Solution And Colligative Properties Formulas
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Cheat Sheet for Solution And Colligative Properties Formulas
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1. Molarity = \(\frac{\text { No. of moles of
solute }}{\text { Volume of solution (litre) }}\)
& Molarity = \(\frac{\text { No.of moles of solute }}{\text {
mass of solvent }(\mathrm{kg})}\)
m = \(\frac{1000 \mathrm{M}}{1000
\mathrm{d}-\mathrm{MM}_{\mathrm{B}}}\) & Molarity ∝
\(\frac{1}{\text { temp. }}\)
XA =
\(\frac{\mathbf{n}_{\mathbf{A}}}{\mathbf{n}_{\mathbf{A}}+\mathbf{n}_{\mathbf{B}}}\)
and XB =
\(\frac{\mathrm{n}_{\mathrm{B}}}{\mathrm{n}_{\mathrm{A}}+\mathrm{n}_{\mathrm{B}}}\)
Mole percent = mass fraction × 100
& Mass fraction of A =
\(\frac{\mathbf{W}_{\mathbf{A}}}{\mathbf{w}_{\mathbf{A}}+\mathbf{w}_{\mathbf{B}}}\)
ppm = \(\frac{\text { Mass of solute }}{\text { Mass of solution }}
\times 10^{6}\)
= \(\frac{\text { wt. of solute }}{\text { wt. of solute }+\text {
wt. of water }} \times 10^{6}\)
Normality = \(\frac{\text { gram equivalent of solute }}{\text {
Volume of solute (liters) }}\)
& N = \(\frac{\mathrm{W}_{\mathrm{B}} \times 1000}{\mathrm{E}
\times \mathrm{V}}\)
2. Raoult’s Law:
P = pA + pB = p0A XA
+ p0BXB
= (1 – XB)p0A + p0B XB
= (p0B – p0A)XB
+ p0A
\(\frac{P_{0}-P_{S}}{P_{0}}=\frac{n}{n+N}\)
& \(\frac{P_{0}-P_{S}}{P_{0}}=\frac{w \cdot M}{W \cdot m}\),
when n << N
3. Ideal Solutions:
ΔHmix = 0 & ΔVmix = 0
4. Non-Ideal solutions:
ΔHmix ≠ 0 & ΔVmix ≠ 0
5. Types of Non-Ideal Solutions:
(a) Non-ideal solutions showing positive deviations
pA > p0A XA, &
pB > p0BXB, &
PT > pA + pB
(b) Non-ideal solutions showing negative deviations:
pA < p0A XA, &
pB < p0BXB, &
PT < pA + pB
6. π = \(\frac{n}{V}\)RT = CRT
& \(\frac{p_{A}^{0}-p_{A}}{p_{A}^{0}}=X_{B}=\frac{n}{n+N}\)
& ΔTb = Kb × m
\(\frac{\mathrm{K}_{\mathrm{b}} \times \mathrm{W}_{\mathrm{B}}
\times 1000}{\mathrm{M}_{\mathrm{B}} \times
\mathrm{W}_{\mathrm{A}}}\)
ΔTf = Kf × m \(\frac{\mathrm{K}_{\mathrm{f}}
\times \mathrm{W}_{\mathrm{B}} \times 1000}{\mathrm{M}_{\mathrm{B}}
\times \mathrm{W}_{\mathrm{A}}}\)
& Kb = \(\frac{\mathrm{RT}_{\mathrm{b}}^{2}}{1000
\ell_{\mathrm{v}}}\)
& Kf = \(\frac{\mathrm{RT}_{\mathrm{f}}^{2}}{1000
\ell_{\mathrm{f}}}\)
Colligative properties ∝ Number of particles
∝ Number of molecules (in case of non electrolytes)
∝ Number of ions (In case of electrolytes)
∝ Number of moles of solute
∝ Mole fraction of solute
7. i = \(\frac{\text { Normal molar mass }}{\text { Observed
molar mass }}\)
= \(\frac{\text { Observed colligative property }}{\text { Normal
colligative property }}\)
i = \(\frac{\text { Observed osmotic pressure }}{\text { Normal
osmotic pressure }}\)
= \(\frac{\text { Actual number of particles }}{\text { No. of
particles for ionisation }}\)
degree of association
& degree of dissociation
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