Enthalpy Heat Capacity

8 MCQs2 revision cards9-step worked example

Source: NCERT ThermodynamicsPYQ coverage: NEET 2021, 2022, 2023, 2024, 2025Official key: NTA-verifiedLast reviewed: May 2026

Lesson

NEET asks you to distinguish between enthalpy and internal energy, apply ΔH = q_p, and connect heat capacity to measurable heat flow. The confusion that costs marks here is not Hess's law or Gibbs energy — those belong to their own topics. The confusion is simpler and more fundamental: mixing up q_p and q_v, or forgetting that ΔH = q_p holds only at constant pressure.

Enthalpy defined. Enthalpy is a state function: H = U + PV, where U is internal energy, P is pressure, and V is volume (NCERT Class 11 Chemistry Chapter 5, page 8). You cannot measure H directly — you measure ΔH, the change.

The constant-pressure link. At constant pressure, the heat absorbed by the system equals the enthalpy change: ΔH = q_p. This is the operational definition that connects calorimetry to thermodynamic tables. At constant volume, it is internal energy that equals the heat: ΔU = q_v. Confusing these two conditions is a common source of wrong answers.

Heat capacity. Heat capacity C is the heat required to raise temperature by 1 K. Two versions matter:

C_p (constant pressure): q_p = nC_pΔT, so ΔH = nC_pΔT.
C_v (constant volume): q_v = nC_vΔT, so ΔU = nC_vΔT.

For an ideal gas, the relation C_p − C_v = R connects them (NCERT Class 11 Chemistry Chapter 5, page 10). This means C_p is always larger than C_v — the system at constant pressure must also do expansion work.

The relationship ΔH = ΔU + ΔnRT (for ideal-gas reactions at constant T and P) follows directly from H = U + PV. Here Δn = moles of gaseous products − moles of gaseous reactants. When Δn = 0, ΔH = ΔU.

Watch out: When a problem gives you C_p and asks for ΔU, you need C_v (or must convert via C_p − C_v = R). Don't substitute C_p into a constant-volume expression.

Practice MCQs

Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.

MCQ 1Easy RecallPractice

The enthalpy of a system is defined as H = U + PV. Which statement about enthalpy is correct?

MCQ 2Easy RecallPractice

For an ideal gas, C_p − C_v equals:

MCQ 3Easy RecallPractice

A reaction in solution is carried out in a coffee-cup calorimeter (open to the atmosphere). The heat measured in this experiment directly gives:

MCQ 4Direct ApplicationPractice

For the gaseous reaction N₂(g) + 3H₂(g) → 2NH₃(g), the relationship between ΔH and ΔU at temperature T is:

MCQ 5Direct ApplicationPractice

2 moles of an ideal gas are heated from 300 K to 500 K at constant pressure. Given C_p = 29.1 J mol⁻¹ K⁻¹, the enthalpy change ΔH is:

MCQ 6Direct ApplicationPractice

In a bomb calorimeter experiment, the heat measured gives q_v. For a gaseous reaction with Δn_g = +1, which relationship is correct at temperature T?

MCQ 7CalculationPractice

For a reaction where ΔH = −100 kJ and Δn_g = −3, at T = 300 K (R = 8.314 J mol⁻¹ K⁻¹), the value of ΔU is closest to:

MCQ 8CalculationPractice

A monatomic ideal gas (C_v = 3R/2) is heated from 200 K to 400 K. The ratio ΔH/ΔU for this process is:

Quick recall before you leave

Worked Example

1
Given
For the combustion reaction: CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l) ΔH = −890 kJ mol⁻¹ at T = 298 K. R = 8.314 J mol⁻¹ K⁻¹.
2
Required
Find ΔU for this reaction.
3
Concept
Enthalpy and internal energy are related by ΔH = ΔU + Δn_g RT, where Δn_g is the change in moles of gaseous species only. Liquids and solids are excluded from Δn_g.
4
Formula
ΔU = ΔH − Δn_g RT
5
Substitution
Gaseous products: CO₂ = 1 mol (H₂O is liquid, excluded). Gaseous reactants: CH₄ + 2O₂ = 1 + 2 = 3 mol. Δn_g = 1 − 3 = −2. ΔU = −890 − (−2)(8.314 × 10⁻³)(298)
6
Calculation
Δn_g RT = (−2)(8.314 × 10⁻³)(298) = −4.955 kJ ΔU = −890 − (−4.955) = −890 + 4.955 = −885.045 kJ **Note on exact values:** The coefficient 2 in Δn_g and the stoichiometric coefficients are exact counting numbers. R = 8.314 J mol⁻¹ K⁻¹ is a defined constant. These do not limit significant figures. The precision is governed by ΔH (3 significant figures).
7
Final answer
ΔU ≈ −885 kJ mol⁻¹ Reported to 3 significant figures, consistent with the given ΔH = −890 kJ mol⁻¹ (which has 3 significant figures per convention, as the trailing zero after 89 in the context of thermochemical data is significant).
8
Common trap
Forgetting that H₂O(l) is a liquid and including it in Δn_g. If you mistakenly count H₂O as gaseous: Δn_g = (1 + 2) − (1 + 2) = 0, giving ΔU = ΔH = −890 kJ — which is wrong. Always check state symbols. Another common error: using the wrong sign for Δn_g (reactants − products instead of products − reactants), which flips the correction term.
9
Similar NEET-style question
For the reaction 2SO₂(g) + O₂(g) → 2SO₃(g), ΔH = −198 kJ mol⁻¹ at 298 K. Calculate ΔU. (Answer: Δn_g = 2 − 3 = −1; ΔU = −198 − (−1)(8.314 × 10⁻³)(298) = −198 + 2.478 ≈ −195.5 kJ mol⁻¹.) ---

Before solving, remember these

Definition

Enthalpy

H = U + PV. At constant pressure, ΔH = q_p (heat absorbed at constant P). For exothermic ΔH<0; endothermic ΔH>0.

-- NCERT Class 11 Chemistry, Ch. 5, p. 8

Formula

Cp - Cv = nR

For ideal gas: C_p - C_v = nR. Per mole: c_p - c_v = R. C_p > C_v because at constant P, heat also does expansion work.

-- NCERT Class 11 Chemistry, Ch. 5, p. 10

Formulas

Enthalpy and ΔH at constant P

H = U + P V; Δ H = q_{p}

Enthalpy = internal energy + PV. At constant pressure, heat absorbed equals enthalpy change.

Symbol	Quantity	SI Unit
H	enthalpy	J
U	internal energy	J
P	pressure	Pa
V	volume	m^3

Valid when

At constant pressure
Closed system

First law of thermodynamics (chemistry)

Δ U = q + w

Internal energy change = heat added to system + work done ON system. Note: chemistry uses w as work done ON system; physics uses w as work done BY.

Symbol	Quantity	SI Unit
ΔU	internal energy change	J
q	heat	J
w	work on system	J

Valid when

Closed system
Sign convention chosen consistently

Gibbs free energy

Δ G = Δ H - T Δ S

Spontaneity criterion. ΔG<0: spontaneous. ΔG=0: equilibrium. ΔG>0: non-spontaneous.

Symbol	Quantity	SI Unit
ΔG	Gibbs energy change	kJ
ΔH	enthalpy	kJ
ΔS	entropy	kJ/K
T	temperature	K

Valid when

Constant T and P

ΔG° and K

Δ G^{\circ} = - R T ln K

Standard free energy change relates to equilibrium constant. K>1: ΔG°<0; K<1: ΔG°>0.

Symbol	Quantity	SI Unit
ΔG°	standard free energy	J/mol
R	gas constant 8.314	J/mol/K
T	temp	K
K	equilibrium constant	-

Valid when

Standard state
Equilibrium

Hess's law

Δ H_{net} = \sum Δ H_{steps}

Total enthalpy change is independent of path. Useful for computing ΔH of reactions not directly measurable.

Symbol	Quantity	SI Unit
ΔH	enthalpy change	J or kJ

Valid when

State function (path-independent)
Same initial/final states

Standard enthalpy of reaction

Δ H_{rxn}^{\circ} = \sum Δ H_{f}^{\circ} (prod) - \sum Δ H_{f}^{\circ} (react)

From standard formation enthalpies. ΔH°_f of element in standard state = 0.

Symbol	Quantity	SI Unit
ΔH°_f	standard formation enthalpy	kJ/mol

Valid when

Standard state (1 bar, 298 K)
Stoichiometric coefficients applied

Exam Traps & Common Mistakes

These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.

Trap

Hess's law: ΔH sign on reversal

Category: Sign Convention

When reversing a reaction, ΔH changes sign. Multiply: same as multiply ΔH.

When it triggers

Hess's law problem with combination of multiple reactions.

How to avoid

If reaction is reversed: ΔH → -ΔH. If multiplied by factor n: ΔH → n×ΔH. Apply systematically when combining.

Mistake

Wrong sign of ΔG° from K. ΔG° = -RT ln K (negative ln means K<1, ΔG°>0).

Root cause: sign error

Correction

K > 1: ln K > 0 → ΔG° < 0 (forward favoured). K < 1: ln K < 0 → ΔG° > 0 (reverse favoured). At equilibrium K=1, ΔG°=0.

Mistake

Forgets to negate ΔH when reversing a reaction in Hess's law combination.

Root cause: sign error

Correction

Reversing a reaction: ΔH → -ΔH. Multiplying by n: ΔH → n·ΔH. Apply consistently before summing.

Mistake

Predicts spontaneity from ΔH alone (ignoring T and ΔS).

