Constants and conversions:
Avogadro’s number: 6.022∙1023/mole
Speed of light: c = 2.998∙108 m/s
Gas constant (in energy units): R = 8.314 J/(K∙mole) = 0.008314 kJ/(K∙mole)
Absolute T: T(K)=T(°C)+273.15
Faraday constant: F = 96,485C/mol
Water dissociation constant: Kw=1.00∙10-14
Standard energy unit: 1 Joule (J) = 1 kg∙m2/s2
1Å =10-10m = 10-8cm
760torr = 1atm
Concentration definitions:
Molality: (unit) m=(mol solute)/(kg solvent)
Molarity: (unit) M=(mol solute)/(Liter solution)
Mass % concentration = [(mass solute)/(mass solution)]∙100%
ppm = [(mass solute)/(mass solution)]∙106
Mole fraction A: XA = (moles A) / (total moles)
Henry’s Law: (Solubility of gas) = k ∙ (pressure)
Kinetics:
Definition of reaction rate: (concentration)/t (change in conc ∕change in time)
Concentration as function of t for 1st order reaction:
𝑙𝑛[𝐴] = 𝑙𝑛[𝐴]0 − 𝑘𝑡 or [𝐴] = [𝐴]0 𝑒 −𝑘𝑡
Relation between k and half-life (t1/2) for 1st order reaction: 𝑡1/2 =
0.693
𝑘
Thermodynamics and equilibrium:
Definition of reaction Gibbs energy in terms of reaction enthalpy and entropy:
Δ𝐺 = Δ𝐻 − 𝑇Δ𝑆
Reaction Gibbs energy in terms of standard reaction Gibbs energy:
Δ𝐺 = Δ𝐺 0 + 𝑅𝑇𝑙𝑛(𝑄);
Q is the reaction quotient.
Relation between standard reaction Gibbs energy and the equilibrium constant:
𝑜
Δ𝐺 0 = −𝑅𝑇𝑙𝑛(𝐾)
𝐾 = 𝑒 −Δ𝐺 ⁄𝑅𝑇
Acids and bases:
Definition of pH, pOH: pH = -log[H+], pOH = -log[OH-]; pH + pOH=14
Definition of pKa: pKa = -logKa
Acid dissociation constant: 𝐾𝑎 =
[𝐻 + ][𝐴− ]
[𝐻𝐴]
Aqueous base dissociation constant: 𝐾𝑏 =
or 𝐾𝑏 =
[𝐻𝐴][𝑂𝐻 − ]
[𝐴− ]
[𝐵𝐻 + ][𝑂𝐻 − ]
[𝐵]
in terms of conjugate acid HA.
Water dissociation constant: 𝐾𝑤 = [𝐻 + ][𝑂𝐻 − ]; at standard T, Kw=1.00∙10-14
Henderson-Hasselbach equation for buffers:
[𝐴− ]
𝑝𝐻 = 𝑝𝐾𝑎 + 𝑙𝑜𝑔
[𝐻𝐴]
Electrochemistry:
Galvanic (voltaic) cells
Reduction occurs at cathode
0
Cell emf from half-cell potentials: ℰ𝑐𝑒𝑙𝑙
= ℰ 0 (𝑐𝑎𝑡ℎ𝑜𝑑𝑒) − ℰ 0 (𝑎𝑛𝑜𝑑𝑒)
Gibbs energy change (= - work available) Δ𝐺 0 = −𝑛𝐹ℰ 0
Units: Joule(J) or kJ
n = moles electrons transferred
F = Faraday constant = 96, 485 C/mol
Equilibrium constant (K): 𝑙𝑛(𝐾) = −
