Core Syllabus Module

Chemical Thermodynamics

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Chapter Elite-20 Challenge Zone

Target Advanced

JEE Advanced 2026

LEVELJEE Advanced

List-I contains various physical/chemical processes, and List-II contains combinations of changes in enthalpy ( $Δ H$ ) and entropy ( $Δ S$ ). Match each entry in List-I to appropriate entry in List-II, and choose the correct option.

List-I

\to

Graphite

(R)

Denaturation of protein

(S)

Propene

\to

Cyclopropane

List-II

(1)

Δ H > 0

and

Δ S > 0

(2)

Δ H < 0

and

Δ S < 0

(3)

Δ H < 0

and

Δ S = 0

(4)

Δ H > 0

and

Δ S < 0

(5)

Δ H < 0

and

Δ S > 0

JEE Advanced 2026

LEVELJEE Advanced

An ideal gas ( $0.5 mol$ ), initially at $2 bar$ pressure, is compressed at a constant temperature of $600 K$ in two steps : first against a constant external pressure of $P bar$ ( $2 < P < 8$ ), and then against constant external pressure of $8 bar$ . At each step, the compression is stopped only when the pressure of the gas becomes equal to the external pressure. The total work done on the gas in these steps is $W$ . Considering all possible values of $P$ ( $2 < P < 8$ ) and taking the gas constant as $R$ (in $J K^{- 1} mol^{- 1}$ ), the minimum value of $∣ W ∣$ (in $J$ ) is

(A)

207 R

(B)

600 R

(C)

630 R

(D)

900 R

JEE Advanced 2023

LEVELJEE Advanced

Comprehension Passage

The entropy versus temperature plot for phases

α

and

β

at 1 bar pressure is given.

S_{T}

and

S_{0}

are entropies of the phases at temperatures T and 0 K, respectively. The transition temperature for

α

β

phase change is 600 K and

C_{P, β} - C_{P, α} = 1 J mol^{- 1} K^{- 1}

. Assume

(C_{P, β} - C_{P, α})

is independent of temperature in the range of 200 to 700 K.

C_{P, α}

and

C_{P, β}

are heat capacities of

α

and

β

phases, respectively.

Question 1:

The value of entropy change, $S_{β} - S_{α}$ (in $J mol^{- 1} K^{- 1}$ ), at 300 K is ______. [Use : $ln 2 = 0.69$ Given : $S_{β} - S_{α} = 0$ at 0 K]

Question 2:

The value of enthalpy change, $H_{β} - H_{α}$ (in $J mol^{- 1}$ ), at 300 K is _______.

JEE Advanced 2018

LEVELJEE Advanced

For a reaction, $A ⇌ P$ , the plots of $[A]$ and $[P]$ with time at temperatures $T_{1}$ and $T_{2}$ are given below. If $T_{2} > T_{1}$ , the correct statement(s) is (are) (Assume $Δ H^{θ}$ and $Δ S^{θ}$ are independent of temperature and ratio of $ln K$ at $T_{1}$ to $ln K$ at $T_{2}$ is greater than $T_{2} / T_{1}$ . Here $H, S, G$ and $K$ are enthalpy, entropy, Gibbs energy and equilibrium constant, respectively.)

* Multiple Correct Options

(A)

Δ H^{θ} < 0, Δ S^{θ} < 0

(B)

Δ G^{θ} < 0, Δ H^{θ} > 0

(C)

Δ G^{θ} < 0, Δ S^{θ} < 0

(D)

Δ G^{θ} < 0, Δ S^{θ} > 0

JEE Advanced 2018

LEVELJEE Advanced

A reversible cyclic process for an ideal gas is shown below. Here, P , V and T are pressure , volume and temperature , respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and internal energy, respectively.

* Multiple Correct Options

(A)

q_{AC} = Δ U_{BC}

and

w_{AB} = P_{2} (V_{2} - V_{1})

(B)

w_{BC} = P_{2} (V_{2} - V_{1})

and

q_{BC} = Δ H_{AC}

(C)

Δ H_{CA} < Δ U_{CA}

and

q_{AC} = Δ U_{BC}

(D)

q_{BC} = Δ H_{AC}

and

Δ H_{CA} > Δ U_{CA}

JEE Advanced 2015

LEVELJEE Advanced

Match the thermodynamic processes given under Column-I with the expressions given under Column-II.

