MHCET Special Formula

1. Solid State

Density of Unit Cell:

$d = \frac{z \cdot M}{a^3 \cdot N_A}$

Edge Length ($a$) vs Atomic Radius ($r$):

• Simple Cubic (SCC): $a = 2r$
• Body-Centered Cubic (BCC): $a = \frac{4r}{\sqrt{3}}$
• Face-Centered Cubic (FCC): $a = \sqrt{8}r = 2\sqrt{2}r$

Packing Efficiency:

$\text{P.E.} = \frac{z \cdot \frac{4}{3}\pi r^3}{a^3} \times 100$

---

2. Solutions

Henry's Law:

$S = K_H \cdot P$

Relative Lowering of Vapor Pressure:

$\frac{P_1^\circ - P_1}{P_1^\circ} = x_2 = \frac{W_2 \cdot M_1}{M_2 \cdot W_1}$

Elevation of Boiling Point:

$\Delta T_b = K_b \cdot m = \frac{1000 \cdot K_b \cdot W_2}{M_2 \cdot W_1}$

Depression of Freezing Point:

$\Delta T_f = K_f \cdot m = \frac{1000 \cdot K_f \cdot W_2}{M_2 \cdot W_1}$

Osmotic Pressure ($\pi$):

$\pi = MRT = \frac{W_2 RT}{M_2 V}$

---

3. Ionic Equilibria

Ostwald’s Dilution Law:

$\alpha = \sqrt{\frac{K_a}{C}}$

pH and pOH Relation:

$pH + pOH = 14$

Henderson-Hasselbalch Equation:

Acidic Buffer: $pH = pK_a + \log_{10} \frac{[\text{Salt}]}{[\text{Acid}]}$

Basic Buffer: $pOH = pK_b + \log_{10} \frac{[\text{Salt}]}{[\text{Base}]}$

Solubility Product ($K_{sp}$):

$K_{sp} = x^x \cdot y^y \cdot S^{(x+y)}$

---

4. Chemical Thermodynamics

Pressure-Volume Work:

$W = -P_{ext} \Delta V$

Maximum Work ($W_{max}$):

$W_{max} = -2.303 nRT \log_{10} \frac{V_2}{V_1}$

Gibbs Free Energy:

$\Delta G = \Delta H - T \Delta S$

$\Delta G^\circ = -2.303 RT \log_{10} K$

---

5. Electrochemistry

Nernst Equation (at 298 K):

$E_{cell} = E^\circ_{cell} - \frac{0.0592}{n} \log_{10} Q$

Molar Conductivity ($\Lambda_m$):

$\Lambda_m = \frac{1000 \cdot \kappa}{C}$

Kohlrausch Law:

$\Lambda_0 = \nu_+ \lambda_+^\circ + \nu_- \lambda_-^\circ$

---

6. Chemical Kinetics

First Order Rate Constant ($k$):

$k = \frac{2.303}{t} \log_{10} \frac{[A]_0}{[A]_t}$

Half-life ($t_{1/2}$):

$t_{1/2} = \frac{0.693}{k}$

---

7. Green Chemistry (MHCET Special)

Atom Economy:

$\% \text{Atom Economy} = \frac{\text{Formula Weight of Desired Product}}{\sum \text{Formula Weight of all Reactants}} \times 100$