Root cause: concept gap

Correction

Spontaneity from ΔG = ΔH - TΔS. Endothermic reactions can be spontaneous if TΔS > ΔH (ice melting at room T).

Past Year Questions

8 questions from NEET 2021, 2022, 2023, 2024, 2025. Answers verified against NTA official keys.

NEET 2025

Phosphoric acid ionizes in three steps with their ionization constant values - 35 - K a 1 , K a 2 a n d K a 3 , respectively, while K is the overall ionization constant. Which of the following statements are true? A. lo g K = lo g K a1 + lo g K a 2 + lo g K a 3 B. H PO is a stronger acid than 3 4 H 2 P O −4 and H P O 24 − C. K a1 > K a 2 > K a 3 D. K a 1 = K a 3 + 2 K a 2 Choose the correct answer from the options given below :

1A, B and C only

2A and B only

3A and C only

4B, C and D only

NTA Answer: Option 1(final)

NEET 2024Revised key

In which of the following processes entropy increases? A. A liquid evaporates to vapour. B. Temperature of a crystalline solid lowered from 130 K to 0 K. C. 2NaHCO → Na CO + CO + H O 3(s) 2 3(s) 2(g) 2 (g) D. Cl → 2Cl 2(g) (g) Choose the correct answer from the options given below:

1A and C

2A, B and D

3A, C and D

4C and D

NTA Answer: Option 3(revised_final)

NEET 2024Revised key

Match List I with List II. List-I List-II (Process) (Conditions) A. Isothermal process I. No heat exchange B. Isochoric process II. Carried out at constant temperature C. Isobaric process III. Carried out at constant volume D. Adiabatic process IV. Carried out at constant pressure Choose the correct answer from the options given below:

1A-IV, B-III, C-II, D-I

2A-IV, B-II, C-III, D-I

3A-I, B-II, C-III, D-IV

4A-II, B-III, C-IV, D-I

NTA Answer: Option 4(revised_final)

NEET 2024Revised key

The work done during reversible isothermal expansion of one mole of hydrogen gas at 25°C from pressure of 20 atmosphere to 10 atmosphere is (Given R = 2.0 cal K–1 mol–1)

10 calorie

2–413.14 calories

3413.14 calories

4100 calories

NTA Answer: Option 2(revised_final)

NEET 2023

Which amongst the following molecules on polymerization produces neoprene? Cl |

1H C C–CHCH

2H CCH–CCH 2 2 2 CH 3 |

3H C C –CHCH

4H CCH–CHCH 2 2 2 2

NTA Answer: Option 1(final)

NEET 2023

The equilibrium concentrations of the species in the reaction AB CDare 2, 3, 10 and 6 mol L–1,  respectively at 300 K. Gº for the reaction is (R = 2 cal/mol K)

1–137.26 cal

2–1381.80 cal

3–13.73 cal

41372.60 cal

NTA Answer: Option 2(final)

NEET 2022

The given graph is a representation of kinetics of a reaction. The y and x axes for zero and first order reactions, respectively are

1zero order (y = rate and x = concentration), first order (y = rate and x = t ) ½

2zero order (y = concentration and x = time), first order (y = t and x = concentration) ½

3zero order (y = concentration and x = time), first order (y = rate constant and x = concentration)

4zero order (y = rate and x = concentration), first order (y = t and x = concentration) ½

NTA Answer: Option 4(final)

NEET 2021

For irreversible expansion of an ideal gas under isothermal condition, the correct option is: ΔU ≠ ΔS ΔU ΔS

10, = 0

2= 0, = 0 total total ΔU ≠ ΔS ≠ ΔU ΔS ≠

30, 0

4= 0, 0 total total

NTA Answer: Option 4(final)

How NEET usually asks this

Recurring question shapes from past papers. Each pattern shows why wrong options look tempting.

Combine multiple thermochemical equations using Hess's law to find ΔH of target reaction.

Multi StepMedium

Common distractors

wrong sign when reversing

Forgets to negate ΔH when reversing equation

Predict spontaneity from ΔH and ΔS at given T using ΔG = ΔH - TΔS.

InterpretationMedium

Common distractors

ignores temperature

Uses ΔH alone for spontaneity

Sources

NCERT refs: Class 11 Chemistry Chapter 5, p.8 | Class 11 Chemistry Chapter 5, p.10

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Enthalpy Heat Capacity

Lesson

Practice MCQs

Quick recall before you leave

Enthalpy definition

C_p − C_v relation

Worked Example

Before solving, remember these

Formulas

Valid when

Valid when

Valid when

Valid when

Valid when

Valid when

Exam Traps & Common Mistakes

When it triggers

How to avoid

Correction

Correction

Correction

Past Year Questions

How NEET usually asks this

Common distractors

Common distractors

Sources

Free NEET study resources