MHT-CET Chemistry · Teaching notes

Chemical Thermodynamics and Energetics — MHT-CET Chemistry

Chemical Thermodynamics is about three questions a paper in MHT-CET Chemistry and almost never HARD — one in thirty of its past-year questions. Most of the marks sit on the first law and its sign convention: ΔU = q + w with w = −P_ext ΔV, the unit conversion 1 dm³ bar = 100 J, and the reversible isothermal work −2.303 nRT log(V₂/V₁). The rest is ΔH = ΔU + Δn_g RT, enthalpies of formation combined into a reaction enthalpy, ΔS_surr = −ΔH/T, and ΔG = ΔH − TΔS with its zero at equilibrium. The pages follow the book from systems to Gibbs energy, and the first-law page is the one to drill. Every PYQ is tagged.

Every subtopic, worked example, formula and trap in one printable document — answers shown, ready to share.

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Subtopic notes

PYQ weightage by concept

16 concepts · 124 PYQs — where the marks actually sit, so you know what to drill first

Thermodynamic Systems, Properties and Processes12 PYQs · 10%

Concept	PYQs	Share
Systems, Intensive Versus Extensive, State Versus Path	7	6%
Isothermal, Isochoric, Isobaric, Adiabatic and Reversible	5	4%

First Law of Thermodynamics, Internal Energy and Work52 PYQs · 42%

Concept	PYQs	Share
ΔU = q + w and the Sign Convention	16	13%
Work Against a Constant External Pressure: w = −P_ext ΔV	13	10%
Reversible Isothermal Work: −2.303 nRT log(V₂/V₁)	9	7%
ΔU From Heat Absorbed and an Expansion	7	6%
Work in a Gas-Phase Reaction: w = −Δn_g RT	7	6%

Enthalpy and the Relation Between ΔH and ΔU18 PYQs · 15%

Concept	PYQs	Share
ΔH = ΔU + Δn_g RT	10	8%
Enthalpy, Heat at Constant Pressure and Phase Changes	8	6%

Thermochemistry, Hess's Law and Bond Enthalpy21 PYQs · 17%

Concept	PYQs	Share
Enthalpy of Formation and the Reaction Enthalpy From It	14	11%
Bond Enthalpy: Bonds Broken Minus Bonds Formed	4	3%
Hess's Law and the Enthalpy of Solution	3	2%

Entropy and the Second Law9 PYQs · 7%

Concept	PYQs	Share
ΔS = q_rev/T, ΔS_surr = −ΔH/T and ΔS_total	6	5%
Predicting the Sign of ΔS	3	2%

Gibbs Free Energy and Spontaneity12 PYQs · 10%

Concept	PYQs	Share
ΔG = ΔH − TΔS and the Sign Table	6	5%
ΔG = 0: Boiling Points, Transition Temperatures and K	6	5%

Formula & revision sheet

15 formulas · 1 reference tables · 16 gotchas across all subtopics — the exam-eve cheat-sheet

Thermodynamic Systems, Properties and Processes

Formulas (1)

Isothermal, Isochoric, Isobaric, Adiabatic and Reversible · What each process fixes $\text{isochoric: } w = 0;\quad \text{isothermal (ideal): } \Delta U = 0;\quad \text{adiabatic: } q = 0;\quad \text{isobaric: } q_P = \Delta H$

Reference tables (1)

Systems, Intensive Versus Extensive, State Versus Path6 rows

Property	Intensive or extensive	State or path
Temperature, pressure	Intensive	State
Boiling point, density, surface tension, viscosity, specific heat	Intensive	State SPECIFIC heat (per gram) is intensive; HEAT CAPACITY (of the sample) is extensive.
Mass, volume, number of moles	Extensive	State
Internal energy U, enthalpy H, entropy S	Extensive	State Internal energy is the planted 'not intensive' option.
Heat capacity	Extensive	—
Heat q, work w	—	Path Work is the only path function among U, w, S, H.

Divide the sample in two and ask what changes.

