Thermodynamics practice · Hard

The standard enthalpies of formation of $\mathrm{NH}_3(\mathrm{g}),\mathrm{CuO}(\mathrm{s})$ and $\mathrm{H}_2 \mathrm{O}({l})$ are $-46,-155$ and $-285 \mathrm{~kJ} /\mathrm{mol},$ respectively. The enthalpy change when $6.80 \mathrm{~g}$ of $\mathrm{NH}_3$ is passed over cupric oxide is

A system undergoes a certain change in state by path I and the corresponding heat absorbed and work done are $10 \mathrm{~kcal}$ and $0 \text{ erg},$ respectively. For the same change in state by path II, the respective quantities are $11 \mathrm{~kcal}$ and $0.5 \, w_{\max },$ where $w_{\max }$ represents the work done if the changes were reversibly carried out. The magnitude of $w_{\max },$ is $(1 \mathrm{~cal}=4.2 \mathrm{~J})$

The vapour pressure of benzene is $1.53 \times 10^4 {Nm}^{-2}$ at $303 {~K}$ and $5.2 \times 10^4 {Nm}^{-2}$ at $333 {~K}$. Calculate the mean latent heat of evaporation of benzene over this temperature range.

Molar heat capacity of $\mathrm{CD}_2 \mathrm{O}$ (deuterated form of formaldehyde) vapour at constant pressure is vapour $14 \mathrm{~cal} / \mathrm{K}-\mathrm{mol}.$ The entropy change associated with the cooling of $3.2 \mathrm{~g}$ of $\mathrm{CD}_2 \mathrm{O}$ vapour from $1000 \mathrm{~K}$ to $900 \mathrm{~K}$ at constant pressure is (assume ideal gas behaviour for $\mathrm{CD}_2 \mathrm{O})$ [ln $0.9=-0.1]$

STATEMENT-1 : All combustion reactions are exothermic.

STATEMENT-2 : Enthalpies of products are greater than enthalpies of reactants $\left(\Sigma v_p \Delta_f H(P)>\Sigma v_R \Delta_f H(R)\right)$

In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is $C{H_3}OH\left( l \right) + \frac{3}{2}{O_2}\left( g \right) \to C{O_2}\left( g \right) + 2{H_2}O\left( l \right)$ At 298 K, standard Gibb’s energies of formation for $C{H_3}OH\left( l \right),\,{H_2}O\left( l \right)\,\,and\,\,C{O_2}\left( g \right)$ are -166.2, -237.2 and $- 394.4\mathrm{ }kJ\mathrm{ }mo{l^{ - 1}}$ respectively. If standard enthalpy of combustion of methanol is $- 726kJ\mathrm{ }mo{l^{ - 1}}$ efficiency of the fuel cell will be:

A gas present in a cylinder fitted with a frictionless piston expands against a constant pressure of $1 {~atm}$ from a volume of 2 litre to a volume of 6 litre. In doing so, it absorbs $800 {~J}$ heat from surroundings. Determine increase in internal energy of process.

The standard enthalpies of formation of $C{O_2}\left( g \right),\,\,{H_2}O\left( l \right)$ and glucose (s) at ${25^\mathrm{o}}\,\,C$ are $- 400\,\,KJ \cdot mo{l^{ - 1}},\,\, - 300\,\,KJ \cdot mo{l^{ - 1}}$ and $- 1300\,\,KJ/mol$ respectively. The standard enthalpy of combustion per gram of glucose at ${25^\mathrm{o}}\,\,C$ is

Enthalpy of vaporisation for water is 186.5 kJ $\mathrm{mo}{\mathrm{l}^{ - 1}}$ . The entropy change during vaorisation is …kJ ${\mathrm{K}^{ - 1}}\mathrm{mo}{\mathrm{l}^{ - 1}}$ .

