Which of the following reactions has the least difference between the change in enthalpy (∆H) and the change in internal energy (∆E) at a given temperature?

1. \(2 \mathrm{SO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{SO}_3(\mathrm{~g})\)
2. \(\mathrm{CaCO}_3(s) \rightarrow \mathrm{CaO}(s)+\mathrm{CO}_2(g)\)
3. \(\mathrm{NH}_4 \mathrm{SH} (s) ~~\rightarrow ~\mathrm{NH}_3(g)+\mathrm{H}_2 \mathrm{~S}(g)\)
4. \(2 \mathrm{NH}_3 (g) ~\rightarrow ~\mathrm{N}_2(g)+3 \mathrm{H}_2(g)\)

The standard enthalpy of vaporization ${∆}_{\mathrm{vap}}{\mathrm{H}}^{\mathrm{o}}$ for water at 100 ^oC is 40.66 kJ mol^–1. The internal energy of vaporization of water at 100 ^oC (in kJ mol^–1) is: 
(Assume water vapour behaves like an ideal gas.)

For the isothermal reversible expansion of an ideal gas: 

1. $∆\mathrm{H}>0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>∆\mathrm{U}=0$

2. $∆\mathrm{H}>0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>∆\mathrm{U}<0$

3. $∆\mathrm{H}=0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>∆\mathrm{U}=0$

4. $∆\mathrm{H}=0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>∆\mathrm{U}>0$

In an exothermic reaction, heat is evolved, and the system loses heat to the surrounding. The correct choice among the following for such a system are-

(a) q_p will be negative

(b) ${∆}_{\mathrm{r}}\mathrm{H}$ will be negative

(c) q_p will be positive

(d) ${∆}_{\mathrm{r}}\mathrm{H}$ will be positive

1. (a, b)

2. (b, c)

3. (c, d)

4. (a, d)

What is the change in internal energy for 5 moles of an ideal gas when it undergoes reversible compression from 100 K to 200 K?
[Given C_V = 28 J K^–1 mol^–1]​​​​​​