Mathematical Formulas in Chapters 14, 15, & 16

Ch. 14 Formulas

100

Average Rate

∆[concentration]/∆time 

200

Rate Law

Rate= k[reactant]ⁿ

Rate= k[A]ⁿ x [B]^m

300

Integrated Rate Law

ln[A]_t - ln[A]₀=-kt

or can be written as 

ln([A]_t/[A]₀)=-kt

400

Integrated Rate Law (zero-order reaction)

[A]_t=-kt + [A]₀

Ch. 14 Formulas

100

Integrated Rate Law (first-order reaction)

ln[A]_t=-kt + ln[A]₀

200

Integrated Rate Law (second-order reaction)

1/[A]_t=kt + 1/[A]₀

300

Half-life expression (zero-order reaction)

t_1/2=[A]₀/2k

400

Half-life expression (first-order reaction)

t_1/2=ln2/k

or 0.693/k

Ch. 14 Formulas

100

Half-life expression (second-order reaction)

t_1/2=k/[A]₀

200

Arrhenius Equation

k=-Ae(-Ea/RT)

300

Arrhenius Equation to find Ea from a graph

ln k=-Ea/R (1/T) + lnA

400

Arrhenius Equation to find Ea non-graphically

ln(k₁/k₂)=Ea/R (1/T₂-1/T₁)

Ch. 15 Formulas

100

Equilibrium Constant (Kc)

for the reaction aA +bB= cC +dD

Kc=[C]^c x [D]^d/ [A]^a x [B]^b

200

Kp (partial pressure)

*2 formulas

Kp=(P_C)^ceqm x (P_D)^deqm/ (P_A)^aeqm x (P_B)^beqm

Kp=Kc(RT)^∆n

300

Initial Change Equilibrium

I + C=E

(initial + change= equilibrium)

400

At equilibrium

Kp=Kc when total moles of products and reactants is the same

Ch. 16 Formulas

100

pH

pH= -log[H⁺]

200

pOH

pOH=-log[OH^-]

300

pKw

pKw= -logKw

400

At 25^°C 

pKw=-logKw