MCAT MCAT G-Chem Formula Formul a Sheet
Nuclear and Atomic Chemistry Avogadro' Avogadro' s number: number: N A
=
Electron Configurations e − quan quantu tum m numb number ers: s: n , l, m l , m s
6. 02 02 × 10 23
n
N A amu (u) = 1 gram 1 u = 1.66 × 10 mp Z
−24
= 1.0073 u,
=
g = 1.66 × 10
m n
= 1.0087
−27
[l = 0
kg
nuclear binding energy:
m l
=
l = 0,
K
↔ s , l = 1↔
+ Nm n ) −
mnu cleus
E B = ( ∆m ) × 9311 MeV u
1,
K,
n − 1
or
7 p
7s
6d
6 p
6s
5f
5d
5 p
5s
4f
4d
4 p
4s
3d
3 p
3s
2 p
2s
p ,
3 ↔ f ]
= − l, − ( l − 1), K , ( l − 1), l
m s = + 21
1 − 2
in subshell l, max # of electrons electrons = 4 l + 2
1 eV = 1.6 × 10 −19 J, 1 MeV = 10 6 eV E photon = hf
2,
l = 2 ↔d, l =
u
# proton protons, s, N = # neu neutro trons ns
mass defect: ∆m = (Zm Z mp
= 1,
in energy level n , max # of of electrons = 2n 2
hc λ 2
electron energy levels: E n = Z 2 ( −13.6 eV) n for any 1-electron (Bohr) atom
1s
Radioactive Decay
Stoichiometry / Lewis Structures
Z = = # protons = atomic number, N = = # neutrons, A = Z + + N = = mass number
mass in grams moles of solute ; molarity: M = MW L of solution mass of X × 100% % composition by mass of X = mass of molecule
Decay α β− β+ EC γ
De Description eject α = 42 He n → p + e− p → n + e+ p + e− → n X* → X + γ
∆Z ∆N −2 −2 +1 −1 −1 +1 −1 +1 0 0
∆A −4 0 0 0 0
Periodic Trends & Bonding Atom Atomic ic Radi Radius us e s e a s r c n i n
Ionization Energy e s e a s r c n i n
Acidity i n c r e a s e s
# moles =
formal charge: charge: FC = V − ( 21 B + L)
V = (# of vale valenc nce e e − ' s), s), B = ( # of bond bondin ing g e− 's), 's), − L = (# of lon lone-p e-pai airr e 's)
Molecular Geometry (VSEPR theory)
Elec Electr tron on Affi Affini nity ty e r e m o e a t i v n e g
# lone pairs on central atom
Electronegativity e s e a s n c r i n
Basicity i n c r e a s e s
electronegativity of some common atoms: F > O > (N ≈ Cl) > Br > (I ≈ S ≈ C) > H intermolecular forces (D = dipole, I = induced, i = instantaneous): ion–ion > ion–D > D–D (incl. H-bonds) > D–ID > iD–ID (London)
Geometric Family Linear Trigonal planar
Tetrahedral
Trigonal bipyramid Octahedral b C o o x n d s o t a n n o t s t o n r e e e d q u t a o t i b o e n m s n e i m a o s r h i z a e d d e . d
0
shape = geometry
1
shape =
Bent
Trigonal pyramid
See-saw
Square pyramid
2
shape =
Bent
T-sha -shape ped d
Squar quare e planar
U © n 2 a 0 u 0 t h 1 o b r y i z e T d h e r e P p r r o i n d c u e c t o t i n o n R p e r v o i h e i w b i ,I t e n d c . .
