Equations for General Chemistry

The following is a list of equations which you should know (have memorized) and be able to explain/manipulate.  The equations with yellow highlight are for second semester Gen. Chem.

Equation Meaning
F = m


Force = mass x acceleration (m/s/s or m/s2).  If a net force is acting on a particle, it will accelerate.  If the net force on a particle is zero, the particle will not accelerate.  Rather it will stay at the same velocity. If it were initially at rest, it will stay at rest.
Fgrav = km1m2/r2   Gravitational force - force of attraction acting between 2 bodies separated by distance r between their centers and of mass m1 and m2 - is inversely proportional to r2
Felectro = kQ1Q2/r2   Electrostatic force (Couloumb's Law) - force of attraction or repulsion acting between 2 charged bodies separated by distance r between their centers and of charge  Q1 and Q2 - is inversely proportional to r2
E = -F(r );   Eelect = -kQ1Q2/r

Force = -ΔE/ΔR (or -ΔE/Δx)  so ΔE = -FΔx
or F = - slope  (minus sign since F goes in opposite direction of increasing potential.

Epot = mgh  Potential energy = mass x acceleration due to gravity (9.8 m./s2) x height
Ekin mv2  Kinetic energy =   x  mass  x velocity2
p = mv  Momentum of particle (p) = mass x velocity
Would you rather be hit by a mosquito or an elephant, each with a
velocity of 1 m/s?
W = -Fext Δ Work  (units of energy) = - force X distance moved
(Fext = friction, the opposing force), work done on rectangle
c = λυ   speed of light (c) = wavelength (λ)  x frequency (υ)
                     m/s                     m    x      1/s                
E = hυ = hc/λ Energy of a photon = Planck constant (h) x frequency (υ) =  h x speed of light(c) divided by wavelength (λ)
p = h/λ    momentum of particle = Planck constant (h) /wavelength
(picture of DeBroglie)
ΔpΔx > h/4π =hbar/2   Heisenberg Uncertainty Principle: uncertainty in momentum x uncertainty in position is greater than or equal to Planck constant/4 π.
q = mcΔT    heat change (J) = mass m x specific heat (J/(goC) x tej change in temperature
ΔH = Σ(nΔHbond enthalpy react. - Σ(nΔHBH prod) change in enthalpy for a written reaction = sum of n x the bond enthalpy of the reactants (energy required to break a bond)  -  sum of n x the bond enthalpy of the reactants
ΔHo = Σ(nΔHoform prod) - Σ(nΔHoform react) standard enthalpy for a written reaction = the sum of n x the standard enthalpy of formation of the products - the sum of n x the standard enthalpy of formation of the reactants (n values are the stoichiometry coefficients from the balanced equation)

standard enthalpy of formation (kJ)  = enthalpy change for the formation of one mole of a substances from the pure elements in the standard state

ΔEsys = E2 - E1 = q + w 
First Law of Thermodynamics: the change in internal energy E of a system is equal to the heat transferred to or from the system plus work done on or by the system.
ΔEsys = E2 - E1 = q + w = q -PextΔV 
First Law of Thermodynamics if only PV work (expansion/contraction of gas) :
ΔEtot = ΔEsys +  ΔEsurr = 0 = ΔEuniv


First Law of Thermodynamics for system and surrounding (= universe)
ΔEsys = E2 - E1 =  qv -PextΔV = qv Change in internal energy at constant V where qv is heat transferred at constant V
ΔEsys = E2 - E1 =  qp -PextΔV Change in internal energy at constant P when only PV work

ΔHsys = qp + PextΔV;  Hsys = qp + PV

constant P and V, ΔHsys = qp


enthalpy and change in enthalpy for a system at constant P
PV=nRT  Ideal Gas Law Ideal gas law where P is pressure, V is volume, n is number of moles, T is temperature in K, and R is the ideal gas constants.  Use the correct units (dimensional analysis)
8.315 J/(K. mol)   = 0.08206 L . Mol/ K.mol)

Note:  all gases at the same P, V, and T have same number of moles, n.

E avg kin/mol = (3/2)RT Gives the meaning of T. 
at given T, gas with higher molar mass has a lower velocity.
DSsurr = -DHsys/T
DStot  =  DSsys  +  DSsurr  >  0  or

DStot  =  DSsys  -  DHsys/T   >  0

Second Law of Thermodynamics, for a spontaneous process
DGsys = DHsys -  TDSsys  = - TDStot    
DSo sys = SnS0prod - SnSoreact   
ΔGo = Σ(nΔGoform prod) - Σ(nΔGoform react)  
Keq = (C)c(D)d]/[(A)a(B)b] for reaction: aA  +  bB    cC  +  dD,  Keq is the equilibrium constant for the reaction where (A), (B), etc are the equilibrium concentrations of reactant A, ...., and a, b, .... are the stoichiometric coefficients in the balanced equation
DGrx=DG0rx  +  RT ln {[(C)c(D)d]/[(A)a(B)b]

