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 = ma

Force = mass x acceleration (m/s/s or m/s^{2}). 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. 
F_{grav} = km_{1}m_{2}/r^{2 }  Gravitational force  force of attraction acting between 2 bodies separated by distance r between their centers and of mass m_{1} and m_{2}  is inversely proportional to r^{2} 
F_{electro} = kQ_{1}Q_{2}/r^{2} ^{ }  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 Q_{1} and Q_{2}  is inversely proportional to r^{2}. 
E = F(r ); E_{elect} = kQ_{1}Q_{2}/r 
Force = ΔE/ΔR
(or ΔE/Δx) so
ΔE = FΔx 
E_{pot }= mgh  Potential energy = mass x acceleration due to gravity (9.8 m./s^{2}) x height 
E_{kin }= � mv^{2}  Kinetic energy = � x mass x velocity^{2} 
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 = F_{ext} Δx  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 =h_{bar}/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/(g^{o}C) x tej change in temperature 
ΔH = Σ(nΔH_{bond enthalpy react.}  Σ(nΔH_{BH 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 
ΔH^{o} = Σ(nΔH^{o}_{form prod})  Σ(nΔH^{o}_{form 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 
ΔE_{sys} = E_{2}  E_{1}
= 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. 
ΔE_{sys} = E_{2}  E_{1}
= q + w = q P_{ext}ΔV

First Law of Thermodynamics if only PV work (expansion/contraction of gas) : 
ΔE_{tot} =
ΔE_{sys} + ΔE_{s}_{urr}
= 0 = ΔE_{univ}

First Law of Thermodynamics for system and surrounding (= universe) 
ΔE_{sys} = E_{2}  E_{1} = q_{v} PextΔV = q_{v}  Change in internal energy at constant V where q_{v }is heat transferred at constant V 
ΔE_{sys} = E_{2}  E_{1} = q_{p} PextΔV  Change in internal energy at constant P when only PV work 
ΔH_{sys} = q_{p} + P_{ext}ΔV; H_{sys} = q_{p} + PV constant P and V, ΔH_{sys} = q_{p }

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


DS^{o} sys = SnS^{0}prod  SnS^{o}react  
ΔG^{o} = Σ(nΔG^{o}_{form prod})  Σ(nΔG^{o}_{form react})  
K_{eq} = (C)^{c}(D)^{d}]/[(A)^{a}(B)^{b}]  for reaction: aA + bB ↔ cC + dD, K_{eq} 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 
DG_{rx}=DG^{0}rx
+
RT ln {[(C)^{c}(D)^{d}]/[(A)^{a}(B)^{b}]
= DG^{0}rx + 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

DG^{0}rx
= 
RT ln K_{eq} = 2.303RTlogK_{eq} DG^{0}rx = DG_{rx} when all reactants/products in std state 
Relationship btw DG^{0}rx and K_{eq} 
K_{a} = [H_{3}O^{+}][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) + H_{2}O(l) ↔ H_{3}O^{+} + A^{} K_{a} is the acid dissociation constant = equilibrium constant assuming water is a constant. 
pH =  log [H_{3}O^{+}]; pK_{a} =  log K_{a}  [H_{3}O^{+}] high, pH low; Ka high, pKa low 
pH = pKa + log [A^{}]/[HA] 
K_{a} = [H_{3}O^{+}][A^{}]/[HA] log Ka = log [H_{3}O^{+}] + log [A^{}]  log [HA] log Ka = log [H_{3}O^{+}]  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 
K_{eq} = (C)^{c}(D)^{d}]/[(A)^{a}(B)^{b}] K_{a} = [H_{3}O^{+}][A^{}]/[HA] a. K_{w = }[H_{3}O^{+}][OH^{}] = 10^{14} b. K_{b} = [OH^{}][BH+]/[B] K_{a}K_{b} = K_{w} = 10^{14} c. K_{sp } = [cation]^{m}[anion]^{n}

Lots of equilibrium type expressions for the following reactions: a. H_{2}0 (l) + H_{2}0 (l) ↔ H_{3}O^{+}(aq) + OH^{}(aq)  for autoionization of water b. B (base) + H_{2}O(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 
E^{o}_{cell} = E^{o}_{cathode}  E^{o}_{anode}
= E^{o}_{cathode} + ( E^{o}_{anode} ) 
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. E^{o}_{cell} is +, then rx proceeds as written; if  then rx proceeds in opposite direction. 
w_{elect} = qV w_{elect }= 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 w_{elect} available for the
stoichiometric number of mol of reactants. Ex: 
w_{elect }(J/mol reactant) = nFE = ΔG_{rx
}
nFE^{o} = ΔG^{0}rx_{ }OR = ΔG^{0}_{rx } = nFE^{o} 
ΔG^{0}_{rx } = nFE^{o} gives relationship btw E^{o} and ΔG^{0}_{rx}. If E^{o} + (when oxidation at anode produces e which flow to cathode in spontaneous process, ΔG^{0}_{rx}. < 0 
ΔG_{rx }= DG^{0}rx
+
RT ln Q nFE = nFE^{o} + RT lnQ or E = E^{o}  (RT/nF) ln Q OR E = E^{o}  (2.303RT/nF) log Q or E = E^{o}  (0.0591/n) log Q (at 25^{o}C) 
E = E^{o}  (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. 
E^{o} = (2.303RT/nF) log Keq or log Keq = nFE^{o}/2.303RT or nE^{o}/0.0591 (25^{o}C) 
At Equilbrium ΔG_{rx }=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 = A_{o}e^{kt} k = 0.693/t _{�} 
For 1st order reaction A → P, A_{o}
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^{1}s^{1} 
v =  k_{f}[A] + k_{r}[P] At equilibrium v_{f} = v_{r} or K_{eq} = [P]_{eq}/[A]_{eq} = k_{f}/k_{r} 
For reversible rx: A ↔ P, where k_{f} is the 1st order forward rate constant, k_{r} 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, 