Chemical Thermodynamics — JEE Main PYQs

Gas 'A' undergoes change from state 'X' to state 'Y'. In this process, the heat absorbed and work done by the gas is 10 J and 18 J respectively. Now gas is brought back to state 'X' by another process during which 6 J of heat is evolved. In the reverse process of 'Y' to 'X',

Given below are two statements:

Statement I: For an ideal gas, heat capacity at constant volume is always greater than the heat capacity at constant pressure.

Statement II: In a constant volume process, no work is produced and all the heat withdrawn goes into the chaotic motion and is reflected by a temperature increase of the ideal gas.

In the light of the above statements, choose the correct answer from the options given below

If 3.365 g of ethanol ($l$) is burnt completely in a bomb calorimeter at 298.15 K, the heat produced is 99.472 kJ. The $|\Delta H_f^\circ|$ of ethanol at 298.15 K is ____________ $\times 10^{2}\ \mathrm{kJ\ mol^{-1}}$. (Nearest integer)

Given: Standard enthalpy for combustion of graphite $= -393.5\ \mathrm{kJ\ mol^{-1}}$

Standard enthalpy of formation of water (l) $= -285.8\ \mathrm{kJ\ mol^{-1}}$

Molar mass in $\mathrm{g\ mol^{-1}}$ of C, H, O are 12, 1 and 16 respectively

The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below

$\mathrm{A(g) \rightleftharpoons B(g) + C(g)}$

$\frac{1}{T}\ (\mathrm{K^{-1}})$	$\log_{10} K_p$
0.05	3.5
0.06	2.5
0.07	1.5

The magnitude of $\frac{\Delta H^\circ}{R}$ calculated from the above data is ________. (Nearest integer)

Consider the following data for the reaction

$\mathrm{X_2(g) + Y_2(g) \rightleftharpoons 2XY(g)}$

at 600 K. The $\Delta_r G^{\ominus}$ (in $\mathrm{kJ\ mol^{-1}}$) for the reaction is :

Compound	$\Delta_f H^{\ominus}_{600\,\mathrm{K}}$ ($\mathrm{kJ\ mol^{-1}}$)	$S^{\ominus}_{600\,\mathrm{K}}$ ($\mathrm{J\ mol^{-1}\ K^{-1}}$)
XY(g)	42	200
$\mathrm{X_2(g)}$	8	140
$\mathrm{Y_2(g)}$	80	250

The correct order of molar heat capacities measured at 298 K and 1 bar is :

Arrange the following isothermal processes in order of the magnitude of the work (p $-$ V) involved between states 1 and 2.

A. Expansion in single stage $\mathrm{w_A}$ B. Expansion in multi stages $\mathrm{w_B}$ C. Compression in single stage $\mathrm{w_C}$ D. Compression in multi stages $\mathrm{w_D}$

Choose the correct option.

Consider the reaction $\mathrm{X \rightleftharpoons Y}$ at 300 K. If $\Delta \mathrm{H^{\theta}}$ and K are 28.40 kJ mol$^{-1}$ and $1.8 \times 10^{-7}$ at the same temperature, then the magnitude of $\Delta \mathrm{S^{\theta}}$ for the reaction in J K$^{-1}$ mol$^{-1}$ is ________. (Nearest integer)

(Given : R = 8.3 J K$^{-1}$ mol$^{-1}$, ln 10 = 2.3, log 3 = 0.48, log 2 = 0.30)

Match List - I with List - II.

Given $V_1$ and $V_2$ are initial and final volumes respectively.

List - I (Isothermal process)	List - II (Expression)
A. Reversible expansion	I. $q = 0$
B. Free expansion	II. $q = nRT\ln\dfrac{V_2}{V_1}$
C. Irreversible Compression	III. $w = -p_{\text{ext}}(V_1 - V_2)$
D. Cyclic reversible	IV. $\dfrac{q_{\text{rev}}}{T} = 0$

Choose the correct answer from the options given below :

Consider the reaction

$\mathrm{2H_2S(g) + 3O_2(g) \rightarrow 2H_2O(l) + 2SO_2(g)}$

The magnitude of enthalpy change for the reaction in kJ mol$^{-1}$ is __________. (Nearest integer)

Given :

$\Delta_f H^{\ominus}(\mathrm{H_2S}) = -20.1\ \mathrm{kJ\,mol^{-1}}$

$\Delta_f H^{\ominus}(\mathrm{H_2O}) = -286.0\ \mathrm{kJ\,mol^{-1}}$

$\Delta_f H^{\ominus}(\mathrm{SO_2}) = -297.0\ \mathrm{kJ\,mol^{-1}}$

[Figure: two vessels B and A connected by a stopcock, immersed in a water bath fitted with a thermometer and a stirrer]

Two vessels A and B are connected via stopcock. The vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and is allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel A expands into vessel B and no change in temperature is observed in the thermometer. Which of the following statement is true ?

Arrange the following in order of magnitude of work done by the system/on the system at constant temperature.

(a) $|w_{\text{reversible}}|$ for expansion in infinite stages.

(b) $|w_{\text{irreversible}}|$ for expansion in single stage.

(c) $|w_{\text{reversible}}|$ for compression in infinite stages.

(d) $|w_{\text{irreversible}}|$ for compression in single stage.

Choose the correct answer from the options given below :

Which of the following graphs correctly represents the variation of thermodynamic properties of Haber's process ?

Given :

$\Delta H^{\ominus}_{\mathrm{sub}}\,[\mathrm{C\,(graphite)}] = 710~\mathrm{kJ~mol^{-1}}$

$\Delta_{\mathrm{C-H}}H^{\ominus} = 414~\mathrm{kJ~mol^{-1}}$

$\Delta_{\mathrm{H-H}}H^{\ominus} = 436~\mathrm{kJ~mol^{-1}}$

$\Delta_{\mathrm{C=C}}H^{\ominus} = 611~\mathrm{kJ~mol^{-1}}$

The $\Delta H_f^{\ominus}$ for $\mathrm{CH_2=CH_2}$ is __________ $\mathrm{kJ~mol^{-1}}$ (nearest integer value)

Given below are two statements:

Statement I : When a system containing ice in equilibrium with water (liquid) is heated, heat is absorbed by the system and there is no change in the temperature of the system until whole ice gets melted.

Statement II : At melting point of ice, there is absorption of heat in order to overcome intermolecular forces of attraction within the molecules of water in ice and kinetic energy of molecules is not increased at melting point.

In the light of the above statements, choose the correct answer from the options given below

[Figure: P–V diagram; P/atm on the y-axis (1.00 and 3.00 marked), V/cm$^3$ on the x-axis (1000 and 2000 marked); path: point 1 (1.00 atm, 1000 cm$^3$) up to point 2 (3.00 atm, 1000 cm$^3$), right to point 3 (3.00 atm, 2000 cm$^3$), down to point 4 (1.00 atm, 2000 cm$^3$)]

A perfect gas (0.1 mol) having $\overline{C}_v = 1.50\mathrm{R}$ (independent of temperature) undergoes the above transformation from point 1 to point 4. If each step is reversible, the total work done (w) while going from point 1 to point 4 is (–) __________ J (nearest integer)

[Given : $\mathrm{R} = 0.082\ \mathrm{L\ atm\ K^{-1}\ mol^{-1}}$]

A sample of n-octane (1.14 g) was completely burnt in excess of oxygen in a bomb calorimeter, whose heat capacity is $5\ \mathrm{kJ\ K^{-1}}$. As a result of combustion reaction, the temperature of the calorimeter is increased by 5 K. The magnitude of the heat of combustion of octane at constant volume is __________ $\mathrm{kJ\ mol^{-1}}$ (nearest integer).

