Chemical Thermodynamics

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

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

Consider the following data.

(i) $\ce{2Al(s) + 6HCl(aq) -> Al2Cl6(aq) + 3H2(g)}$ + 1200 kJ/mol

(ii) $\ce{H2(g) + Cl2(g) -> 2HCl(g)}$ + 164 kJ/mol.

(iii) $\ce{HCl(g) + aq -> HCl(aq)}$ + 83 kJ/mol.

(iv) $\ce{Al2Cl6(s) + aq -> Al2Cl6(aq)}$ + 663 kJ/mol

The enthalpy of formation of anhydrous solid $\ce{Al2Cl6}$ is :

At the transition temperature $T$, $\ce{A <=> B}$ and $\Delta G^0=105-35\log T$ where A and B are two states of substance X. The transition temperature in °C when pressure is 1 atm is ________. (Nearest integer)

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',

Consider the following two half-cell reactions along with the standard reduction potential given :
$$\ce{CO2 + 6H+ + 6e- -> CH3OH + H2O}\qquad E^\circ_\text{red}=0.02\ \mathrm V$$
$$\ce{1/2O2 + 2H+ + 2e- -> H2O}\qquad E^\circ_\text{red}=1.23\ \mathrm V$$
A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of 1 bar pressure and 298 K temperature. The fuel cell works with 80% efficiency. If the work derived from the cell using 1 mol of $\ce{CH3OH}$ is used to compress an ideal gas isothermally against a constant pressure of 1 kPa, then the change in the volume of the gas, $\Delta V$ = ________ m³. (nearest integer)
Given : $F=96500$ C mol$^{-1}$

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 ________ $\times10^2$ kJ mol$^{-1}$. (Nearest integer)
Given: Standard enthalpy for combustion of graphite = −393.5 kJ mol$^{-1}$
Standard enthalpy of formation of water (l) = −285.8 kJ mol$^{-1}$
Molar mass in 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

$\ce{A(g) <=> B(g) + C(g)}$

$\frac{1}{T}$ (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

$\ce{X2(g) + Y2(g) <=> 2XY(g)}$

at 600 K. The $\Delta_rG^\circ$ (in kJ mol$^{-1}$) for the reaction is :

Compound	$\Delta_fH^\circ_{600\,\mathrm K}$ (kJ mol$^{-1}$)	$S^\circ_{600\,\mathrm K}$ (J mol$^{-1}$ K$^{-1}$)
XY(g)	42	200
X₂(g)	8	140
Y₂(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 $w_A$

B. Expansion in multi stages $w_B$

C. Compression in single stage $w_C$

D. Compression in multi stages $w_D$

Choose the correct option.

Consider the reaction $\ce{X <=> Y}$ at 300 K. If $\Delta H^\circ$ and K are 28.40 kJ mol$^{-1}$ and $1.8\times10^{-7}$ at the same temperature, then the magnitude of $\Delta S^\circ$ 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.

Choose the correct answer from the options given below :

Consider the reaction

$\ce{2H2S(g) + 3O2(g) -> 2H2O(l) + 2SO2(g)}$

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

Given : $\Delta_fH^\ominus(\ce{H2S})=-20.1$ kJ mol$^{-1}$, $\Delta_fH^\ominus(\ce{H2O})=-286.0$ kJ mol$^{-1}$, $\Delta_fH^\ominus(\ce{SO2})=-297.0$ kJ mol$^{-1}$

Considering ideal gas behavior, the expansion work done (in kJ) when 144 g of water is electrolyzed completely under constant pressure at 300 K is _____.

Use: Universal gas constant (R) $= 8.3\ \mathrm{J\,K^{-1}\,mol^{-1}}$; Atomic mass (in amu): H = 1, O = 16

Consider the following volume−temperature (V−T) diagram for the expansion of 5 moles of an ideal monoatomic gas.

Considering only P-V work is involved, the total change in enthalpy (in Joule) for the transformation of state in the sequence X→Y→Z is _____.

[Use the given data: Molar heat capacity of the gas for the given temperature range, $C_{V,m} = 12\,\mathrm{J\,K^{-1}\,mol^{-1}}$ and gas constant, $R = 8.3\,\mathrm{J\,K^{-1}\,mol^{-1}}$]

One mole of an ideal monoatomic gas undergoes two reversible processes ($\mathrm{A}\to\mathrm{B}$ and $\mathrm{B}\to\mathrm{C}$) as shown in the given figure:

$\mathrm{A}\to\mathrm{B}$ is an adiabatic process. If the total heat absorbed in the entire process ($\mathrm{A}\to\mathrm{B}$ and $\mathrm{B}\to\mathrm{C}$) is $RT_2\ln 10$, the value of $2\log V_3$ is _____.

[Use, molar heat capacity of the gas at constant pressure, $C_{\mathrm{p,m}} = \frac52 R$]

The value of entropy change, $S_\beta - S_\alpha$ (in $\mathrm{J\,mol^{-1}\,K^{-1}}$), at 300 K is _____.

[Use: $\ln 2 = 0.69$. Given: $S_\beta - S_\alpha = 0$ at 0 K]

The value of enthalpy change, $H_\beta - H_\alpha$ (in $\mathrm{J\,mol^{-1}}$), at 300 K is _____.