products are favoured
- dG +ve: K < 1 (but still positive) - reactants favoured
Le Chatelier’s principle
When a system in equilibrium is subjected to a change, the composition of the equilibrium mixture will alter in such a way as to counteract the change
Van’t Hoff Equation (derivation) and explain relation between K and temperature
- dH +ve (endo): dlnK/dT +ve
K increases with T
From Van’t Hoff Equation, how lnK varies with temperature (derivation)
Variation of equilibrium with pressure (looking at partial pressures and degree of dissociation)
Pressure is increased, degree of dissociation falls
increasing pressure moves equilibrium towards the reactants
Cell conventions
- LHS and RHS half cell
- each half cell is written as a reduction (e- on LHS)
- Conventional cell reaction is RHS - LHS
- Cell potential is that of the RHS measured relative to the LHS
dG in terms of E (equation)
dS(cell) in terms of E (equation and derivation)
Chemical potentials in terms of activities (equation)
As concentration tends of 0, activity can be approximated by the concentration divided by standard concentration
Nernst equation (derivation)
Nernst equation for half cells (equation)
Link between half cell potential and oxidising or reducing ability
- the greater the half cell potential, the more strongly oxidising Aox becomes
- the smaller the half cell potential, the more strongly reducing Ared becomes