Consider the given data :

(a) $\mathrm{HCl(g) + 10\ H_2O(l) \rightarrow HCl.10\ H_2O}$ $\Delta H = -69.01\ \mathrm{kJ\ mol^{-1}}$

(b) $\mathrm{HCl(g) + 40\ H_2O(l) \rightarrow HCl.40\ H_2O}$ $\Delta H = -72.79\ \mathrm{kJ\ mol^{-1}}$

Choose the correct statement :

Total enthalpy change for freezing of 1 mol of water at 10°C to ice at $-10$°C is __________

(Given: $\Delta_{\text{fus}}H = x$ kJ/mol

$C_p[\mathrm{H_2O(l)}] = y\ \mathrm{J\ mol^{-1}\ K^{-1}}$

$C_p[\mathrm{H_2O(s)}] = z\ \mathrm{J\ mol^{-1}\ K^{-1}}$

The correct statement amongst the following is :

The hydration energies of $\mathrm{K^+}$ and $\mathrm{Cl^-}$ are $-x$ and $-y$ kJ/mol respectively. If lattice energy of KCl is $-z$ kJ/mol, then the heat of solution of KCl is :

Resonance in $\mathrm{X_2Y}$ can be represented as

$$\overset{\ominus}{\ddot{X}}{=}X{=}\overset{\oplus}{\ddot{Y}} \longleftrightarrow \overset{\oplus}{X}{\equiv}X{-}\overset{\ominus}{\ddot{Y}}{:}$$

The enthalpy of formation of $\mathrm{X_2Y}$ $\left(\mathrm{X{=}X}(g) + \frac{1}{2}\mathrm{Y{=}Y}(g) \rightarrow \mathrm{X_2Y}(g)\right)$ is 80 kJ mol$^{-1}$. The magnitude of resonance energy of $\mathrm{X_2Y}$ is __________ kJ mol$^{-1}$ (nearest integer value)

Given : Bond energies of $\mathrm{X \equiv X}$, $\mathrm{X = X}$, $\mathrm{Y = Y}$ and $\mathrm{X = Y}$ are 940, 410, 500 and 602 kJ mol$^{-1}$ respectively.

valence X: 3 , Y: 2

A liquid when kept inside a thermally insulated closed vessel at $25°\mathrm{C}$ was mechanically stirred from outside. What will be the correct option for the following thermodynamic parameters ?

Consider the following cases of standard enthalpy of reaction $\left(\Delta H_r^{\circ}\ \text{in kJ mol}^{-1}\right)$

$$\mathrm{C_2H_6(g)} + \frac{7}{2}\mathrm{O_2(g)} \rightarrow 2\mathrm{CO_2(g)} + 3\mathrm{H_2O(l)} \quad \Delta H_1^{\circ} = -1550$$

$$\mathrm{C(graphite)} + \mathrm{O_2(g)} \rightarrow \mathrm{CO_2(g)} \quad \Delta H_2^{\circ} = -393.5$$

$$\mathrm{H_2(g)} + \frac{1}{2}\mathrm{O_2(g)} \rightarrow \mathrm{H_2O(l)} \quad \Delta H_3^{\circ} = -286$$

The magnitude of $\Delta H^{\circ}_{f\,\mathrm{C_2H_6(g)}}$ is __________ kJ mol$^{-1}$ (Nearest integer).

Ice at $-5°\mathrm{C}$ is heated to become vapor with temperature of $110°\mathrm{C}$ at atmospheric pressure. The entropy change associated with this process can be obtained from

The standard enthalpy and standard entropy of decomposition of $\mathrm{N_2O_4}$ to $\mathrm{NO_2}$ are 55.0 kJ mol$^{-1}$ and 175.0 J/K/mol respectively. The standard free energy change for this reaction at 25°C in J mol$^{-1}$ is _____ (Nearest integer)

The effect of temperature on spontaneity of reactions are represented as :

	$\Delta H$	$\Delta S$	Temperature	Spontaneity
(A)	$+$	$-$	any T	Non spontaneous
(B)	$+$	$+$	low T	spontaneous
(C)	$-$	$-$	low T	Non spontaneous
(D)	$-$	$+$	any T	spontaneous