        = DG0rx  +  RT ln Q

for reaction: aA  +  bB    cC  +  dD    where (A), (B), etc are the actual concentrations of reactant A, etc at a given time and Q is the reaction quotient
DG0rx  = -  RT ln Keq = -2.303RTlogKeq

DG0rx  = DGrx when all reactants/products in std state

Relationship btw DG0rx  and Keq
Ka = [H3O+][A-]/[HA]

For the reaction of an acid (HA)and water to form the hydronium ion and the conjugate base of the acid (A-):

HA(aq)  +  H2O(l)  ↔  H3O+  +  A-     

Ka is the  acid dissociation constant = equilibrium constant assuming water is a constant.

pH = - log [H3O+];  pKa = - log Ka [H3O+] high, pH low; Ka high, pKa low
pH = pKa + log [A-]/[HA]

Henderson-Hasselbach equation

Ka = [H3O+][A-]/[HA]

log Ka = log [H3O+] + log [A-] - log [HA]

-log Ka = -log [H3O+] - log [A-] + log [HA]

pKa = pH - log [A-]/[HA]

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

Gives pH as function of pKa, and concentrations of weak acid and its conjugate base; Useful in buffer calculations

Keq = (C)c(D)d]/[(A)a(B)b]

Ka = [H3O+][A-]/[HA]

a.   Kw = [H3O+][OH-] = 10-14

b.   Kb = [OH-][BH+]/[B]

      KaKb = Kw = 10-14

c.   Ksp  = [cation]m[anion]n


Lots of equilibrium type expressions for the following reactions:

a.  H20 (l)  +  H20 (l)  ↔   H3O+(aq)  +  OH-(aq)  - for autoionization of water

b.  B (base)  +  H2O(l)  ↔  OH- (aq)  +  BH+(aq) -   for reaction of a base in water.  

c.   salt (s)  ↔ m [cation]  +  n [anion]  where m and n are stoichiometric coefficients.

C = i t C = charge in Coulombs =  current i (amps, A = 1 C/s) x time (seconds)

Note:  1.60218 x 10-19 C/e- or 96,465 C/mol = 1 Faraday

Eocell =  Eocathode - Eoanode 

          = Eocathode + (- Eoanode )

The standard reduction potential of a cell (consisting of two half cells) is the standard reduction potential of the reaction that occurs at the cathode (reduction) + the negative of the standard reduction potential of the reaction that occurs at the anode (oxidation).  The negative sign is required since the standard reduction potential at the anode (where oxidation occurs) is written for the reaction as a reduction, not an oxidation.

Eocell is +, then rx proceeds as written; if - then rx proceeds in opposite direction.

welect = qV

welect = nFE

electrical work available (J) = charge q (C)  x Voltage (V or J/C)

electrical work available  (J) = number of mol e- in each 1/2 rx times the Farady constant (C/mol)  times the cell potential (J/C) .  This will give the welect available for the stoichiometric number of mol of reactants.  Ex:
Zn(s) + HgO(s) → ZnO(s) + Hg(l) for Hg cell, n =2 but welect calculated will be per 1 mol of Zn(s)

welect (J/mol reactant) = nFE = -ΔGrx 

nFEo = -ΔG0rx   OR = ΔG0rx  = -nFEo

ΔG0rx  = -nFEo gives relationship btw Eo and ΔG0rx.  If Eo + (when oxidation at anode produces e which flow to cathode in spontaneous process, ΔG0rx. < 0
ΔGrx   = DG0rx  +  RT ln Q

-nFE = -nFEo + RT lnQ or

E = Eo - (RT/nF)  ln Q  OR

E = Eo - (2.303RT/nF)  log Q  or

E = Eo - (0.0591/n)  log Q  (at 25oC)

E = Eo - (RT/nF)  lnQ is Nernst Equation gives relationship between standard cell potential (under standard state condition), and the actual cell potential under nonstandard state concentrations of reactants and products.
Eo = (2.303RT/nF)  log Keq  or

log Keq = nFEo/2.303RT or nEo/0.0591 (25oC)

At Equilbrium ΔGrx  =0, E =0,
v = k[A] = - ΔA/ΔT = + ΔP/ΔT For 1st order reaction A P, k is 1st order rate constant, units s-1 
A = Aoe-kt

k = 0.693/t

For 1st order reaction A P, Ao is the initial [A]

t is the half life of the reaction (time for half reactants to react)

v = k[A]2 For 2nd order rx:  A +  A  P, k is 2nd order rate constant, units  M-1s-1
v = - kf[A] + kr[P]

At equilibrium vf = vr or Keq = [P]eq/[A]eq = kf/kr

For reversible rx:  A ↔ P, where kf is the 1st order forward rate constant, kr is the 2nd order reverse rate constant
v = k [A]x[B]y For the general reaction aA  + bB  → cC  +  dD,

where x and y are the stoichimetric coefficients for the particular step in a reaction mechanism

v = - (1/a) ΔA/ΔT = - (1/b) ΔB/ΔT = (1/c) ΔC/ΔT = 
(1/d) ΔD/ΔT
For the general reaction aA  + bB  → cC  +  dD,