Consider the given reaction:
\(2 \mathrm{Cl}(\mathrm{~g}) \rightarrow \mathrm{Cl}_2(\mathrm{~g})\)

What are the values of \(∆\mathrm{H}\) and \(∆\mathrm{S}\), respectively?
1. \(\Delta \mathrm{H}=0, \Delta \mathrm{~S}=-\mathrm{ve}\)
2. \(\Delta \mathrm{H}=0, \Delta \mathrm{~S}=0\)
3. \(\Delta \mathrm{H}=-\mathrm{ve}, \Delta \mathrm{~S}=-\mathrm{ve}\)
4. \(\Delta \mathrm{H}=+\mathrm{ve}, \Delta \mathrm{~S}=+\mathrm{ve}\)

 For the reaction A + B → C + D + q (kJ/mol), entropy change is positive. The reaction will be :

1. Possible only at high temperature

2. Possible only at low temperature

3. Not possible at any temperature

4. Possible at any temperature

The enthalpy of combustion of methane, graphite, and dihydrogen at 298 K are, –890.3 kJ mol^–1 , –393.5 kJ mol-¹, and –285.8 kJ mol^–1 respectively. The enthalpy of formation of CH₄(g) is:

Which among the following statements about open, closed, and isolated systems is correct?

What happens to the specific heat of a gas when its volume is reduced to half of its initial value?

2. Less than Δ_fU°
3. Greater than Δ_fU°
4. Equal to Δ_fU°

Calculate the correct values of heat transfer (q), change in temperature (ΔT), and work done (W) for the free expansion of an ideal gas under adiabatic conditions.

The pressure-volume work for an ideal gas can be calculated by using the expression $\mathrm{W}={\int }_{{\mathrm{V}}_{\mathrm{i}}}^{{\mathrm{V}}_{\mathrm{f}}}{\mathrm{p}}_{\mathrm{ext}}d\mathrm{V}$.

The work can also be calculated from the pV-plot by using the area under the curve within the specified limits.
An ideal gas is compressed (a) reversibly or (b) irreversibly from volume ${\mathrm{V}}_{\mathrm{i}}$ to ${\mathrm{V}}_{\mathrm{f}}$.
The correct option is:

1. $\mathrm{W}<mspace\; width="1em"></mspace>\left(\mathrm{reversible}\right)=\mathrm{W}<mspace\; width="1em"></mspace>\left(\mathrm{irreversible}\right)$

2. $\mathrm{W}<mspace\; width="1em"></mspace>\left(\mathrm{reversible}\right)<\mathrm{W}\hspace{0.17em}\left(\mathrm{irreversible}\right)$

3. $\mathrm{W}<mspace\; width="1em"></mspace>(\mathrm{reversible})\; >\mathrm{W}<mspace\; width="1em"></mspace>(\mathrm{irreversible})$

4. $\mathrm{W}<mspace\; width="1em"></mspace>\left(\mathrm{reversible}\right)=\mathrm{W}<mspace\; width="1em"></mspace>\left(\mathrm{irreversible}\right)+{\mathrm{p}}_{\mathrm{ext}}.∆\mathrm{V}$

The entropy change can be calculated by using the expression $∆\mathrm{S}=\frac{{\mathrm{q}}_{\mathrm{rev}}}{\mathrm{T}}$. When water freezes in a glass beaker, the correct statement among the following is:

Based on the reactions, ascertain the valid algebraic relationship:
$\left(i\right)$ $C\left(g\right)$ $+4H$ $\left(g\right)$ $\to C{H}_4\left(g\right);$ $$
$∆H_r$ $=x$ $kJ$ $mo{l}^{-1}$
$\left(ii\right)$ $C\left(graphite\right)$ $+$ $2H_2$ $\left(g\right)$ $\to$ $$ $C{H}_4;$ $$
$∆H_r$ $$ $=$ $y$ $kJ$ $mo{l}^{-1}$