Review of calculations involving thermodynamics:

Δ H, Δ G, K_eq

Δ H_reaction = ΔH^o _products – ΔH^o _reactants

From tabulated data for Δ H_f^o

(std heat of formation of the compounds)

Δ H_reaction = Σ n ΔH_f^o _products – Σ n ΔH_f^o _reactants

Free energy: Δ G

Δ G_reaction = Σ n ΔG_f^o _products – Σ n ΔG_f^o _reactants

so equilibrium constants can be calculated from tabulated ΔG_f^o values

ΔG^o = -RT ln K_eq

Entropy, S
S^o = n S^o _prod - n S^o_reactants

To find ΔG^o at other than standard temperature.

ΔG^o = ΔH^o – T ΔS
Some indication of what the magnitudes of K mean:

ΔG^o	Keq
+200 kJ/mol	9.1 x10^-36	No reaction
+50	1.7 x10^-9	Some reaction
+10	6.7 x10^-2	Calculation of concs is necessary
-10	5.6 x10^1
-50	5.8 x10^8	Little reactant left
-200	1.1 x10^35	Reaction goes to completion

Equilibrium:

N₂ + O₂ → 2NO

Keq =	[ NO ]^2
	[ N2 ] [ O2 ]

Equilibrium constants for gases can also be expressed in terms of partial pressures.

Kp =	p NO^2
	p N2 p O2

Kinetic Calculations

Rates of reactions – not related to equilibrium position.

Order	Rate law	Rate equation	Half life
0	Rate = k	[A]t = -kt + [A]o	[A]o / 2k
1	Rate = k [A]	ln [A]t = -kt + ln [A]o	0.693 / k
2	Rate = k [A]^2	1/ [A]t = kt + 1/[A]o	1/ k [A]o

Photochemical Reactions

Absorption: XY + hν → XY* giving an activated species which may then go on to react with other molecules

Decomposition: XY + hν → X + Y

Rates of photochemical reactions depend on the radiation, rather than chemical concentrations. Rate constants are designated f.

f = ∫ J_λ σ_λ φ_λ dλ

where the integral is over the wavelengths of the radiation (from λ₁ to λ₂)

q J is the radiative flux

q σ_λ is the absorption cross section of the molecules –the ability to absorb radiation of the various wavelengths

q φ_λ is the quantum yield (proportion of molecules which absorb actually react).

Other ways excited molecules can be deactivated

q XY* + M → XY + M + kinetic energy

q XY* + AB → XY + AB*

Also possible to have quantum efficiency > 1—when an activated molecule sets off a chain reaction.

Gas Calculations

Concentration units

ppm_V differs from ppm_m so best to use more descriptive terms, eg mg/kg, mixing ratio also called mole fraction

All gases contain same number of moles when at same temp and pressure (at least when they are acting as ideal gases)

So can use partial pressure as a substitution for moles/liter concentration for gases

Ideal gas law: PV = nRT

P = Pressure in atmospheres

V = Volume in liters

n = number of moles

R = gas constant 0.082 L atm/mol K

T = Temperature in Kelvin degrees