The incorrect combinations are :

The bond dissociation enthalpy of $X_2$, $\Delta H^{\circ}_{\text{bond}}$ calculated from the given data is ________ $\mathrm{kJ\ mol^{-1}}$. (Nearest integer)

$$\mathrm{M^{+}X^{-}(s) \rightarrow M^{+}(g) + X^{-}(g)} \quad \Delta H^{\circ}_{\text{lattice}} = 800\ \mathrm{kJ\ mol^{-1}}$$

$$\mathrm{M(s) \rightarrow M(g)} \quad \Delta H^{\circ}_{\text{sub}} = 100\ \mathrm{kJ\ mol^{-1}}$$

$$\mathrm{M(g) \rightarrow M^{+}(g) + e^{-}(g)} \quad \Delta H^{\circ}_{i} = 500\ \mathrm{kJ\ mol^{-1}}$$

$$\mathrm{X(g) + e^{-}(g) \rightarrow X^{-}(g)} \quad \Delta H^{\circ}_{\text{eg}} = -300\ \mathrm{kJ\ mol^{-1}}$$

$$\mathrm{M(s) + \tfrac{1}{2}X_2(g) \rightarrow M^{+}X^{-}(s)} \quad \Delta H^{\circ}_{f} = -400\ \mathrm{kJ\ mol^{-1}}$$

[Given : $\mathrm{M^{+}X^{-}}$ is a pure ionic compound and X forms a diatomic molecule $X_2$ in gaseous state]

Let us consider an endothermic reaction which is non-spontaneous at the freezing point of water. However, the reaction is spontaneous at boiling point of water. Choose the correct option.

Standard entropies of $\mathrm{X_2}$, $\mathrm{Y_2}$ and $\mathrm{XY_5}$ are 70, 50 and 110 J K$^{-1}$ mol$^{-1}$ respectively. The temperature in Kelvin at which the reaction $$\frac{1}{2}\mathrm{X_2} + \frac{5}{2}\mathrm{Y_2} \rightleftharpoons \mathrm{XY_5} \qquad \Delta H^{\ominus} = -35\ \mathrm{kJ\ mol^{-1}}$$ will be at equilibrium is ______ (nearest integer).

Which of the following mixing of 1M base and 1M acid leads to the largest increase in temperature ?

$$\mathrm{S(g)} + \frac{3}{2}\mathrm{O_2(g)} \rightarrow \mathrm{SO_3(g)} + 2x\ \mathrm{kcal}$$

$$\mathrm{SO_2(g)} + \frac{1}{2}\mathrm{O_2(g)} \rightarrow \mathrm{SO_3(g)} + y\ \mathrm{kcal}$$

The heat of formation of $\mathrm{SO_2(g)}$ is given by :

The formation enthalpies, $\Delta H_f^{\ominus}$ for $\mathrm{H_{(g)}}$ and $\mathrm{O_{(g)}}$ are 220.0 and 250.0 $\mathrm{kJ\ mol^{-1}}$, respectively, at 298.15 K, and $\Delta H_f^{\ominus}$ for $\mathrm{H_2O_{(g)}}$ is $-242.0\ \mathrm{kJ\ mol^{-1}}$ at the same temperature. The average bond enthalpy of the $\mathrm{O{-}H}$ bond in water at 298.15 K is _______ $\mathrm{kJ\ mol^{-1}}$ (nearest integer).

An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path $A \to B \to C \to D \to A$ as shown in the three cases above.

Choose the correct option regarding $\Delta U$ :

[Figure: three $V$ (dm$^3$) vs $p$ (kPa) plots — Case-I (curved loop A-B-C-D), Case-II (rectangular loop), Case-III (rhombus/diamond loop), each a closed cyclic path A→B→C→D→A]

Consider the following data :

Heat of formation of $\mathrm{CO_2(g)} = -393.5\ \mathrm{kJ\ mol^{-1}}$ Heat of formation of $\mathrm{H_2O(l)} = -286.0\ \mathrm{kJ\ mol^{-1}}$ Heat of combustion of benzene $= -3267.0\ \mathrm{kJ\ mol^{-1}}$

The heat of formation of benzene is __________ $\mathrm{kJ\ mol^{-1}}$.

