Equations

Electric Potential Energy

PE_E = (kq)/r

pH Formula

pH = -log[H⁺]

Rydberg Formula

1/λ = R_H (1/n_i² - 1/n_f²); ΔE = R_H(1/n_i² - 1/n_f²)

Photon Energy

E = hf = hc/v

Z_eff =

Z (atomic number) - S (shielding electrons)

Formal Charge =

VE - Bonds - LPE

Limiting Reagent =

Moles Reactant x 1mol/mass x Mol Product/Mol reactant

Percent Yield

(Actual/Theoretical) x 100

Theoretical Yield

Same calculation as limiting reagent but x molar mass of product

K_eq (Equilibrium Constant) =

K_forward/K_reverse = [Product 1]^x…/[Reactant 1]^x…

Q (Reaction Quotient) =

Same as K_eq (Products over Reactants)

Kelvin =

Celsius + 273

ΔU (Internal Energy) =

Q - W

q (heat transfer) =

mcΔT

ΔH (Enthalpy) =

ΔU + PΔV = (Q - PΔV) + PΔV = Q

Work (thermal) =

PΔV

Work (physics) =

Fdcosθ (=0 when no movement)

ΔH^o_rxn =

ΔH^o_products - ΔH^o_reactants (kg/mol)

ΔH (Bond Dissociated Energy) =

ΔH_{bonds broken} - ΔH_{bonds formed}

ΔS^o_reaction =

ΔS^o_products - ΔS^o_reactants (J/K*mol)

ΔG (Gibbs Free Energy) =

ΔH - TΔS (J/mol)

ΔG_rxn = (Nonstandard conditions)

ΔG^o_rxn (-RTlnK_eq) + RTlnQ

ΔG^o_rxn = (Standard Conditions)

-RTlnK_eq

lnA = b →

Ae^b (e = 2.7 = 3)

log_ab = c →

a^c = b

ln1 =

0

q_f and q_v (Heats of Fusion/Vaporization) =

nΔH (kJ/mol); n = number of moles; use for phase changes

q = mL

Variation of q = nΔH where L = latent heat of fusion

Celsius → Fahrenheit

9/5C^o + 32 (2C^o +32)

Boyle’s Law (at constant temperature and moles):

P₁V₁ = P₂V₂; PV = constant

Charle’s Law (at constant pressure and moles):

V₁/T₁ = V₂/T₂ (V/T = constant)

Gay-Lussac’s Law (Constant Volume and moles):

P₁/T₁ = P₂/T₂ (P/T = constant)

Ideal Gas Law

PV = nRT

Van der Waal’s Equation (low priority)

nRT = (P + an²/V²)(V - nb)

a = attractive force

b = volume occupied by a mole of gas

X_gas (Mole Fraction of Gas) =

n_gas/n_total

Derived X_gas =

P_gas/P_total

P_gas (Partial Pressure) =

X_gasP_total

P_total =

ΣP_partial = P_{gas 1} + P_{gas 2}…

Molarity (M) =

mol solute/Liter solution (mol/L)

Molality (m) =

mol solute/kg solven (mol/kg)

Supersaturated Solution

When heating, more solute can be dissolved in solvent and upon cooling, the solute will remain dissolved

Crystallization

Crystal formation in supersaturated solution (solute precipitates out)

ppm (parts/million)

mg/L

ppt (parts/thousand)

g/L

Raoult’s Law (Vapor Pressure Reduction):

P = X_AP_A^o

P = reduced vapor pressure

X_A = mole fraction of solvent

P_A^o = pure vapor pressure

Boiling Point Elevation

ΔT_b = iK_bm

ΔT_b = how much the BP increases

i = ionization factor

Freezing Point Depression

ΔT_f = iK_fm

ΔT_f = how much the freezing point decreases

i = ionization factor

Ionization (van ‘t Hoff) Factor

How many ions are in the solute (NaCl i = 2, C₆H₁₂O₆ i = 0)

