CHEMCA
EXAM MASTER FORMULA SHEET
States of Matter (Gaseous & Liquid State)
Essential Revision for JEE Main, Advanced & NEET
\(0.0821 \text{ L atm/K mol}\)
\(8.314 \text{ J/K mol}\)
\(1.987 \approx 2 \text{ cal/K mol}\)
\(8.314 \text{ Pa m}^3\text{/K mol}\)
1. Ideal Gas Laws
Boyle's Law (\(T, n\) const):
\(P_1V_1 = P_2V_2\)
Charles's Law (\(P, n\) const):
\(\frac{V_1}{T_1} = \frac{V_2}{T_2}\)
Ideal Gas Equation:
\[ PV = nRT \implies PV = \frac{w}{M}RT \implies PM = dRT \]
\(d\) = Density of gas
2. Dalton's & Graham's Law
Dalton's Law of Partial Pressure:
\[ P_{total} = p_1 + p_2 + p_3 + \dots \]
\(p_i = \chi_i \times P_{total}\) (Partial pressure = Mole fraction \(\times\) Total pressure)
Graham's Law of Effusion/Diffusion:
\[ \frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}} = \sqrt{\frac{d_2}{d_1}} = \frac{V_1/t_1}{V_2/t_2} \]
Rate (\(r\)) is inversely proportional to square root of molar mass.
3. Kinetic Theory of Gases (KTG)
RMS Speed (\(u_{rms}\))
\[ \sqrt{\frac{3RT}{M}} \]
Average Speed (\(u_{av}\))
\[ \sqrt{\frac{8RT}{\pi M}} \]
Most Probable Speed (\(u_{mp}\))
\[ \sqrt{\frac{2RT}{M}} \]
Ratio: \(u_{mp} : u_{av} : u_{rms} = 1 : 1.128 : 1.224\)
Kinetic Energy (\(K.E.\)):
\[ K.E. = \frac{3}{2}nRT \text{ (Total)} \quad | \quad K.E. = \frac{3}{2}kT \text{ (Per molecule)} \]
\(k\) = Boltzmann constant (\(R/N_A\))
4. Real Gases & Liquefaction
van der Waals Equation:
\[ \left( P + \frac{an^2}{V^2} \right) (V - nb) = nRT \]
\(a\) = Intermolecular attraction | \(b\) = Excluded volume (Co-volume)
Compressibility Factor (\(Z\)):
\[ Z = \frac{PV}{nRT} = \frac{V_{real}}{V_{ideal}} \]
\(Z=1\) (Ideal)
\(Z<1\) (\(-ve\) dev)
\(Z>1\) (\(+ve\) dev)
Boyle's Temp (\(T_b\)):
\[ T_b = \frac{a}{Rb} \]
Critical Constants:
Critical Temp (\(T_c\))
\[ \frac{8a}{27Rb} \]Critical Pressure (\(P_c\))
\[ \frac{a}{27b^2} \]Critical Volume (\(V_c\))
\[ 3b \]5. Liquid State Properties
Surface Tension (\(\gamma\))
Force per unit length acting perpendicular to the line drawn on the surface. Unit: \(N/m\) or \(J/m^2\).
Viscosity Coefficient (\(\eta\))
Defined by Newton's equation: \( F = \eta A \frac{dv}{dx} \). Unit: Poise or \(Pa \cdot s\).
Note: Both Surface Tension and Viscosity decrease with an increase in Temperature.
No comments:
Post a Comment