(Nearest integer)

The enthalpy of formation of ethane ($\mathrm{C_2H_6}$) from ethylene by addition of hydrogen where the bond-energies of $\mathrm{C-H}$, $\mathrm{C-C}$, $\mathrm{C{=}C}$, $\mathrm{H-H}$ are 414 kJ, 347 kJ, 615 kJ and 435 kJ respectively is $-$________ kJ

Three moles of an ideal gas are compressed isothermally from 60 L to 20 L using constant pressure of 5 atm. Heat exchange Q for the compression is – ________ Lit. atm.

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R)

Assertion (A) : Enthalpy of neutralisation of strong monobasic acid with strong monoacidic base is always $-57~\mathrm{kJ~mol^{-1}}$

Reason (R) : Enthalpy of neutralisation is the amount of heat liberated when one mole of $\mathrm{H^+}$ ions furnished by acid combine with one mole of $\mathrm{{}^-OH}$ ions furnished by base to form one mole of water.

In the light of the above statements, choose the correct answer from the options given below.

The heat of combustion of solid benzoic acid at constant volume is $-321.30$ kJ at $27\,°\mathrm{C}$. The heat of combustion at constant pressure is $(-321.30 - x\mathrm{R})$ kJ, the value of $x$ is ________.

Combustion of 1 mole of benzene is expressed at

$$\mathrm{C_6H_6(l) + \frac{15}{2} O_2(g) \rightarrow 6\,CO_2(g) + 3\,H_2O(l)}.$$

The standard enthalpy of combustion of 2 mol of benzene is $-\,'x'$ kJ.

$x =$ ________.

Given :

1. standard Enthalpy of formation of 1 mol of $\mathrm{C_6H_6(l)}$, for the reaction $\mathrm{6\,C\,(graphite) + 3\,H_2(g) \rightarrow C_6H_6(l)}$ is $48.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$.

2. Standard Enthalpy of formation of 1 mol of $\mathrm{CO_2(g)}$, for the reaction $\mathrm{C\,(graphite) + O_2(g) \rightarrow CO_2(g)}$ is $-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$.

3. Standard and Enthalpy of formation of 1 mol of $\mathrm{H_2O(l)}$, for the reaction $\mathrm{H_2(g) + \frac{1}{2} O_2(g) \rightarrow H_2O\,(l)}$ is $-286 \mathrm{~kJ} \mathrm{~mol}^{-1}$.

An ideal gas, $\bar{C}_v = \frac{5}{2}R$, is expanded adiabatically against a constant pressure of 1 atm untill it doubles in volume. If the initial temperature and pressure is 298 K and 5 atm, respectively then the final temperature is _________ K (nearest integer).

[$\bar{C}_v$ is the molar heat capacity at constant volume]

For the reaction at 298 K, $\mathrm{2A + B \to C}$. $\Delta H = 400\ \mathrm{kJ\ mol^{-1}}$ and $\Delta S = 0.2\ \mathrm{kJ\ mol^{-1}\ K^{-1}}$. The reaction will become spontaneous above ________ K.

[Figure: vertical cylinder fitted with a piston; lower position A at 10 L and upper position B at 90 L]

Consider the figure provided.