List-I

(P)

Freezing of water at

273 K

and

1 atm

(Q)

Expansion of

1 mol

of an ideal gas into a vacuum under isolated conditions

(R)

Mixing of equal volumes of two ideal gases at constant temperature and pressure in an isolated container

(S)

Reversible heating of

H_{2} (g)

1 atm

from

300 K

600 K

followed by reversible cooling to

300 K

1 atm

List-II

(1)

q = 0

(2)

w = 0

(3)

Δ S_{sys} < 0

(4)

Δ U = 0

(5)

Δ G = 0

JEE Advanced 2022

LEVELJEE Advanced

2 mol of Hg(g) is combusted in a fixed volume bomb calorimeter with excess of O $_{2}$ at 298 K and 1 atm into HgO(s). During the reaction, temperature increases from 298.0 K to 312.8 K. If heat capacity of the bomb calorimeter and enthalpy of formation of Hg(g) are 20.00 kJ K $^{- 1}$ and 61.32 kJ mol $^{- 1}$ at 298 K, respectively, the calculated standard molar enthalpy of formation of HgO(s) at 298 K is X kJ mol $^{- 1}$ . The value of |X| is ______. [Given : Gas constant R = 8.3 J K $^{- 1}$ mol $^{- 1}$ ]

JEE Advanced 2017

LEVELJEE Advanced

The standard state Gibbs free energies of formation of C(graphite) and C(diamond) at $T = 298 K$ are $Δ_{f} G^{\circ} [C(graphite)] = 0 kJ mol^{- 1}$ $Δ_{f} G^{\circ} [C(diamond)] = 2.9 kJ mol^{- 1}$ The standard state means that the pressure should be $1 bar$ , and substance should be pure at a given temperature. The conversion of graphite [C(graphite)] to diamond [C(diamond)] reduces its volume by $2 \times 1 0^{- 6} m^{3} mol^{- 1}$ . If C(graphite) is converted to C(diamond) isothermally at $T = 298 K$ , the pressure at which C(graphite) is in equilibrium with C(diamond), is [Useful information : $1 J = 1 kg m^{2} s^{- 2}$ ; $1 Pa = 1 kg m^{- 1} s^{- 2}$ ; $1 bar = 1 0^{5} Pa$ ]

Comprehension Passage

For the reaction

X (s) ⇌ Y (s) + Z (g)

, the plot of

ln \frac{p _{z}}{p ^{⊖}}

versus

\frac{1 0 ^{4}}{T}

is given below (in solid line), where

p_{z}

is the pressure (in bar) of the gas

Z

at temperature

T

and

p^{⊖} = 1 bar

. (Given,

\frac{d ( l n K )}{d ( \frac{1}{T} )} = - \frac{Δ H ^{⊖}}{R}

, where the equilibrium constant,

K = \frac{p _{z}}{p ^{⊖}}

and the gas constant,

R = 8.314 J K^{- 1} mol^{- 1}

)

Question 1:

The value of standard enthalpy, $Δ H^{⊖}$ (in $kJ mol^{- 1}$ ) for the reaction is________.

Question 2:

The value of $Δ S^{⊖}$ (in $J K^{- 1} mol^{- 1}$ ) for the given reaction, at $1000 K$ is________.

JEE Advanced 2018

LEVELJEE Advanced

The surface of copper gets tarnished by the formation of copper oxide. $N_{2}$ gas was passed to prevent the oxide formation during heating of copper at $1250 K$ . However, the $N_{2}$ gas contains $1 mole %$ of water vapour as impurity. The water vapour oxidises copper as per the reaction given below : $2 Cu(s) + H_{2} O(g) \to Cu_{2} O(s) + H_{2} (g)$ $p_{H_{2}}$ is the minimum partial pressure of $H_{2}$ (in bar) needed to prevent the oxidation at $1250 K$ . The value of $ln (p_{H_{2}})$ is ______. (Given : total pressure $= 1 bar$ , $R$ (universal gas constant) $= 8 J K^{- 1} mol^{- 1}$ , $ln (10) = 2.3$ . $Cu(s)$ and $Cu_{2} O(s)$ are mutually immiscible. At $1250 K$ : $2 Cu(s) + \frac{1}{2} O_{2} (g) \to Cu_{2} O(s)$ ; $Δ G^{θ} = - 78, 000 J mol^{- 1}$ $H_{2} (g) + \frac{1}{2} O_{2} (g) \to H_{2} O(g)$ ; $Δ G^{θ} = - 1, 78, 000 J mol^{- 1}$ ; $G$ is the Gibbs energy)