Δ𝐺 0
𝑅𝑇
=
(charge of one mole of electrons)
𝑛𝐹ℰ 0
𝑅𝑇
R = gas constant in energy units = 8.3145 J/(K∙mol)
Nernst equation for non-standard conditions:
In terms of reaction quotient Q, and n = number of electrons transferred
𝑅𝑇
𝑙𝑛(𝑄)
𝑛𝐹
A useful form of Nernst equation for standard T (298 K):
ℇ𝑐𝑒𝑙𝑙 = ℇ0𝑐𝑒𝑙𝑙 −
ℇ𝑐𝑒𝑙𝑙 = ℇ0𝑐𝑒𝑙𝑙 −
0.05916𝑉
𝑙𝑜𝑔(𝑄)
𝑛
Electrolysis
Charge 𝒒 = 𝐼 ∙ 𝑡
Units: Coulomb(C) = Amp(A)∙sec(s)
Factor relating charge to moles electrons: 1 𝑚𝑜𝑙 𝑒 − ∼ 96,485 𝐶
Nuclear reactions
Nuclear decay (same as 1st order kinetics – see above)
N=number, concentration, mass, or any measure of amount of nuclear material
𝑙𝑛𝑁 = 𝑙𝑛𝑁0 − 𝑘𝑡
𝑡1/2 =
0.693
𝑘
𝑘=
0.693
𝑡1/2
Mass energy relation:
ΔE = Δm𝑐 2 where c = speed of light = 2.998∙108 m/s
Units: kg∙m2/s2 = Joule (J) - not kJ
Standard reduction potentials:
E0 (V)
+2.87
Half-Reaction
F2(g) + 2 e- -----> F-(aq)
H2O2(aq) + 2 H+(aq) + 2 e- -----> 2 H2O
PbO2(s) + 4 H
+
(aq)
+
SO42-(aq)
+1.77
-
+ 2 e -----> PbSO4(s) + 2 H2O
MnO4-(aq) + 8 H+(aq) + 5 e- -----> Mn2+(aq) + 4 H2O
3+
Au
-
+ 3 e -----> Au(s)
(aq)
+ 14 H
+
(aq)
+1.36
-
3+
+ 6 e -----> 2 Cr
(aq)
+ 7 H2O
O2(g) + 4 H+(aq) + 4 e- -----> 2 H2O
-
+1.51
+1.50
Cl2(g) + 2 e- -----> 2 Cl-(aq)
Cr2O72-(aq)
+1.70
-
+1.33
+1.23
Br2(l) + 2 e -----> 2 Br (aq)
+1.07
NO3-(aq)
+0.96
+4H
+
(aq)
-
+ 3 e -----> NO(g) + 2 H2O
Ag+(aq) + e- -----> Ag(s)
3+
Fe
-
2+
+ e -----> Fe
(aq)
(aq)
MnO4-(aq) + 2 H2O + 3 e- -----> MnO2(s) + 4 OH-(aq)
-
-
+0.80
+0.77
+0.59
I2(s) + 2 e -----> 2 I (aq)
+0.53
Cu2+(aq) + 2 e- -----> Cu(s)
+0.34
2+
Cu
+
2H
(aq)
(aq)
-
+ e -----> Cu
+
(aq)
-
+ 2 e -----> H2(g)
Pb2+(aq) + 2 e- -----> Pb(s)
Ni
2+
(aq)
-
+ 2 e -----> Ni(s)
PbSO4(s) + 2 e- -----> Pb(s) + SO42-(aq)
2+
Fe
-
+0.13
0.00
-0.13
-0.25
-0.31
+ 2 e -----> Fe(s)
-0.44
Cr3+(aq) + 3 e- -----> Cr(s)
-0.74
Zn2+(aq) + 2 e- -----> Zn(s)
-0.76
(aq)
-
-1.66
Mg2+(aq) + 2 e- -----> Mg(s)
-2.37
Al
3+
+
Na
(aq)
(aq)
+ 3 e -----> Al(s)
-
+ e -----> Na(s)
Ca2+(aq) + 2 e- -----> Ca(s)
+
K
Li
(aq)
+
(aq)
-2.71
-2.87
-
-2.93
-
-3.05
+ e -----> K(s)
+ e -----> Li(s)