$∆{\mathrm{H}}_{\mathrm{f}}^0$ (298K) of methanol is given by the chemical equation:

1. \(\mathrm{C}(\text { diamond })+\frac{1}{2} \mathrm{O}_{2(\mathrm{~g})}+2 \mathrm{H}_{2(\mathrm{~g})} \rightarrow \mathrm{CH}_3 \mathrm{OH}_{(\mathrm{l})}\)

2. \(\mathrm{CH}_{4(\mathrm{~g})}+\frac{1}{2} \mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{CH}_3 \mathrm{OH}_{(\mathrm{g})}\)

3. \(\mathrm{CO}_{(\mathrm{g})}+2 \mathrm{H}_{2(\mathrm{~g})} \rightarrow \mathrm{CH}_3 \mathrm{OH}_{(\mathrm{l})}\)

4. \(\mathrm{C}(\text { graphite })+\frac{1}{2} \mathrm{O}_{2(\mathrm{~g})}+2 \mathrm{H}_{2(\mathrm{~g})} \rightarrow \mathrm{CH}_3 \mathrm{OH}_{(\mathrm{l})}\)

A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of 37.0ºC. As it does so, it absorbs 208 J of heat. The values of q and w for the process will be-
(R = 8.314 J/mol K) (ln 7.5 = 2.01)

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?

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 \(10^{5}~Nm^{-2}\)?

Entropy decreases during:

1. Crystallization of sucrose from solution

2. Rusting of iron

3. Melting of ice

4. Vaporization of camphor

For the following given equations and $∆\mathrm{H}°$ values, determine the enthalpy of reaction at 298 K for the reaction:

C₂H₄(g) + 6F₂(g) $\to$ 2CF₄(g) + 4HF(g)

H₂(g) + F₂(g) $\to$ 2HF(g)       $∆{\mathrm{H}}_1^{°}$= -537 kJ

C(s) + 2F₂(g) $\to$CF₄(g)         $∆{\mathrm{H}}_2^{°}$=-680 kJ

2C(s) + 2H₂(g) $\to$C₂H₄(g)    $∆{\mathrm{H}}_3^{°}$= 52 kJ

1. –1165 kJ

2. –2486 kJ

3. +1165 kJ

4. +2486 kJ

The volume versus temperature graph for two moles of monoatomic gas is shown in the figure. The ratio of work done by the gas to the heat absorbed by it in the process \(A\) to \(B\) is:

          
1. \(2R\)
2. \(3R\)
3. \(5R\)
4. \(7R\)

When 4 g of iron is burnt to ferric oxide at a constant pressure, 29.28 kJ of heat is evolved.

The enthalpy of formation of ferric oxide will be-

(At. mass of Fe = 56) ?

1. $-$81.98 kJ

2. $-$ 819.8 kJ

3. $-$ 40.99 kJ

4.  +819.8 kJ

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: