Chemical Kinetics and Solutions — NEET Chemistry

Thermodynamics tells you whether a reaction can happen; kinetics tells you how fast — and that is what a chemist, a pharmacologist and a cell actually control. Solutions, meanwhile, are where almost all chemistry and all biology occur, and their colligative properties let us weigh molecules just by watching a solvent's freezing point drop. NEET draws 3–4 questions across this block — order of reaction, half-life, the Arrhenius equation and colligative-property numericals recur every year. This chapter derives each rate law and colligative relation and drills the exact calculations the exam sets.

Part A — Chemical Kinetics

1. Rate of reaction

The rate is the change in concentration of a reactant or product per unit time. For $aA+bB\to cC+dD$:

$\text{rate}=-\frac{1}{a}\frac{d[A]}{dt}=-\frac{1}{b}\frac{d[B]}{dt}=+\frac{1}{c}\frac{d[C]}{dt}=+\frac{1}{d}\frac{d[D]}{dt}$

The stoichiometric coefficients make the single rate consistent whichever species you follow. Average rate is measured over an interval; instantaneous rate is the slope at one instant. Rate always decreases with time as reactants are consumed. Units: mol L⁻¹ s⁻¹.

Worked example 1.1. For N₂ + 3H₂ → 2NH₃, if H₂ is consumed at 0.06 mol L⁻¹ s⁻¹, how fast is NH₃ formed? $-\frac{1}{3}\frac{d[H_2]}{dt}=+\frac{1}{2}\frac{d[N{H}_3]}{dt}$. So $\frac{d[N{H}_3]}{dt}=\frac{2}{3}\times 0.06=0.04$ mol L⁻¹ s⁻¹.

2. Rate law, order and molecularity

The rate law is found experimentally: rate $=k[A{]}^x[B{]}^y$. The exponents $x,y$ are the orders with respect to each reactant; the overall order is $x+y$. The rate constant $k$ is independent of concentration but depends on temperature.

Order vs molecularity — a NEET favourite to distinguish:

Units of $k$ depend on order: $k$ has units $({\text{mol L}}^{-1}{)}^{1-n}{\text{s}}^{-1}$. So zero order: mol L⁻¹ s⁻¹; first order: s⁻¹; second order: L mol⁻¹ s⁻¹.

Worked example 2.1. A reaction rate $=k[A][B{]}^2$. Overall order and units of $k$? Overall order $=1+2=3$. Units of $k$ $=({\text{mol L}}^{-1}{)}^{1-3}{\text{s}}^{-1}={\text{L}}^2{\text{mol}}^{-2}{\text{s}}^{-1}$.

3. Integrated rate laws and half-life

Zero order (rate independent of concentration): $[A]=[A{]}_0-kt$. A plot of $[A]$ vs $t$ is a straight line; $t_{1/2}=\frac{[A{]}_0}{2k}$ (depends on initial concentration).

First order:

$k=\frac{2.303}{t}\log \frac{[A{]}_0}{[A]},t_{1/2}=\frac{0.693}{k}$

The first-order half-life is independent of concentration — a signature property (shared with radioactive decay). A plot of $\log [A]$ vs $t$ is linear with slope $-k/2.303$.

Worked example 3.1. A first-order reaction has $k=0.0693$ min⁻¹. Its half-life? $t_{1/2}=\frac{0.693}{k}=\frac{0.693}{0.0693}=10$ min.

Worked example 3.2. What fraction of a first-order reactant remains after 3 half-lives? Each half-life halves the amount: $(1/2{)}^3=1/8$ remains (independent of the starting amount).

4. Temperature, the Arrhenius equation and catalysis

Reaction rate rises sharply with temperature — roughly doubling for every 10 °C (temperature coefficient ≈ 2–3). The Arrhenius equation quantifies this:

$k=A{e}^{-E_a/RT},\ln \frac{k_2}{k_1}=\frac{E_a}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)$

where $E_a$ = activation energy (the energy barrier reactants must cross) and $A$ = frequency factor. A higher $E_a$ means a slower, more temperature-sensitive reaction. A plot of $\ln k$ vs $1/T$ is a straight line of slope $-E_a/R$.

