WBJEE Physical Chemistry Syllabus

Give the value of the universal gas constant $R$ in SI and in $\text{L atm}$ units.

$R = 8.314\ \text{J K}^{-1}\text{mol}^{-1} = 0.0821\ \text{L atm K}^{-1}\text{mol}^{-1}$.

State Dalton's law of partial pressures.

The total pressure of a non-reacting gas mixture equals the sum of partial pressures: $P_{total} = P_1 + P_2 + P_3 + \cdots$. Also $P_i = x_i P_{total}$, where $x_i$ is mole fraction.

Write the expression for the root-mean-square speed of gas molecules.

$u_{rms} = \sqrt{\dfrac{3RT}{M}}$, where $M$ is molar mass. It is proportional to $\sqrt{T}$ and inversely to $\sqrt{M}$.

Order the three molecular speeds (most probable, average, rms) by magnitude with their ratio.

$u_{mp} < u_{avg} < u_{rms}$, in the ratio $\sqrt{2} : \sqrt{\dfrac{8}{\pi}} : \sqrt{3} \approx 1 : 1.128 : 1.224$.

State the postulate of kinetic theory regarding the average kinetic energy of gas molecules.

The average kinetic energy per molecule is directly proportional to absolute temperature: $\bar{KE} = \dfrac{3}{2}k_B T$ per molecule, independent of the gas's identity.

Write the van der Waals equation for $n$ moles of a real gas.

$\left(P + \dfrac{an^{2}}{V^{2}}\right)(V - nb) = nRT$, where $a$ corrects for intermolecular attraction and $b$ for molecular volume.

What is the compressibility factor $Z$, and what does its value indicate?

$Z = \dfrac{PV}{nRT}$. $Z=1$: ideal; $Z<1$: attractive forces dominate (more compressible); $Z>1$: repulsion/finite volume dominates (less compressible).

Define critical temperature ($T_c$).

The temperature above which a gas cannot be liquefied by applying pressure alone, no matter how high. Each gas has a characteristic $T_c$.

Express critical constants $T_c$, $P_c$, $V_c$ in terms of van der Waals constants $a$ and $b$.

$V_c = 3b$, $\quad P_c = \dfrac{a}{27b^{2}}$, $\quad T_c = \dfrac{8a}{27Rb}$.

What is the Boyle temperature?

The temperature at which a real gas obeys Boyle's law (behaves ideally) over an appreciable pressure range, where $Z=1$ and $\left(\dfrac{\partial Z}{\partial P}\right)_T = 0$. $T_B = \dfrac{a}{Rb}$.

Name the four common types of unit cells in the cubic system and the number of atoms per cell in each.

Simple/primitive cubic: $1$ atom; body-centered cubic (BCC): $2$ atoms; face-centered cubic (FCC): $4$ atoms.

Give the relationship between edge length $a$ and atomic radius $r$ for FCC, BCC, and simple cubic.

Simple cubic: $a = 2r$; FCC: $a = 2\sqrt{2}\,r$ (i.e. $r=\tfrac{a}{2\sqrt2}$); BCC: $\sqrt{3}\,a = 4r$ (i.e. $r=\tfrac{\sqrt3 a}{4}$).

State the packing efficiencies of simple cubic, BCC, FCC, and HCP lattices.

Simple cubic: $52.4\%$; BCC: $68\%$; FCC and HCP: $74\%$ (close packing).

What are the coordination numbers for simple cubic, BCC, and FCC structures?

Simple cubic: $6$; BCC: $8$; FCC (and HCP): $12$.

Write the formula relating density of a unit cell to its parameters.

$\rho = \dfrac{Z \cdot M}{a^{3} \cdot N_A}$, where $Z$ = atoms per unit cell, $M$ = molar mass, $a$ = edge length, $N_A$ = Avogadro's number.

Compare Schottky and Frenkel defects.

