SN2 Equations

Chemistry of solutions equations (SN2)

Properties of Solutions

Concentrations

The solute (called A):
is the compound dissolved in the solvent.
The solvent:
is the compound dissolving the solute A
The solution:
is the combination of both A and the solvent.

molarity (M) =	mole of solute	= mol/L
	liter of solution

normality (N) =	equivalent of solute	= Eq/L (mostly used for acid-base or redox reaction)
	liter of solution

Normality could be ambiguous. The equivalence unit (Eq) depends both on the reactant and the type of reaction present.
If H₂SO₄ is used in an acid-base reaction (neutralization); then 1 mole of H₂SO₄ = 2 equivalents of H⁺. Therefore, 1 M H₂SO₄ = 2 N H⁺ (correctly, it should be written H₃O⁺).
However, if H₂SO₄ is used in a precipitation reaction with Ba²⁺ then 1 mol H₂SO₄ reacts with 1 mol Ba²⁺ then 1 M H₂SO₄ = 1 N H₂SO₄
IUPAC and NIST discourage the use of normality.

molality (m) =	mole of solute	= mol/kg
	kg of solvent

mass percent (A%) =	mass of A	x 100% = %
	total mass of solution

mole fraction (χ_A) =	mole of A	no unit.
	total mole of the solution

%dissociation =	mole of solute ionized	x 100% = %
	mole of formula unit added

Gases

Dalton's law of partial pressure

P_total = P_A + P_B + P_C + ... + P_n

χ_A(gas phase) =	P_A
	P_Tot

Colligative properties

Boiling point elevation

ΔT_b = K_b⋅m_solute (for an electrolyte: ΔT_b = i K_b⋅m_solute)

Freezing point depression

ΔT_f = K_f⋅m_solute (for an electrolyte: ΔT_f = i K_f⋅m_solute)

van't Hoff factor

i =	mole of particle in solution	no unit.
	mole of formula unit added

Equilibrium

Equilibrium constant

For the equilibrium: aA + bB ⇌ cC + dD

K =	[C]^c [D]^d
	[A]^a [B]^b

note: K = K_c (based on molarity)

Reaction quotient (Q)

Q =	[C]_o^c [D]_o^d
	[A]_o^a [B]_o^b

note: [ ]_o = initial concentration (not at equilibrium)

Relation between K_c and K_p

K_p: pressures in atmosphere
Δn: difference between n_{gas product} - n_{gas reactant}
R: 0.08206 L.atm.K^-1mol^-1

K_p = K_c(RT)^Δn

Acid-base and pH

acid strength

% dissociation =	number of mole dissociated at equilibrium	x 100%
	number of mole initially added

pH measurement

pH = -log[H⁺] , [H⁺] = 10^-pH

pOH = -log[OH^-] , [OH^-] = 10^-pOH

pH + pOH = 14.00 at 25°C

K_w = [H⁺][OH^-] = 1.0x10^-14 at 25°C

Henderson - Hasselbach equation

pH = pK_a + log (	[A^-]	) for the conjugate system HA ⇌ H⁺ + A^-
	[HA]

Solubility

solubility product

MX₃(s) ⇌ M³⁺(aq) + 3X⁺(aq) then K_sp = [M³⁺] [X⁺]³

Kinetic

Rate of a reaction

Consider the reaction: aA → bB

Rate =	change of concentration
	change in time

=	-Δ[A]
	a Δtime

=	+Δ[B]	= M/s
	b Δtime

Rate law

k: rate constant (variable units)
n , m: order of the reactant
n + m = overall order of the reaction

Rate = k [A]ⁿ single reactant.

Rate = k [A]ⁿ [B]^m ... multiple reactants.

Integrated rate law

Order

zero

one

two

Rate law

Rate = k

Rate = k[A]

Rate = k[A]²

Integrated rate law

[A] = [A]_o - kt

Ln[A] = Ln[A]_o - kt

	1	=
	[A]

	1	+ kt
	[A]_o

Plot axes to get a line

[A] vs. t

Ln[A] vs. t

	1	vs. t
	[A]

Rate constant units

M.s^-1

s^-1

M^-1.s^-1

Half-life (t_1/2)

t_1/2 =	[A]_o
	2k

t_1/2 =	Ln 2
	k

t_1/2 =	1
	k[A]_o

Arrhenius equation

A = frequency factor (M.s^-1)
R = 8.314 J.K^-1.mol^-1
T = temperature in Kelvin
E_a = activation energy (J.mol^-1)

k = A e ^-Ea/RT

Arrhenius equation (linearized form)

Lnk = LnA -	E_a	×
	R

	1	The plot Lnk of 1/T should give a straight line with a slope of -E_a/R.
	T

Arrhenius equation (for two temperatures)

Ln	k₂	=
	k₁

	-E_a
	R

(	1
	T₂

-	1	)
	T₁

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