Collision theory: molecules must collide with sufficient energy ($\ge E_a$) and the correct orientation to react. Raising temperature increases the fraction of molecules exceeding $E_a$ (from the Maxwell distribution), which is why rate climbs so steeply.

A catalyst provides an alternative path with lower $E_a$, speeding both forward and reverse reactions equally — so it raises the rate and helps equilibrium arrive sooner, but does not shift the equilibrium position or change $\Delta H$.

Worked example 4.1. Why does a small temperature rise cause a large rate increase? Rate depends on the fraction of molecules with energy $\ge E_a$, which is $e^{-E_a/RT}$ from the Maxwell–Boltzmann tail. A modest rise in $T$ shifts many more molecules above the barrier, so $k$ (and the rate) can double or triple for each 10 °C.

Worked example 4.2. How does a catalyst affect $E_a$ and $\Delta H$ of a reaction? It lowers $E_a$ (both forward and reverse), speeding the reaction, but leaves $\Delta H$ (the energy difference between reactants and products) unchanged — a catalyst never alters thermodynamics.

Part B — Solutions

5. Concentration units

A solution is a homogeneous mixture; the component in excess is the solvent. Ways to express concentration:

• Molarity $M=\frac{\text{mol solute}}{\text{L solution}}$ — temperature-dependent (volume changes).
• Molality $m=\frac{\text{mol solute}}{\text{kg solvent}}$ — temperature-independent (mass fixed); preferred for colligative properties.
• Mole fraction $x_i=\frac{n_i}{n_{\text{total}}}$ (sum = 1).
• Mass %, ppm (parts per million, for very dilute solutions).

Worked example 5.1. Molality of a solution with 0.5 mol solute in 250 g solvent? $m=\frac{\text{mol}}{\text{kg solvent}}=\frac{0.5}{0.250}=2$ mol/kg.

6. Solubility of gases: Henry's law

The solubility of a gas in a liquid is proportional to its partial pressure above the liquid — Henry's law:

$p=K_{H}x$

where $x$ = mole fraction of dissolved gas and $K_H$ = Henry's constant. Higher $K_H$ → lower solubility. Gas solubility decreases with temperature (why warm soda goes flat, and why aquatic life suffers in warm water). Applications: the fizz in carbonated drinks (bottled under high CO₂ pressure) and the bends in divers (nitrogen dissolving under pressure, then bubbling out on rapid ascent).

7. Raoult's law and ideal solutions

For a solution of volatile liquids, Raoult's law states each component's partial vapour pressure equals its mole fraction times its pure vapour pressure:

$p_A=x_A{p}_A^0,p_{\text{total}}=x_A{p}_A^0+x_B{p}_B^0$

An ideal solution obeys Raoult's law at all compositions ($\Delta H_{\text{mix}}=0$, $\Delta V_{\text{mix}}=0$) — e.g. benzene + toluene. Non-ideal solutions deviate:

• Positive deviation — weaker A–B forces than A–A/B–B; higher vapour pressure (ethanol + water); minimum-boiling azeotrope.
• Negative deviation — stronger A–B forces; lower vapour pressure (HNO₃ + water); maximum-boiling azeotrope.

8. Colligative properties

Colligative properties depend only on the number of solute particles, not their identity. Four of them:

1. Relative lowering of vapour pressure (Raoult's law for a non-volatile solute):

$\frac{p^0-p}{p^0}=x_{\text{solute}}$

2. Elevation of boiling point: $\Delta T_b=K_{b}m$ (a solution boils higher than the pure solvent).

3. Depression of freezing point: $\Delta T_f=K_{f}m$ (a solution freezes lower — why salt de-ices roads and antifreeze works).

4. Osmotic pressure: $\pi =CRT=\frac{n}{V}RT$ — the pressure needed to stop osmosis across a semipermeable membrane. It is the most sensitive colligative property, used to find the molar mass of proteins.