Watch out for (2)

Heat capacity as intensive
→ Systems, Intensive Versus Extensive, State Versus Path
'Isothermal' read as 'no heat exchange'
→ Isothermal, Isochoric, Isobaric, Adiabatic and Reversible

First Law of Thermodynamics, Internal Energy and Work

Formulas (5)

ΔU = q + w and the Sign Convention · First law $\Delta U = q + w,\qquad q_{\text{absorbed}} > 0,\quad w_{\text{on system}} > 0$
Work Against a Constant External Pressure: w = −P_ext ΔV · PV work $w = -P_{\text{ext}}\,\Delta V,\qquad 1\ \text{dm}^3\,\text{bar} = 100\ \text{J},\quad 1\ \text{L atm} = 101.3\ \text{J}$
ΔU From Heat Absorbed and an Expansion · First law with expansion work $\Delta U = q - P_{\text{ext}}\,\Delta V$
Work in a Gas-Phase Reaction: w = −Δn_g RT · Reaction work $w = -\Delta n_g\,RT$
Reversible Isothermal Work: −2.303 nRT log(V₂/V₁) · Maximum (reversible) work $w_{\text{rev}} = -2.303\,nRT\log_{10}\frac{V_2}{V_1} = -2.303\,nRT\log_{10}\frac{P_1}{P_2}$

Watch out for (5)

'Work done BY the system' entered as positive
→ ΔU = q + w and the Sign Convention
Leaving the answer in dm³ bar when joules are asked
→ Work Against a Constant External Pressure: w = −P_ext ΔV
Adding the work instead of subtracting it
→ ΔU From Heat Absorbed and an Expansion
Counting liquids and solids in Δn
→ Work in a Gas-Phase Reaction: w = −Δn_g RT
Using the pressure ratio the same way as the volume ratio
→ Reversible Isothermal Work: −2.303 nRT log(V₂/V₁)

Enthalpy and the Relation Between ΔH and ΔU

Formulas (2)

Enthalpy, Heat at Constant Pressure and Phase Changes · Enthalpy $H = U + PV,\qquad \Delta H = q_P,\qquad \Delta H_{\text{vap}} = \frac{q}{n}$
ΔH = ΔU + Δn_g RT · ΔH and ΔU $\Delta H = \Delta U + \Delta n_g\,RT$

Watch out for (2)

Dividing the heat by the grams
→ Enthalpy, Heat at Constant Pressure and Phase Changes
Counting liquid water as a gas
→ ΔH = ΔU + Δn_g RT

Thermochemistry, Hess's Law and Bond Enthalpy

Formulas (3)

Enthalpy of Formation and the Reaction Enthalpy From It · Reaction enthalpy from formation enthalpies $\Delta_r H^\circ = \sum \nu_p\,\Delta_f H^\circ_{\text{products}} - \sum \nu_r\,\Delta_f H^\circ_{\text{reactants}}$
Hess's Law and the Enthalpy of Solution · Hess's law; enthalpy of solution $\Delta H_{\text{overall}} = \sum \Delta H_{\text{steps}},\qquad \Delta_{\text{soln}}H = \Delta_L H + \Delta_{\text{hyd}}H$
Bond Enthalpy: Bonds Broken Minus Bonds Formed · Reaction enthalpy from bond enthalpies $\Delta_r H = \sum \Delta H_{\text{broken}} - \sum \Delta H_{\text{formed}}$

Watch out for (3)

Reporting the equation's ΔH as the formation enthalpy
→ Enthalpy of Formation and the Reaction Enthalpy From It
Subtracting hydration from lattice enthalpy
→ Hess's Law and the Enthalpy of Solution
Using a whole N₂ for the formation enthalpy of NH₃
→ Bond Enthalpy: Bonds Broken Minus Bonds Formed

Entropy and the Second Law

Formulas (2)

Predicting the Sign of ΔS · Rule of thumb $\Delta n_g > 0 \Rightarrow \Delta S > 0;\qquad \Delta n_g < 0 \text{ or gas} \to \text{liquid/solid} \Rightarrow \Delta S < 0$
ΔS = q_rev/T, ΔS_surr = −ΔH/T and ΔS_total · Entropy of surroundings and total $\Delta S_{\text{surr}} = -\frac{\Delta H_{\text{sys}}}{T},\qquad \Delta S_{\text{total}} = \Delta S_{\text{sys}} - \frac{\Delta H_{\text{sys}}}{T}$

Watch out for (2)

Counting moles without looking at phases
→ Predicting the Sign of ΔS
Dividing kilojoules by kelvin
→ ΔS = q_rev/T, ΔS_surr = −ΔH/T and ΔS_total

Gibbs Free Energy and Spontaneity

Formulas (2)

ΔG = ΔH − TΔS and the Sign Table · Gibbs energy $\Delta G = \Delta H - T\Delta S$
ΔG = 0: Boiling Points, Transition Temperatures and K · Equilibrium conditions $T_{\text{eq}} = \frac{\Delta H}{\Delta S},\qquad \Delta G^\circ = -2.303\,RT\log_{10} K$

Watch out for (2)

Subtracting joules from kilojoules
→ ΔG = ΔH − TΔS and the Sign Table
Inverting to T = ΔS/ΔH
→ ΔG = 0: Boiling Points, Transition Temperatures and K