JEE Advanced 2017

LEVELJEE Advanced

An ideal gas is expanded from $(p_{1}, V_{1}, T_{1})$ to $(p_{2}, V_{2}, T_{2})$ under different conditions. The correct statement(s) among the following is(are)

* Multiple Correct Options

(A)

The work done on the gas is maximum when it is compressed irreversibly from

(p_{2}, V_{2})

(p_{1}, V_{1})

against constant pressure

p_{1}

(B)

The work done on the gas is less when it is expanded reversibly from

V_{1}

V_{2}

under adiabatic conditions as compared to that when expanded reversibly from

V_{1}

V_{2}

under isothermal conditions.

(C)

The change in internal energy of the gas (i) zero, if it is expanded reversibly with

T_{1} = T_{2}

, and (ii) positive, if it is expanded reversibly under adiabatic conditions with

T_{1} \neq = T_{2}

(D)

If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic.

JEE Advanced 2021

LEVELJEE Advanced

One mole of an ideal gas at $900 K$ , undergoes two reversible processes, I followed by II, as shown below. If the work done by the gas in the two processes are same, the value of $ln \frac{V _{3}}{V _{2}}$ is ___. ( $U$ : internal energy, $S$ : entropy, $p$ : pressure, $V$ : volume, $R$ : gas constant) (Given: molar heat capacity at constant volume, $C_{V, m}$ of the gas is $\frac{5}{2} R$ )

JEE Advanced 2023

LEVELJEE Advanced

One mole of an ideal monoatomic gas undergoes two reversible processes (A $\to$ B and B $\to$ C) as shown in the given figure : A $\to$ B is an adiabatic process. If the total heat absorbed in the entire process (A $\to$ B and B $\to$ C) is $R T_{2} ln 10$ , the value of $2 lo g V_{3}$ is _________. [Use, molar heat capacity of the gas at constant pressure, $C_{p, m} = \frac{5}{2} R$ ]

JEE Advanced 2017

LEVELJEE Advanced

For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant K in terms of change in entropy is described by

* Multiple Correct Options

(A)

With increase in temperature, the value of K for exothermic reaction decreases because the entropy change of the system is positive

(B)

With increase in temperature, the value of K for endothermic reaction increases because unfavourable change in entropy of the surroundings decreases

(C)

With increase in temperature, the value of K for exothermic reaction decreases because favourable change in entropy of the surroundings decreases

(D)

With increase in temperature, the value of K for endothermic reaction increases because the entropy change of the system negative

JEE Advanced 2023

LEVELJEE Advanced

In a one-litre flask, 6 moles of A undergoes the reaction A (g) $⇌$ P (g). The progress of product formation at two temperatures (in Kelvin), $T_{1}$ and $T_{2}$ , is shown in the figure: If $T_{1} = 2 T_{2}$ and $(Δ G_{2}^{⊖} - Δ G_{1}^{⊖}) = R T_{2} ln x$ , then the value of x is ______. [ $Δ G_{1}^{⊖}$ and $Δ G_{2}^{⊖}$ are standard Gibb's free energy change for the reaction at temperatures $T_{1}$ and $T_{2}$ , respectively.]

JEE Advanced 2021

LEVELJEE Advanced

An ideal gas undergoes a reversible isothermal expansion from state I to state II followed by a reversible adiabatic expansion from state II to state III. The correct plot(s) representing the changes from state I to state III is(are) ( $p$ : pressure, $V$ : volume, $T$ : temperature, $H$ : enthalpy, $S$ : entropy)

* Multiple Correct Options

One mole of an ideal gas at $300 K$ in thermal contact with surroundings expands isothermally from $1.0 L$ to $2.0 L$ against a constant pressure of $3.0 atm$ . In this process, the change in entropy of surroundings ( $Δ S_{surr}$ ) in $J K^{- 1}$ is - (Given: $1 L atm = 101.3 J$ )

(A)

5.763

(B)

1.013

(C)

- 1.013

(D)

- 5.763

JEE Advanced 2020

LEVELJEE Advanced

Consider the reaction $A ⇌ B$ at $1000 K$ . At time $t^{'}$ , the temperature of the system was increased to $2000 K$ and the system was allowed to reach equilibrium. Throughout this experiment the partial pressure of A was maintained at $1 bar$ . Given below is the plot of the partial pressure of B with time. What is the ratio of the standard Gibbs energy of the reaction at $1000 K$ to that at $2000 K$ ?