Gases STP: T = 0 °C = 273 K, P = 1 atm = 760 torr = 760 mmHg Avogadro’s law: V ∝ n Vat STP = n (22.4 L) Boyle’s law: V ∝ 1/ P (at constant T ) Charles’ law: V ∝ T (at constant P ) Combined: P 1V 1 / T1 = P 2V 2 / T2 Ideal-Gas law: PV = nRT Dalton’s law of partial pressures: P = Σ p i Graham’s law of effusion: rate of effusion of gas 2 m m 1 v 2,rms = v 1,rms m 1 ⇒ = m 2 2 rate of effusion of gas 1
Colligative Properties molality: m =
moles of solute kg of solvent
normality: N =
equivalents (eq) L of solution
BP elevation: ∆T b = k bim FP depression: ∆T f = – k fim moles of S mole fraction: X S = total moles o Raoult’s law: PA = XAP A o vapor pressure depression: ∆PA = −(1 − XA )P A osmotic pressure: Π = iMRT
Kinetics
∆[reactant] ∆[product] or + time time 1 ∆[reactant] 1 ∆[product] reaction rate = − or + coeff time coeff time rate law for rate-determining step: rate = k [ reactant1 ]coeff1 L concentration rate = −
Arrhenius equation: k = Ae − E a
RT
Equilibrium for generic balanced reaction a A + bB equilibrium constant: K eq
=
c C + d D,
[C]cat eq [D]d at eq b [A]aat eq [B]at eq
excluding pure solids and liquids
(gas rxns use partial pressures in K eq expression) K eq is a constant at a given temperature. K eq < 1 ⇔ equilibrium favors reactants K eq > 1 ⇔ equilibrium favors products reaction quotient: Q =
[C]c [D]d [A]a [B]b
Law of Mass Action (Le Châtelier's principle): Q Q Q
< K eq ⇔ = K eq ⇔ > K eq ⇔
rxn proceeds forward rxn at equilibrium rxn proceeds in reverse
Acids and Bases pH = –log [H+] = –log [H 3O+] pOH = –log [ – OH] K w = [H +][ – OH] = 1 × 10 –14 at 25 °C pH + pOH = 14 at 25 °C [H+ ][A − ] Ka = , pK a = − log K a [HA] [ − OH][HB + ] , pK b = − log K b [B] K aK b = K w = ion-product constant for water Kb =
Henderson–Hasselbalch equations: pH = pK a + log
[conjugate base] [weak acid]
pOH = pK b + log
[weak acid]
= pK a − log [conjugate base]
[conjugate acid] [weak base]
[weak base]
= pK b − log [conjugate acid]
acid–base neutralization: N aV a = N bV b
Thermochemistry T (in K) = T °C + 273, 1 cal ≈ 4.2 J, q = heat q = mc ∆T = C ∆T (if no phase change) q = n ∆H phase change (∆T = 0 during phase change) enthalpy change: ∆H = heat of rxn at const P ∆H < 0 ⇔ exothermic, ∆H > 0 ⇔ endothermic standard state: one most stable at 25 °C, 1 atm o o o ∆H rxn = ∑ n∆H f,products − ∑ n∆H f,reactants Laws of Thermodynamics (E = energy, S = entropy): 1) E universe is constant. ∆E system = q + W . 2) Spontaneous rxn ⇒ ∆S universe > 0 3) S = 0 for pure crystal at T = 0 K Gibbs Free Energy: ∆G = ∆H – T ∆S [const. T ] ∆G < 0 ⇔ spontaneous ∆G = 0 ⇔ at equilibrium ∆G > 0 ⇔ reverse rxn is spontaneous ∆G o ≈ – RT ln K ≈ –2.3RT log K ≈
kJ (–5.7 mol ) log K
Redox and Electrochemistry Rules for determining oxidation state ( OS ):* 1) sum of OS ’s = 0 in neutral molecule; sum of OS ’s = charge on ion 2) Group 1 metals: OS = +1; Group 2 metals: OS = +2 3) OS of F = –1 4) OS of H = +1 5) OS of O = –2 6) OS of halogens = –1; OS of O family = –2 If one rule contradicts another, rule higher in list takes precedence. [*These rules work 99% of the time.] F = faraday ≈ 96,500 C/mol e – ∆G = – nFE cell E cell > 0 ⇔ spontaneous E cell < 0 ⇔ reverse rxn is spontaneous 0.06 Nernst equation: E ≈ E o − logQ n Faraday’s Law of Electrolysis: The amount of chemical change is proportional to the amount of electricity that flows through the cell.