Solution and colligative properties

Number of moles, $n = W/M$ mol

Molarity = $n/V$ mol $dm^{-3}$ (or M)

Normality = ${\text"gram eq."}/{V}$ gram eq. $dm^{-3}$ (or N)

Molality = $n/{\text"Wt. of solvent in kg"}$ mol $kg^{-1}$ (or m)

Raoult’s law: $P_{soln} = x_{1} P_o$

${P_{o} – P}/{P_o} = {W_{2} M_{1}}/{W_{1} M_{2}}$

$ΔT_b = K_b m$ and $Δ T_f = K_f m$

$ΔT_b = K_b * {1000 W_2}/{W_1 M_2}$

$ΔT_f = K_f * {1000 W_2}/{W_1 M_2}$

At constant temperature: ${π_2}/{π_1} = {C_2}/{C_1}$
At constant concentration: ${π_2}/{π_1} = {T_2}/{T_1}$

van’t Hoff equation:

1. π = CRT
2. π = $n/V$ RT
3. π = ${WRT}/{MV}$

van’t Hoff factor:
i = ${ΔT_{b(ob)}}/{ΔT_{b(th)}} = {ΔT_{f(ob)}}/{ΔT_{f(th)}} = {π_{ob}}/{π_{th}} = {M_{th}}/{M_{ob}}$

α = ${1}/{(n-1)} [{M_{th} – M_{ob}}/{M_{th}}]$ (For dissociation) ($M_{ob}$ < $M_{th}$)

α = $({n}/{n-1}) [{M_{ob} – M_{th}}/{M_{ob}}]$ (For dissociation) ($M_{ob}$ > $M_{th}$)

α = ${i – 1}/{n-1}$ (For dissociation)

α = $({n}/{n-1}) (1-i)$ (For association)

S = K x P

$K_b = {C α^2}/{1-α}$