The correct statement among the following is-

If the volume of a gas is reduced to half from its original volume, then the specific heat will-

${∆}_{\mathrm{f}}{\mathrm{U}}^{⊝}$ of formation of ${\mathrm{CH}}_4\left(\mathrm{g}\right)$ at certain temperature is $-393 \mathrm{kJ} {\mathrm{mol}}^{-1}$. The value of ${∆}_{\mathrm{f}}{\mathrm{H}}^{⊝}$ is-

In an adiabatic process, no transfer of heat takes place between the system and its surroundings. The correct option for free expansion of an ideal gas under adiabatic condition from the following is -

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

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 -

Consider the reactions given below. On the basis of these reactions find out which of the

the algebraic relationships is correct?

$$\begin{gathered} \left(i\right) C\left(g\right) +4H \left(g\right) \to C{H}_4\left(g\right); \\ ∆H_r =x kJ mo{l}^{-1} \\ \left(ii\right) C\left(graphite\right) + 2H_2 \left(g\right) \to C{H}_4; \\ ∆H_r = y kJ mo{l}^{-1} \end{gathered}$$

The enthalpies of elements in their standard states are taken as zero. The enthalpy of formation of a compound is -

Consider the following statement:

"A thermodynamic quantity is a state function"

The correct option is-

A necessary condition for an adiabatic change is-

The enthalpy of formation of all elements in their standard state is-

$∆\mathrm{U}°$for combustion of methane is -x kJ mol^-1.

The value of $∆\mathrm{H}°$ for the same reaction would be -

$$\begin{gathered} 1. = ∆\mathrm{U}° \\ 2. > ∆\mathrm{U}° \\ 3. < ∆\mathrm{U}° \\ 4. =0 \end{gathered}$$

701 J of heat is absorbed by a system and 394 J of work is done by the system.

The change in internal energy for the process is-

$$\begin{gathered} 1. 307 \mathrm{J} \\ 2. -307 \mathrm{J} \\ 3. 1095 \mathrm{J} \\ 4. -701 \mathrm{J} \end{gathered}$$

The reaction of cyanamide, ${\mathrm{NH}}_2\mathrm{CN} \left(\mathrm{s}\right)$ with dioxygen, was carried out in a bomb calorimeter, and ∆U was found to be $-742.7 \mathrm{kJ} {\mathrm{mol}}^{-1}$ at 298 K.

$$\begin{gathered} {\mathrm{NH}}_2\mathrm{CN} \left(\mathrm{s}\right) + \frac{3}{2}{\mathrm{O}}_2\left(\mathrm{g}\right) \to \\ {\mathrm{N}}_2 \left(\mathrm{g}\right) + {\mathrm{CO}}_2\left(\mathrm{g}\right) + {\mathrm{H}}_2\mathrm{O} \left(\mathrm{l}\right) \end{gathered}$$

The enthalpy change for the reaction at 298 K would be -

$$\begin{gathered} 1. -741.3 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 2. + 753.9 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 3. + 772. 7 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 4. -845. 1 \mathrm{kJ} {\mathrm{mol}}^{-1} \end{gathered}$$

The amount of heat needed to raise the temperature of 60.0 g of aluminum from 35°C to 55°C would be -

(Molar heat capacity of Al is $24 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}$)

$$\begin{gathered} 1. 1.07 \mathrm{J} \\ 2. 1.07 \mathrm{kJ} \\ 3. 106.7 \mathrm{kJ} \\ 4. 100.7 \mathrm{kJ} \end{gathered}$$

The enthalpy of formation of ${\mathrm{CO}}_{\left(\mathrm{g}\right)}, {\mathrm{CO}}_{2\left(\mathrm{g}\right)}, {\mathrm{N}}_2{\mathrm{O}}_{\left(\mathrm{g}\right)} , \mathrm{and} {\mathrm{N}}_2{\mathrm{O}}_{4\left(\mathrm{g}\right)}$are

–110 kJ ${\mathrm{mol}}^{-1}$, – 393 kJ ${\mathrm{mol}}^{-1}$, 81 kJ ${\mathrm{mol}}^{-\mathrm{1,}}$ and 9.7 kJ $mo{l}^{-1}$ respectively.

The value of ${∆}_{\mathrm{r}}\mathrm{H}$ for the reaction would be-

${\mathrm{N}}_2{\mathrm{O}}_{4\left(\mathrm{g}\right)}+3{\mathrm{CO}}_{\left(\mathrm{g}\right)}\to {\mathrm{N}}_2{\mathrm{O}}_{\left(\mathrm{g}\right)}+3{\mathrm{CO}}_{2\left(\mathrm{g}\right)}$

$$\begin{gathered} 1. -777.7 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 2. +777.7 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 3. +824.9 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 4. - 345.4 \mathrm{kJ} {\mathrm{mol}}^{-1} \end{gathered}$$

 ${\mathrm{N}}_2 + 3 {\mathrm{H}}_2 \to 2{\mathrm{NH}}_{3 ;} {∆}_{\mathrm{r}}{\mathrm{H}}^{°} = -92.4 \mathrm{kJ} {\mathrm{mol}}^{-1}$

The standard enthalpy of formation of ${\mathrm{NH}}_3$ gas in the above reaction would be-

$$\begin{gathered} 1. -92.4 \mathrm{J} {\mathrm{mol}}^{-1} \\ 2. -46.2 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 3. + 46.2 \mathrm{J} {\mathrm{mol}}^{-1} \\ 4. + 92.4 \mathrm{kJ} {\mathrm{mol}}^{-1} \end{gathered}$$

