What is the correct relationship between changes in enthalpy and internal energy within the following options?
1. \(\Delta \mathrm{H}+\Delta \mathrm{U}=\Delta \mathrm{nR} \)
2. \(\Delta \mathrm{H}=\Delta \mathrm{U -\Delta n_gRT}\)
3. \(\Delta \mathrm{H}=\Delta \mathrm{U+\Delta n_gRT }\)
4. \(\Delta \mathrm{H} -\Delta \mathrm{U=-\Delta n_gRT}\)

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

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

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. \(C_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}\)

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?

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

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 $w=0$