$K_b$ and $K_f$ are the molal elevation/depression constants of the solvent (for water, $K_f=1.86$, $K_b=0.52$ K kg mol⁻¹).

Worked example 8.1. The freezing point of a solution of 0.1 mol of a non-electrolyte in 1 kg of water ($K_f=1.86$)? $\Delta T_f=K_{f}m=1.86\times 0.1=0.186$ K, so the solution freezes at $-0.186°$C.

Worked example 8.2. Osmotic pressure of a 0.1 M solution at 300 K ($R=0.0821$ L atm K⁻¹ mol⁻¹)? $\pi =CRT=0.1\times 0.0821\times 300=2.46$ atm.

9. The van't Hoff factor and abnormal molar mass

Electrolytes dissociate (or some solutes associate), changing the number of particles, so their colligative effect is abnormal. The van't Hoff factor $i$ corrects for this:

$i=\frac{\text{observed colligative property}}{\text{calculated (assuming no dissociation)}}=\frac{\text{particles after}}{\text{particles before}}$

Every colligative formula gains a factor $i$: $\Delta T_f=i{K}_{f}m$, $\pi =iCRT$, etc.

• Dissociation: $i>1$ (NaCl → 2 ions, $i\approx 2$; CaCl₂ → 3 ions, $i\approx 3$).
• Association: $i<1$ (acetic acid dimerises in benzene, $i\approx 0.5$).

Because measured molar mass $\propto 1/(\text{particle count})$, dissociation gives an abnormally low molar mass and association an abnormally high one.

Worked example 9.1. For 0.1 m NaCl (assume complete dissociation, $i=2$), find $\Delta T_f$ ($K_f=1.86$). $\Delta T_f=i{K}_{f}m=2\times 1.86\times 0.1=0.372$ K — twice the value for a non-electrolyte, because NaCl gives two ions per formula unit.

10. Common traps NEET sets here

• Order is experimental; molecularity is theoretical — order can be zero/fractional, molecularity cannot.
• First-order $t_{1/2}$ is independent of concentration; zero-order $t_{1/2}$ depends on $[A{]}_0$.
• Units of $k$ vary with order — $({\text{mol L}}^{-1}{)}^{1-n}{\text{s}}^{-1}$.
• Catalyst lowers $E_a$, not $\Delta H$ — and never shifts equilibrium.
• Gas solubility falls with temperature (Henry) — opposite to most solids.
• Colligative properties count particles, so remember the van't Hoff factor $i$ for electrolytes.
• Depression of freezing point / elevation of boiling point use molality, not molarity.
• Dissociation → low abnormal molar mass; association → high.

11. Memory aids

• "Order is measured, molecularity is counted" — the key distinction.
• "First-order half-life forgets the start" — $t_{1/2}=0.693/k$, concentration-free.
• "$k=A{e}^{-E_a/RT}$; catalyst cuts $E_a$" — Arrhenius and catalysis.
• "Warm drinks go flat" — gas solubility drops with temperature (Henry).
• "Colligative counts heads, not names" — depends on particle number only.
• "$i$ for ions" — multiply colligative formulas by the van't Hoff factor.
• "Salt lowers freezing, raises boiling" — ΔT_f down, ΔT_b up with solute.

12. Exam protocol

1. Write the rate in terms of each species using stoichiometric coefficients.
2. Get order from the experimental rate law; deduce units of $k$; distinguish from molecularity.
3. First order: $k=\frac{2.303}{t}\log \frac{[A{]}_0}{[A]}$, $t_{1/2}=0.693/k$ (concentration-independent).
4. Temperature/catalysis: Arrhenius $k=A{e}^{-E_a/RT}$; a catalyst lowers $E_a$ only.
5. Choose the right concentration unit — molality for colligative work.
6. Apply Henry ($p=K_{H}x$, solubility falls with $T$) and Raoult (ideal vs deviations).
7. Colligative: $\Delta T_f=i{K}_{f}m$, $\Delta T_b=i{K}_{b}m$, $\pi =iCRT$; include $i$ for electrolytes and read off abnormal molar mass.