The standard enthalpy of formation of ${\mathrm{CH}}_3{\mathrm{OH}}_{\left(\mathrm{l}\right)}$ from the following data is -

$$\begin{gathered} {\mathrm{CH}}_3{\mathrm{OH}}_{\left(\mathrm{l}\right)}+ \frac{3}{2}{{\mathrm{O}}_2}_{\left(\mathrm{g}\right)} \to {{\mathrm{CO}}_2}_{\left(\mathrm{g}\right)} + 2{\mathrm{H}}_2{\mathrm{O}}_{\left(\mathrm{l}\right)}; \\ {∆}_{\mathrm{r}}\mathrm{H}° = -726 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ {\mathrm{C(s)}}_{} + {{\mathrm{O}}_2}_{\left(\mathrm{g}\right)} \to {{\mathrm{CO}}_2}_{\left(\mathrm{g}\right)} ; \\ {∆}_{\mathrm{c}}\mathrm{H}° = -393 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ {{\mathrm{H}}_2}_{\left(\mathrm{g}\right)} + \frac{1}{2}{{\mathrm{O}}_2}_{\left(\mathrm{g}\right)} \to {\mathrm{H}}_2{\mathrm{O}}_{\left(\mathrm{l}\right)} ; \\ {∆}_{\mathrm{f}}{\mathrm{H}}^{°} = -286 \mathrm{kJ} {\mathrm{mol}}^{-1} \end{gathered}$$

$$\begin{gathered} 1. -239 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 2. + 239 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 3. -47 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 4. +47 \mathrm{kJ} {\mathrm{mol}}^{-1} \end{gathered}$$

$$\begin{gathered} {∆}_{\mathrm{vap}}\mathrm{H}° \left({\mathrm{CCl}}_4\right) = 30.5 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ {∆}_{\mathrm{f}}\mathrm{H}° \left({\mathrm{CCl}}_4\right) = - 135.5 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ {∆}_{\mathrm{a}}\mathrm{H}° \left(\mathrm{C}\right) = 715.0 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ {∆}_{\mathrm{a}}\mathrm{H}° \left({\mathrm{Cl}}_2\right)\hspace{0.17em}= 242 \mathrm{kJ} {\mathrm{mol}}^{-1} \end{gathered}$$

The enthalpy change for the reaction

 ${\mathrm{CCl}}_4 \left(\mathrm{g}\right) \to \mathrm{C}\left(\mathrm{g}\right) + 4\mathrm{Cl} \left(\mathrm{g}\right)$ would be -

$$\begin{gathered} 1. 326 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 2. 1304 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 3. -328 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 4. -1304 \mathrm{kJ} {\mathrm{mol}}^{-1} \end{gathered}$$

For an isolated system with ∆U = 0, the ∆S value will be-

For the reaction at 298 K,

2A + B → C

$∆\mathrm{H} = 400 \mathrm{kJ} {\mathrm{mol}}^{-1} \mathrm{and} ∆\mathrm{S} = 0.2 \mathrm{kJ} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$ .Reaction will become spontaneous at-

$$\begin{gathered} 1. 1500 \mathrm{K} \\ 2. 2000 \mathrm{K} \\ 3. 100 \mathrm{K} \\ 4. 1900\mathrm{K} \end{gathered}$$

For the reaction $2\mathrm{A} \left(\mathrm{g}\right) + \mathrm{B}\left(\mathrm{g}\right) \to 2\mathrm{D} \left(\mathrm{g}\right)$; $∆\mathrm{U}° = -10.5 \mathrm{kJ} \mathrm{and} ∆\mathrm{S}° = -44.1 \mathrm{J} {\mathrm{K}}^{-1}$ , the value of $∆\mathrm{G}°$ for the given reaction would be-

The equilibrium constant for a reaction is 10. The value of $∆\mathrm{G}°$ will be-

($\mathrm{R} = 8.314 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1} ; \mathrm{T} = 300 \mathrm{K}$)

$$\begin{gathered} 1. -5.74 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 2. - 5.74 \mathrm{J} {\mathrm{mol}}^{-1} \\ 3. + 4.57 \mathrm{kJ} {\mathrm{mol}}^{-1} \\ 4. -57.4 \mathrm{kJ} {\mathrm{mol}}^{-1} \end{gathered}$$

Entropy change in surroundings when 1.00 mol of $H_2{O}_{\left(l\right)}$ is formed under standard conditions. ${∆}_f{H}^{\theta }=-286 kJ mo{l}^{-1}$ is

$$\begin{gathered} 1. -959.73 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1} \\ 2. 234.98 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1} \\ 3. 959.73 \mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1} \\ 4. 312.56 \mathrm{J} {\mathrm{K}}^{-1 }{\mathrm{mol}}^{-1} \end{gathered}$$

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

Consider the following processes :

                                       ∆H (kJ/mol)
½ A → B                            + 150
3B → 2C + D                      –125
E + A → 2D                        +350

For B + D → E + 2C, ∆H will be-

For vaporization of water at 1 atmospheric pressure, the values of ∆H and ∆S are 40.63 kJ mol^–1 and 108.8 JK^–1 mol^–1, respectively. The temperature when Gibbs energy change (∆G) for this transformation will be zero, is -

Three moles of an ideal gas expanded spontaneously into vaccum. The work done will be