Thermodynamic processes :
IUPAC Sign convention about Heat and Work :
Work done on the system = Positive
Work done by the system = Negative
1st Law of Thermodynamics
ΔU = (U2 - U1) = q + w
Law of equipartion of energy :
(only for ideal gas)
where f= degrees of freedom for that gas. (Translational + Rotational)
f = 3 formonoatomic
= 5 for diatomic or linear polyatmic
= 6 for non - linear polyatmic
Calculation of heat (q):
Total heat capacity:
Molar heat capacity :
Specific heat capacity (s):
WORK DONE (w) :
Isothermal Reversible expansion/compression of an ideal gas :
W = - nRT In (Vf/Vi)
Reversible and irreversible isochoric processes.
Since dV = 0
So dW = - Pext . dV = 0.
Reversible isobaric process:
W = P (Vf - Vi)
Adiabatic reversible expansion :
Irreversible Work :
Free expansion - Always going to be irrerversible and since Pext = 0
so dW = -Pext..dV = 0
If no. heat is supplied q = 0
then ΔE = 0 so ΔT = 0.
Application of 1st Law :
ΔU = ΔQ + ΔW ⇒ ΔW = -P ΔV
∴ ΔU = ΔQ -PΔV
Constant volume process
Heat given at constant volume = change in internal energy
∴du = (dq)v
du = nCvdT
Constant pressure process:
H ≡ Enthalpy (state function and extensive property)
H = U + PV
⇒ Cp - Cv = R (only for ideal gas)
Second Law Of Thermodynamics :
fo r a spontaneous process.
Entropy calculation for an ideal gas undergoin a process :
(only for an ideal gas)
Third Law Of Thermodynamics :
The entropy of perfect crystals of all pure elements & compounds is zero at the absolute zero of temperature.
Gibb’s free energy (G) : (State function and an extensive property)
Criteria of spontaneity:
(i) If ΔGsystem is (-ve) < 0 ⇒ process is spontaneous
(ii) If ΔGsystem is > 0 ⇒ process is non spontaneous
(iii) lf ΔGsystem = 0 = 3 system is at equilibrium.
Physical interpretation of ΔG :
The maximum amount of non-expansional (compression) work which can be performed.
Standard Free Energy Change (ΔG°) :
1. ΔG° = -2.303 RTIog10K
2. At equilibrium ΔG = 0.
3. The decrease in free energy (-ΔG) is given as :
4. for elemental state = 0
Change in standard enthalpy
= heat added at constant pressure. = CPΔT.
If Hproducts > Hreactants
Temperature Dependence Of ΔH : (Kirchoff's equation):
For a constant volume reaction
where ΔCP = Cp (products) - Cp (reactants).
For a constant volume reaction
Enthalpy of Reaction from Enthalpies of Formation :
The enthalpy of reaction can be calculated by
is the stoichiometric coefficient.
Estimation of Enthalpy of a reaction from bond Enthalpies :
At equilibrium :
(i) Rate of forward reaction = rate of backward reaction
(ii) Concentration (mole/litre) of reactant and product becomes constant.
(iii) ΔG = 0.
(iv) Q = Keq
Equilibrium constant (K) :
Equilibrium constant in terms of concentration (Kc) :
Equilibrium constant in terms of partial pressure (Kp):
Equilibrium constant in terms of mole fraction (Kx) :
Relation between Kp & Kc :
Kp = Kc.(RT)Δn.
Relation between KP & KX :
KP = KX(P)Δn
ΔH = Enthalpy of reaction
Relation between equilibrium constant & standard free energy change :
ΔG° = - 2.303 RT log K
Reaction Quotient (Q):
The values of expression Q =
Degree of Dissociation (α):
α = no. of moles dissociated / initial no. of moles taken
= fraction of moles dissociated out of 1 mole.
Note: % dissociation = α x 100
Observed molecular weight and Observed Vapour Density of the mixture :
Observed molecular weight of An(g) =
External factor affecting equilibrium :
Le Chatelier's Principle: If a system at equilibrium is subjected to a disturbance or stress that changes any of the factors that determine the state of equilibrium, the system will react in such a way as to minimize the effect of the disturbance.
Effect of concentration:
Effect of volume:
Effect of pressure:
If pressure is increased at equilibrium then reaction will try to decrease the pressure, hence it will shift in the direction in which less no. of moles of gases are formed.
Effect of inert gas addition :
(i) Constant pressure: If inert gas is added then to maintain the pressure constant, volume is increased. Hence equilibrium will shift in the direction in which larger no. of moles of gas is formed
Δn > 0 reaction will shift in the forward direction
Δn < 0 reaction will shift in the backward direction
Δn = 0 reaction will not shift.
(ii) Constant volume: Inert gas addition has no effect at constant volume.
Effect of Temperature:
Equilibrium constant is only dependent upon the temperature.
If plot of lnk vs 1/T is plotted then it is a straight line with slope = and intercept =
Vapour Pressure of Liquid
Relative Humidity =
Thermodynamics of Equilibrium :
ΔG = ΔG°+ 2.303 RT log10Q
Vant Hoff equation-
OSTWALD DILUTION LAW:
Acidity and pH scale :
∴ pH = - log aH+ (where aH+ is the activity of H+ ions = molar concentration for dilute solution).
[Note : pH can also be negative or > 14]
PROPERTIES OF WATER :
pH Calculations of Different Types of Solutions :
SALT HYDROLYSIS :
Hydrolysis of ployvalent anions or cations
For [Na3PO4] = C.
Ka1 x Kh3 = Kw
Ka1 x Kh2 = Kw
Ka3 x Kh1 = Kw
Generally pH is calculated only using the first step Hydrolysis
Hydrolysis of Amphiprotic Anion. (Cation is not Hydrolysed e.g. NaHCO3, NaHS, etc.)
Similarly for amphiprotic anions.
BUFFER SOLUTION :
(a) Acidic Buffer: e.g. CH3COOH and CH3COONa. (weak acid and salt of its conjugate base).
(b) Basic Buffer: e.g. NH4OH + NH4CI. (weak base and salt of its conjugate acid).
Buffer capacity (index) :
Buffer capacity =
SIGNIFICANCE OF INDICATORS :
Extent of reaction of different bases with acid (HCI) using two indicators :
SOLUBILITY PRODUCT :
Ksp = (xs)x (ys)y = xx.yy.(s)x+y
CONDITION FOR PRECIPITATION :
If ionic product KI.P > Ksp precipitation occurs,
if KI.P = Ksp saturated solution (precipitation just begins or is just prevented).