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)
1. zero J
2. 150 J
3. +4014.6 J
4. -4014.6 J

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

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

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