Π (Osmotic Pressure) =

iMRT

i = van ‘t Hoff

M = Molarity (mol/L)

R = .08206

K_sp (Solubility Product Constant) =

[x]^x[x]^x (Do not include solids/solvent); x are usually ions, whatever dissociated

Arrhenius Equation: (low priority)

k = Ae^-E_a/RT

A = frequency factor

Rate =

-1/aΔ[Reactant]/Δt = -1/bΔ[Reactant] = 1/cΔ[Product]… (M/s)

Rate/Rate law =

k[A]^x[B]^y (reactants only; do not include solid or liquid)

Rate Constant (k) =

Rate/[A]^x[B]^y

Order of Reaction

Sum of exponents in the rate law

Order of Reaction Unit Determination (for k)

1/M = k(M)^x

K_w =

[H₃O⁺][OH^-]/[H₂O]; K_a x K_b

K_a =

[H₃O⁺][A^-]/[HA]

K_b =

[HB⁺][OH^-]/[B]

pH =

-log[H₃O⁺]

pOH =

-log[OH^-]

pOH + pH =

14

pK_a =

-log(K_a)

pK_b =

-log(K_b)

ICE Table

Used for finding pH of weak acids/bases

I - Initial concentration

C - Change in concentration

E - Equilibrium Concentration

Henderson-Hasselbalch Equation (pH of buffer solution)

pH = pK_a + log[A^-]/[HA]

Amount of acid/base needed to neutralize acid/base:

aM_aV_a = bM_bV_b

Isoelectric Point =

1. Average of highest two pK_a for basic AA

2. Average of lowest two pK_a for acidic AA

E^o_cell =

E^o_cathode - E^o_anode (Reduced - Oxidized)

Moles of metal = (electroplating)

I*t/nF (F = 1 × 10⁵ C/mol)

Redox Titration Equation

n₁M₁V₁ = n₂M₂V₂

n = number of electrons transferred

Maximum # of stereoisomers =

2ⁿ, n = number of stereocenters

[a] (specific rotation) =

a/cl

Enantiomeric Excess % =

[a]_observed/[a]_pure

Must add up to 100% but can’t be 50% unless racemic

100 = x + (x - %)

Wavelength =

v/f (speed/frequency)

R_f (TLC Plate) =

Distance traveled by sample/Distance traveled by solvent

Distance =

v * t (m/s *s)

4 Major Kinematics Equations:

1. Δx = v_avgt = ½(v_i + v_f)t

2. v_f = v_i + at (Δv = at)

3. Δx = v_it + ½at²

4. v_f² = v_i² + 2aΔx

g_{perpendicular} =

gcosθ

g_parallel =

gsinθ

F_g =

mg (N)

f_k =

u_kF_N

f_s =

u_sF_N

Center of Mass (x_center) =

(x₁m₁ + x₂m_2….)/(m₁ + m₂)

F_{gravitational} =

(Gm₁m₂)/r²

Hooke’s Law

F_spring = -kx

k = spring constant (N*m)

x = length compressed/stretched

τ (torque) =

Fdsin(θ) (N*m)

d = distance between fulcrum and applied force

Work =

Fdcosθ (J = kg*m/s²)

Mechanical advantage =

Length incline/height incline

Power =

Work/Δt = ∆KE/t (Watt = J/s) = F*v sometimes

KE =

½mv² (J)

PE_grav =

mgΔh (J)

Conservation of Energy

ΣE_final = ΣE_initial

KE_i + PE_i = KE_f + PE_f

PE_k =

½kx² (J)

Work-Energy Theorem

W = ∆KE = KE_f - KE_i

Work in Terms of Pressure and Volume =

P∆V = PA∆x

v_rms =

sqrt(3RT/molar mass)

KE_{ideal gas} =

½mv_rms = ½m(3RT/MM)

∆L =

a_LL∆T

∆V =

a_vV∆T