The work done when 1 mole of gas expands reversibly and isothermally from a pressure of 5 atm to 1 atm at 300 K is:
(Given log 5 = 0.6989 and R = 8.314 J K^-1 mol^-1)

Which one among the following is the correct option for right relationship between C_p and C_V for one mole of an ideal gas?

1. ${\mathrm{C}}_{\mathrm{P}}={\mathrm{RC}}_{\mathrm{V}}$

2. ${\mathrm{C}}_{\mathrm{V}}={\mathrm{RC}}_{\mathrm{P}}$

3. ${\mathrm{C}}_{\mathrm{P}}+{\mathrm{C}}_{\mathrm{V}}=\mathrm{R}$

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

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)

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

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.  $q=0,$ $∆T=0$ $and$ $w=0$