DAT General Chemistry Equations

Dilutions

M1V1 = M2V2

Percent Error

(actual-theoretical)/theoretical x 100

Absorbance (Spectrophotometer)

Absorbance = εcl

ε = molar absorptivity

c = concentration

l = path length

Energy of a Photon

Ephoton = hf = hc/λ

h = Planck's constant = 6.63e-34 J*s

c = speed of light

Absorption/ Emission Line Spectra

ΔE = Ephoton

Kinetic Energy of an electron

(photoelectric effect)

KEe- = Ephoton - φ

φ = work function = minimum energy needed to ionize electron

Molarity

M = moles solute/liters solution

Molality

m = moles solute/kg solvent

Henry's Law

PA = kH*[A]

PA = partial pressure of gas A

kH = Henry's law constant

[A] = concentration of gas A

Freezing Point Depression

ΔTf = -i*Kf*m

i = van't Hoff

Kf = F.P. constant

m = molality

Boiling Point Elevation

ΔTb = i*Kb*m

i = van't Hoff

Kb = B.P. constant

m = molality

Vapor Pressure Depression aka Raoult's Law

Psoln = χsolv*Psolv°

Psoln = VP of solution

χsolv = mole fraction of solvent

Psolv° = VP of solvent

Osmotic Pressure (π)

π = iMRT

R = .0821 L*atm/mol*K

T = temp in Kelvin

Pressure

P = F/A

F = Force

A = Area

Average Kinetic Energy

KEavg = 3/2 RT

R= 8.314 J/mol*K

T = Kelvin

Root-Mean-Square Speed (v)

v = √(3RT/Mm)

R = 8.314 J/mol*K

Mm = molar mass

Ideal Gas Law

PV = nRT

R = .0821 L*atm/mol*K

Boyle's Law

Volume is inversely proportional to Pressure

Charles' Law

Volume is directly proportional to Temperature

Avogadro's Law

Volume is directly proportional to # of Moles

Combined Gas Law

P1V1/n1T1 = P2V2/n2T2

STP

1 atm

T = 273 K

1 mole of gas = 22.4 at STP

Standard Conditions

all aq species at 1M

all gas species at 1atm

T = 298K

Density

Density = P*Mm/RT = m/v

Dalton's Law of Partial Pressures

Ptotal = Pa + Pb + ...

AND

Pa = χa*Ptotal

χa = mole frac. of gas A

Graham's Law of Effusion

r1/r2 = √(Mm2/Mm1)

r = rate of effusion

Mm = molar mass

Real Gas Equation

(P + an^2/v^2)(V-nb) = nRT

+an^2/v^2 corrects for intramolecular forces

-nb corrects for volume

a and b are constants diff for each gas

General Rate Law

A + B -> C + D

rate = k[A]^m[B]^n

m and n are experimentally determined

k = rate constant

0 order rate constant units

k = M^1*s^-1

1st order rate constant units

k = s^-1

2nd order rate constant units

k = M^-1 * s^-1

3rd order rate constant units

k = M^-2 * s^-1

Arrhenius Equation

Ae^(-Ea/RT)

A = unique for each rxn

Ea = energy of activation

R = 8.314 J/mol*K

T = temp in Kelvin

Equilibrium Constant Expressions

Kc = [products]/[reactants]

Keq = k(forward)/k(reverse)

Kp = P(products)/P(reactants)

Reaction Quotient

Q = [products]/[reactants]

Q>K = shift left

Q

Q=K = equilibrium

Solubility Product Constant (Ksp)

Ksp = [products]/[reactants]

Ionization of water constant

Kw = [H3O+]*[OH-] = 1e-14 (at 298 K)

Kw = Ka * Kb = 1e-14

Weak Acids

HA + H2O ⇌ H3O+ + A-

Ka = [H30+][A-]/[HA]

[H+] = √(Ka*[HA])

Weak Bases

A- + H2O ⇌ HA + OH-

Kb = [HA][OH-]/[A-]

[OH-] = √Kb[A-]

Neutralization Reaction

naMaVa = nbMbVb

na = moles H+

nb = moles OH-

Buffers

pH = pKa + log([A-]/[HA])

[A-]= conc. base

[HA] conc. acid

Nuclear Reactions Kinetics

ALWAYS 1st order

N = N°*e^-kt

final= initial*e^-kt

lnN = lnN° - kt

ln(final) = ln(inital) - kt

t(1/2) = 0.693/k

t(1/2) for Nuclear Reaction Kinetics

t(1/2) = .693/k

Nuclear Binding Energy

E = Δmc^2

m must be in kg

Enthalpy of Formation

ΣnΔH°f(product) - ΣnΔH°f(reactant)

n = coefficient from balanced reaction

First Law of Thermodynamics

ΔE = q + w

ΔE = change in internal energy

q = heat

w = work

Pressure-Volume Work Equation

w = -PΔV

P = external Pressure

Calorimetry Thermal Energy (q)

q = -Ccalorimeter*ΔT

Ccalorimeter = specific heat of calorimeter

Heat Curves and Thermal Energy (q)

q = mcΔT

q = mcΔH(fusion)

q = mcΔH(vaporization)

m = mass

c = specific heat

Entropy

ΔS = ΣnS(products) - ΣnS(reactants)

n = coefficient in balanced equation

Sgas > Sliquid > Ssolid

Saq>Ssolid

Bond Dissociation Energy

ΔH = ΣΔHbroken - ΣΔHformed

ΔH = ΣΔHreactants - ΣΔHproducts

making bonds is exothermic aka -ΔH

breaking bonds is endothermic aka +ΔH

Gibbs Free Energy

ΔG° = ΔH° + TΔS°

ΔG = ΔG° + RTlnQ

ΔG° = -RTlnKeq

R = 8.314 J/mol*K

Q = reaction quotient

Standard Cell Potential

E° = E°reduction + E°oxidation

E° = E°cathode + E°anode

Nernst Equation

Ecell = E° - (.0592/n)logQ

n= # electrons transferred

Ecell = nonstandard cell potential

Faraday's Law

mass of product = (I*ts*MWpdt)/(n*F)

moles of product = (I*ts)/(n*F)

I = Current in amps

ts = time in seconds

n = # electrons transferred

F = faraday's constant = 96485 coulombs/mol e-