1 mol of an ideal gas is kept in a cylinder, fitted with a piston, at the position A, at 18° C. If the piston is moved to position B, keeping the temperature unchanged, then 'x' L atm work is done in this reversible process.

x = __________ L atm. (nearest integer)

[Given : Absolute temperature = °C + 273.15, R = 0.08206 $\mathrm{L\ atm\ mol^{-1}\ K^{-1}}$]

$\Delta_{\mathrm{vap}}\mathrm{H^{\ominus}}$ for water is $+40.79\ \mathrm{kJ\ mol^{-1}}$ at 1 bar and 100 $^{\circ}\mathrm{C}$. Change in internal energy for this vapourisation under same condition is ________ $\mathrm{kJ\ mol^{-1}}$. (Integer answer)

(Given $R = 8.3\ \mathrm{JK^{-1}\ mol^{-1}}$)

The heat of solution of anhydrous $\mathrm{CuSO_4}$ and $\mathrm{CuSO_4 \cdot 5H_2O}$ are $-70\ \mathrm{kJ\ mol^{-1}}$ and $+12\ \mathrm{kJ\ mol^{-1}}$ respectively. The heat of hydration of $\mathrm{CuSO_4}$ to $\mathrm{CuSO_4 \cdot 5H_2O}$ is $-x$ kJ. The value of $x$ is ________. (nearest integer).

When equal volume of 1M HCl and 1M $\mathrm{H_2SO_4}$ are separately neutralised by excess volume of 1M NaOH solution, $x$ and $y$ kJ of heat is liberated respectively. The value of $y/x$ is ________.

When $\Delta H_{\mathrm{vap}} = 30$ kJ/mol and $\Delta S_{\mathrm{vap}} = 75$ J mol$^{-1}$K$^{-1}$, then the temperature of vapour, at one atmosphere is ________ K.

Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following :

For a certain reaction at 300K, $K = 10$, then $\Delta G^\circ$ for the same reaction is $-$________ $\times 10^{-1}\ \mathrm{kJ\ mol^{-1}}$. (Given $R = 8.314\ \mathrm{JK^{-1}\ mol^{-1}}$)

If three moles of an ideal gas at 300 K expand isothermally from $30\ \mathrm{dm^3}$ to $45\ \mathrm{dm^3}$ against a constant opposing pressure of 80 kPa, then the amount of heat transferred is ________ J.

Which of the following is not correct?

[Figure: P–V diagram with V ($\mathrm{dm^3}$) on the y-axis and P (kPa) on the x-axis; point A at (10 kPa, 10 $\mathrm{dm^3}$), point B at (10 kPa, 30 $\mathrm{dm^3}$), point C at (30 kPa, 10 $\mathrm{dm^3}$); path A$\to$B vertical (constant P), B$\to$C straight diagonal, C$\to$A horizontal (constant V)]

An ideal gas undergoes a cyclic transformation starting from the point A and coming back to the same point by tracing the path A$\to$B$\to$C$\to$A as shown in the diagram above. The total work done in the process is ________ J.

Two reactions are given below:

$$\mathrm{2Fe_{(s)} + \tfrac{3}{2}O_{2(g)} \rightarrow Fe_2O_{3(s)}},\quad \Delta \mathrm{H^\circ = -822\ kJ/mol}$$ $$\mathrm{C_{(s)} + \tfrac{1}{2}O_{2(g)} \rightarrow CO_{(g)}},\quad \Delta \mathrm{H^\circ = -110\ kJ/mol}$$

Then enthalpy change for following reaction $\mathrm{3C_{(s)} + Fe_2O_{3(s)} \rightarrow 2Fe_{(s)} + 3CO_{(g)}}$ is _________ kJ/mol.

Consider the following reaction at 298 K. $\frac{3}{2}\mathrm{O_{2(g)}} \rightleftharpoons \mathrm{O_{3(g)}}$. $\mathrm{K_P} = 2.47 \times 10^{-29}$. $\Delta_r G^{\ominus}$ for the reaction is ________ kJ. (Given $R = 8.314\,\mathrm{JK^{-1}\,mol^{-1}}$)

If 5 moles of an ideal gas expands from 10 L to a volume of 100 L at 300 K under isothermal and reversible condition then work, w, is $-x$ J. The value of $x$ is _________.

(Given $\mathrm{R} = 8.314\ \mathrm{J\ K^{-1}\ mol^{-1}}$)