The correct option for free expansion of an ideal gas under adiabatic condition is:

1.  $q=0,$ $∆T<0$ and $w>0$

2.  $q<0,$ $∆T=0$ and $w=0$

3.  $q>0,$ $∆T>0$ and $w>0$

4.  $q=0,$ $∆T=0$ and $w=0$

For the reaction, 2Cl(g) $\to$ Cl₂(g), the correct option is:

1. ${∆}_{\mathrm{r}}\mathrm{H}>0 \mathrm{and} {∆}_{\mathrm{r}}\mathrm{S}<0$

2. ${∆}_{\mathrm{r}}\mathrm{H}<0 \mathrm{and} {∆}_{\mathrm{r}}\mathrm{S}>0$

3. ${∆}_{\mathrm{r}}\mathrm{H}<0 \mathrm{and} {∆}_{\mathrm{r}}\mathrm{S}<0$

4. ${∆}_{\mathrm{r}}\mathrm{H}>0 \mathrm{and} {∆}_{\mathrm{r}}\mathrm{S}>0$

Hydrolysis of sucrose is given by the following reaction

Sucrose + H₂O $\rightleftharpoons$ Glucose + Fructose

If the equilibrium constant (K_c) is 2$\times$10¹³ at 300 K, the value of ${∆}_r{G}^{⊝}$ at the same temperature will be:

1. 8.314 J mol^–1 K^–1$\times$300 K$\times$ln (2$\times$10¹³)

2. 8.314 J mol^–1 K^–1$\times$300 K$\times$ln (3$\times$10¹³)

3. –8.314 J mol^–1 K^–1$\times$300 K$\times$ln (4$\times$10¹³)

4. –8.314 J mol^–1 K^–1$\times$300 K$\times$ln (2$\times$10¹³)

If for a certain reaction ${∆}_{r}H$ is 30 kJ mol^–1 at 450 K, the value of ${∆}_{r}S$ (in JK^–1 mol^–1) for which the same reaction will be spontaneous at the same temperature is:

1. 70

2. –33

3. 33

4. –70

At standard conditions, if the change in the enthalpy for the following reaction is –109 kJ mol^–1 
H_2(g)+Br_2(g)$\to$2HBr_(g) and the bond energy of H₂ and Br₂ is 435 kJ mol^–1 and 192 kJ mol^–1 respectively, what is the bond energy (in kJ mol^–1) of HBr?

Reversible expansion of an ideal gas under isothermal and adiabatic conditions are as shown in the figure:

 

AB$\to$Isothermal expansion

AC$\to$Adiabatic expansion

Which of the following options is not correct?

1. $∆S_{isothermal}>∆S_{adiabatic}$

2. $T_A=T_B$

3. $W_{isothermal}>W_{adiabatic}$

4. $T_C>T_A$

An ideal gas expands isothermally from ${10}^{-3}{m}^3 to {10}^{-2} m^3$ at 300 K against a constant pressure of ${10}^5 N{m}^{-2}$. The work done by  the gas is:

Which of the following options correctly represents the relationship between \(C_p \text { and } C_V\) for one mole of an ideal gas?

1. \(C_P=R C_V \)
2. \(C_V=RC_P \)
3. \(C_P+C_V=R \)
4. \(C_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}\)

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

1. $∆\mathrm{U}=0, ∆{\mathrm{S}}_{\mathrm{total}}\ne 0$

2. $∆\mathrm{U}\ne 0, ∆{\mathrm{S}}_{\mathrm{total}}=0$

3. $∆\mathrm{U}=0, ∆{\mathrm{S}}_{\mathrm{total}}=0$

4. $∆\mathrm{U}\ne 0, ∆{\mathrm{S}}_{\mathrm{total}}\ne 0$

A process among the following shows decrease in entropy is :

1. \(2 \text H \left(g\right)\) \(\rightarrow\) \(\text H_{2} \left(g\right)\)

2. Evaporation of water

3. Expansion of a gas at a constant temperature

4. Sublimation of solid to gas