Entropy and Free Energy

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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 2021

LEVELJEE Advanced

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 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 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 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 Main

Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the minimum temperature (in K) at which the reduction of cassiterite by coke would take place. At 298 K : $Δ_{f} H^{\circ} (SnO_{2} (s)) = - 581.0 kJ mol^{- 1}$ , $Δ_{f} H^{\circ} (CO_{2} (g)) = - 394.0 kJ mol^{- 1}$ $S^{\circ} (SnO_{2} (s)) = 56.0 J K^{- 1} mol^{- 1}$ , $S^{\circ} (Sn (s)) = 52.0 J K^{- 1} mol^{- 1}$ , $S^{\circ} (C (s)) = 6.0 J K^{- 1} mol^{- 1}$ , $S^{\circ} (CO_{2} (g)) = 210.0 J K^{- 1} mol^{- 1}$ . Assume that the enthalpies and the entropies are temperature independent.

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 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 : $1 J = 1 kg m^{2} s^{- 2}$ ; $1 Pa = 1 kg m^{- 1} s^{- 2}$ ; $1 bar = 1 0^{5} Pa$ ]

For the process $H_{2} O (l) \to H_{2} O (g)$ at $T = 10 0^{\circ} C$ and $1$ atmosphere pressure, the correct choice is

(A)

Δ S_{system} > 0

and

Δ S_{surroundings} > 0

(B)

Δ S_{system} > 0

and

Δ S_{surroundings} < 0

(C)

Δ S_{system} < 0

and

Δ S_{surroundings} > 0

(D)

Δ S_{system} < 0

and

Δ S_{surroundings} < 0

JEE Main 2021

LEVELJEE Main

For the reaction, $A (g) ⟶ B (g)$ , the value of the equilibrium constant at $300 K$ and $1 atm$ is equal to $100.0$ . The value of $Δ_{r} G$ for the reaction at $300 K$ and $1 atm$ in $J mol^{- 1}$ is $- x R$ , where $x$ is ......... . (Rounded off to the nearest integer) ( $R = 8.31 J mol^{- 1} K^{- 1}$ and $ln 10 = 2.3$ )

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 2019

LEVELJEE Main

The standard reaction Gibbs energy for a chemical reaction at an absolute temperature $T$ is given by, $Δ_{r} G^{\circ} = A - B T$ Where $A$ and $B$ are non-zero constants. Which of the following is true about this reaction?

(A)

Endothermic if,

A < 0

and

B > 0

(B)

Exothermic if,

B < 0

(C)

Exothermic if,

A > 0

and

B < 0

(D)

Endothermic if,

A > 0

JEE Main 2021

LEVELJEE Main

The incorrect expression among the following is

(A)

\frac{Δ G _{System}}{Δ S _{Total}} = - T

(at constant

p

)

(B)

ln k = \frac{Δ H ^{\circ} - T Δ S ^{\circ}}{R T}

(C)

k = e^{- \frac{Δ G ^{\circ}}{R T}}

(D)

For isothermal process,

W_{reversible} = - n R T ln \frac{V _{f}}{V _{i}}

JEE Main 2020

LEVELJEE Advanced

For a dimerisation reaction $2 A (g) ⟶ A_{2} (g)$ , at $298 K$ , $Δ U^{⊖} = - 20 kJ mol^{- 1}$ , $Δ S^{⊖} = - 30 JK^{- 1} mol^{- 1}$ , then the $Δ G^{⊖}$ will be ......... $J$ .

JEE Main 2021

LEVELJEE Main

During which of the following processes, does entropy decrease ? A. Freezing of water to ice at $0^{\circ} C$ . B. Freezing of water to ice at $- 1 0^{\circ} C$ . C. $N_{2} (g) + 3 H_{2} (g) ⟶ 2 NH_{3} (g)$ D. Adsorption of $CO (g)$ and lead surface. E. Dissolution of $NaCl$ in water.

A reaction is non-spontaneous at the freezing point of water but is spontaneous at the boiling point of water, then

(A)

Δ H = + ve, Δ S = + ve

(B)

Δ H = - ve, Δ S = - ve

(C)

Δ H = - ve, Δ S = + ve

(D)

Δ H = + ve, Δ S = - ve

JEE Main 2019

LEVELJEE Main

For the equilibrium, $2 H_{2} O ⇌ H_{3} O^{+} + O H^{-}$ , the value of $Δ G^{\circ}$ at $298 K$ is approximately

(A)

- 80 kJ mol^{- 1}

(B)

100 kJ mol^{- 1}

(C)

80 kJ mol^{- 1}

(D)

- 100 kJ mol^{- 1}

JEE Main 2019

LEVELJEE Main

The process with negative entropy change is

(A)

synthesis of ammonia from

N_{2}

and

H_{2}

(B)

dissociation of

C a S O_{4} (s)

C a O (s)

and

S O_{3} (g)

(C)

dissolution of iodine in water

(D)

sublimation of dry ice

JEE Main 2020

LEVELJEE Main

The true statement amongst the following is

(A)

S

is not a function of temperature but

Δ S

is a function of temperature.

(B)

Both

Δ S

and

S

are functions of temperature.

(C)

Both

S

and

Δ S

are not functions of temperature.

(D)

S

is a function of temperature but

Δ S

is not a function of temperature.

LEVELJEE Main

For a spontaneous reaction, the $Δ G$ , equilibrium constant ( $K$ ) and $E_{cell}^{\circ}$ will be respectively

(A)

- ve, > 1, - ve

(B)

- ve, < 1, - ve

(C)

+ ve, > 1, - ve

(D)

- ve, > 1, + ve

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________.

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 _______.

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

List-I

List-II

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; } For the process H2​O(l)→H2​O(g) at T=100∘C and 1 atmosphere pressure, the correct choice is

The incorrect expression among the following is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For a dimerisation reaction 2A(g)⟶A2​(g), at 298 K, ΔU⊖=−20 kJ mol−1, ΔS⊖=−30 JK−1 mol−1, then the ΔG⊖ will be ......... J.

A reaction is non-spontaneous at the freezing point of water but is spontaneous at the boiling point of water, then

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For the equilibrium, 2H2​O⇌H3​O++OH−, the value of ΔG∘ at 298 K is approximately

The process with negative entropy change is

The true statement amongst the following is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For a spontaneous reaction, the ΔG, equilibrium constant (K) and Ecell∘​ will be respectively

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________.

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 _______.

For the process $H_{2} O (l) \to H_{2} O (g)$ at $T = 10 0^{\circ} C$ and $1$ atmosphere pressure, the correct choice is

For a dimerisation reaction $2 A (g) ⟶ A_{2} (g)$ , at $298 K$ , $Δ U^{⊖} = - 20 kJ mol^{- 1}$ , $Δ S^{⊖} = - 30 JK^{- 1} mol^{- 1}$ , then the $Δ G^{⊖}$ will be ......... $J$ .

For the equilibrium, $2 H_{2} O ⇌ H_{3} O^{+} + O H^{-}$ , the value of $Δ G^{\circ}$ at $298 K$ is approximately

For a spontaneous reaction, the $Δ G$ , equilibrium constant ( $K$ ) and $E_{cell}^{\circ}$ will be respectively