Schottky: equal numbers of cations and anions missing (vacancy pairs) — density decreases; common in ionic solids with similar ion sizes (e.g. $\ce{NaCl}$). Frenkel: an ion (usually smaller cation) displaced to an interstitial site — density unchanged; e.g. $\ce{AgBr}$, $\ce{ZnS}$.

What are F-centres and how do they arise?

F-centres are anion vacancies occupied by trapped electrons (from metal excess defect). They impart colour to crystals, e.g. excess Na gives $\ce{NaCl}$ a yellow colour.

Distinguish n-type and p-type semiconductors by doping.

n-type: Group 14 doped with Group 15 (e.g. P) gives extra electrons as carriers. p-type: doped with Group 13 (e.g. B) creates electron holes as positive carriers.

Give the formula for molarity and molality.

Molarity $M = \dfrac{\text{moles of solute}}{\text{volume of solution (L)}}$; Molality $m = \dfrac{\text{moles of solute}}{\text{mass of solvent (kg)}}$. Molality is temperature-independent.

Define mole fraction of a component in a binary solution.

$x_A = \dfrac{n_A}{n_A + n_B}$, where $n_A$ and $n_B$ are moles of the components. Note $x_A + x_B = 1$.

State Raoult's law for a solution of a non-volatile solute.

The vapour pressure of the solvent over the solution equals its mole fraction times the pure solvent's vapour pressure: $P = x_{solvent}\, P^{\circ}$. Equivalently, relative lowering $\dfrac{P^{\circ}-P}{P^{\circ}} = x_{solute}$.

What is an ideal solution, and what are its enthalpy and volume changes of mixing?

A solution obeying Raoult's law over all compositions, with $\Delta H_{mix} = 0$ and $\Delta V_{mix} = 0$; solute–solvent interactions equal solute–solute and solvent–solvent interactions.

List the four colligative properties.

Relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure. They depend on the number of solute particles, not their nature.

Write the equations for boiling point elevation and freezing point depression.

$\Delta T_b = K_b \cdot m$ and $\Delta T_f = K_f \cdot m$, where $m$ is molality, $K_b$ is the molal elevation (ebullioscopic) constant, and $K_f$ is the molal depression (cryoscopic) constant.

What is the van't Hoff factor $i$, and how is it expressed in terms of degree of dissociation $\alpha$?

$i = \dfrac{\text{observed colligative property}}{\text{calculated (normal) value}}$. For dissociation into $n$ ions: $i = 1 + (n-1)\alpha$. For association: $i = 1 + \left(\dfrac{1}{n}-1\right)\alpha$.

Define osmosis and osmotic pressure.

Osmosis is the net flow of solvent through a semipermeable membrane from lower to higher solute concentration. Osmotic pressure $\pi$ is the external pressure needed to stop this flow.

Write the van't Hoff equation for osmotic pressure of a dilute solution.

$\pi = CRT = \dfrac{n}{V}RT$, where $C$ is molar concentration. For electrolytes, $\pi = iCRT$.

Define isotonic, hypertonic, and hypotonic solutions.

Isotonic: equal osmotic pressure (no net flow). Hypertonic: higher osmotic pressure (causes cell crenation). Hypotonic: lower osmotic pressure (causes cell swelling/haemolysis).

State the first law of thermodynamics with its mathematical expression.

Energy is conserved: the change in internal energy equals heat added to the system minus work done by it. $\Delta U = q + w$ (with $w$ as work done on the system).

Define enthalpy and relate $\Delta H$ to $\Delta U$.

Enthalpy $H = U + PV$. At constant pressure, $\Delta H = \Delta U + P\Delta V$; for gaseous reactions $\Delta H = \Delta U + \Delta n_g RT$, where $\Delta n_g$ is the change in moles of gas.

State Hess's law of constant heat summation.

The total enthalpy change of a reaction is the same whether it occurs in one step or several steps, since enthalpy is a state function. Thermochemical equations can be added algebraically.