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

Under the isothermal condition, a gas at \(300 \mathrm{~K}\) expands from \(0.1 \mathrm{~L}\) to \(0.25 \mathrm{~L}\) against a constant external pressure of 2 bar. The work done by the gas is:

What is the amount of work done by an ideal gas, if the gas expands isothermally from \(10^{-3}~m^3\) to \(10^{-2}~m^3\) at \(300~K\)against a constant pressure of \(10^{5}~Nm^{-2}\)?

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

AB$\to$Isothermal expansion

AC$\to$Adiabatic expansion

Which of the following options is not correct?

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)

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 $w=0$

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:

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?

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