# 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 = $$\frac{\text { Observed osmotic pressure }}{\text { Normal osmotic pressure }}$$
= $$\frac{\text { Actual number of particles }}{\text { No. of particles for ionisation }}$$
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