JEE Main 2020

LEVELJEE Advanced

The variation of equilibrium constant with temperature is given below: $Temperature T_{1} = 2 5^{\circ} C T_{2} = 10 0^{\circ} C Equilibrium constant K_{1} = 10 K_{2} = 100$ The values of $Δ H^{\circ}$ , $Δ G^{\circ}$ at $T_{1}$ and $Δ G^{\circ}$ at $T_{2}$ (in $kJ mol^{- 1}$ ) respectively, are close to [use $R = 8.314 J K^{- 1} mol^{- 1}$ ]

(A)

28.4, - 7.14 and - 5.71

(B)

0.64, - 7.14 and - 5.71

(C)

28.4, - 5.71 and - 14.29

(D)

0.64, - 5.71 and - 14.29

JEE Main 2021

LEVELJEE Advanced

At $298.2 K$ the relationship between enthalpy of bond dissociation (in $kJ mol^{- 1}$ ) for hydrogen ( $E_{H}$ ) and its isotope, deuterium ( $E_{D}$ ), is best described by

(A)

E_{H} = \frac{1}{2} E_{D}

(B)

E_{H} = E_{D}

(C)

E_{H} ≃ E_{D} - 7.5

(D)

E_{H} = 2 E_{D}

Micro-Topic Strategy Matrix

First Law of Thermodynamics

Enthalpy and Hess's Law

Entropy and Free Energy

Chapter Elite-20 Challenge Zone

List-I

List-II

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of entropy change, Sβ​−Sα​ (in J mol−1 K−1), at 300 K is ______. [Use : ln2=0.69 Given : Sβ​−Sα​=0 at 0 K]

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of enthalpy change, Hβ​−Hα​ (in J mol−1), at 300 K is _______.

A reversible cyclic process for an ideal gas is shown below. Here, P , V and T are pressure , volume and temperature , respectively. The thermodynamic parameters q, w, H and U are heat, work, enthalpy and internal energy, respectively.

Match the thermodynamic processes given under Column-I with the expressions given under Column-II.

List-I

List-II

Comprehension Passage

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of standard enthalpy, ΔH⊖ (in kJ mol−1) for the reaction is________.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The value of ΔS⊖ (in J K−1 mol−1) for the given reaction, at 1000 K is________.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } An ideal gas is expanded from (p1​,V1​,T1​) to (p2​,V2​,T2​) under different conditions. The correct statement(s) among the following is(are)

For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant K in terms of change in entropy is described by

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } At 298.2 K the relationship between enthalpy of bond dissociation (in kJ mol−1) for hydrogen (EH​) and its isotope, deuterium (ED​), is best described by

The value of entropy change, $S_{β} - S_{α}$ (in $J mol^{- 1} K^{- 1}$ ), at 300 K is ______. [Use : $ln 2 = 0.69$ Given : $S_{β} - S_{α} = 0$ at 0 K]

The value of enthalpy change, $H_{β} - H_{α}$ (in $J mol^{- 1}$ ), at 300 K is _______.

The value of standard enthalpy, $Δ H^{⊖}$ (in $kJ mol^{- 1}$ ) for the reaction is________.

The value of $Δ S^{⊖}$ (in $J K^{- 1} mol^{- 1}$ ) for the given reaction, at $1000 K$ is________.

An ideal gas is expanded from $(p_{1}, V_{1}, T_{1})$ to $(p_{2}, V_{2}, T_{2})$ under different conditions. The correct statement(s) among the following is(are)

At $298.2 K$ the relationship between enthalpy of bond dissociation (in $kJ mol^{- 1}$ ) for hydrogen ( $E_{H}$ ) and its isotope, deuterium ( $E_{D}$ ), is best described by