For adiabatic expansion of a perfect gas $\frac{d P}{P}$ is :

When a certain mass of an ideal gas is adiabatically compressed so that its volume is reduced to $1 / 32$ times, its absolute temperature is increased 4 times. The number of atoms in a molecule (atomicity) of the gas is

The hydrogen bond between $\mathrm{F}^{-}$and $\mathrm{CHCOOH}$ is very strong and its strength may be analysed by setting up a Born-Haber cycle with the following data. Lattice energy of $\mathrm{KF.CH}_3 \mathrm{COOH}=734;$ enthalpy of vaporization of $\mathrm{CH}_3 \mathrm{COOH}=20;$ enthalpy of solution of $\mathrm{KF}= 35;$ solvation energy of $\mathrm{K}^{+}(\mathrm{g}) =-325;$ solvation energy of $\mathrm{F}^{-}=-389;$ enthalpy of formation of $\mathrm{KF} \cdot \mathrm{CH}_3 \mathrm{COOH}(\mathrm{s})$ from $\mathrm{KF}(\mathrm{s})$ and $\mathrm{CH}_3 \mathrm{COOH}(l) =-25.$ Find the energy of the hydrogen bond between $\mathrm{F}^{-}$ and $\mathrm{CH}_3 \mathrm{COOH}$ in the gas phase (in $\mathrm{kJ} / \mathrm{mol}$).

Enthalpies of formation of $\mathrm{CO}_2(\mathrm{g}), \mathrm{CO}(\mathrm{g}), \mathrm{N}_2 \mathrm{O}(\mathrm{g})$ and $\mathrm{NO}_2(\mathrm{g})$ in $\mathrm{kJ} \mathrm{~mol}^{-1}$ are respectively $-393,-110,81$ and $34$ respectively. Calculate $\Delta_{\mathrm{r}} H$ in $\mathrm{kJ}$ of the following reaction.
$2 \mathrm{NO}_2(\mathrm{g})+2 \mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{N}_2 \mathrm{O}(\mathrm{g})+3 \mathrm{CO}_2(\mathrm{g})$

Two moles of an ideal gas $\left[C_{\mathrm{v}, \mathrm{m}}\left(/ \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)=20+0.01 T(/ \mathrm{K})\right]$ is heated at constant pressure from $27^{\circ} \mathrm{C}$ to $127^{\circ} \mathrm{C}.$ The amount of heat absorbed by the gas is

The combustion of benzene $(l)$ gives $C{O_2}\left( g \right)$ and ${H_2}O\left( l \right)$. Given that heat of combustion of benzene at constant volume is $-3263.9\,kJ\,mo{l^{ - 1}}$ at $25^\circ C$, heat of combustion (in $kJ\,\,mo{l^{ - 1}}\mathrm{)}$ of benzene at constant pressure will be
$\left( {R = 8.314\,J{K^{ - 1}}\,mo{l^{ - 1}}} \right)$

Using the data provided, calculate the multiple bond energy $(kJ\,mo{l^{ - 1}})$of a C≡C bond in ${\mathrm{C}_2}{\mathrm{H}_2}.$ Given that the heat of formation of ${\mathrm{C}_2}{\mathrm{H}_2}$ is $225kJmo{l^{ - 1}}$ (take the bond energy of C─H bond as $350\,\,kJ\,\,mo{l^{ - 1}}.):$
$2\mathrm{C}\left( s \right) \to 2\mathrm{C}\left( \mathrm{g} \right)\Delta H = 1410\,\,\mathrm{kJ\,\,mo}{\mathrm{l}^{ - 1}}$
$2\mathrm{C}\left( s \right) \to 2\mathrm{C}\left( \mathrm{g} \right)\Delta H = 1410\,\,\mathrm{kJ\,\,mo}{\mathrm{l}^{ - 1}}$
${\mathrm{H}_2}\left( \mathrm{g} \right) \to 2\mathrm{H}\left( \mathrm{g} \right)\Delta H = 330\,\,\mathrm{kJ\,\,mo}{\mathrm{l}^{ - 1}}$

$\mathrm{CCl}_2 \mathrm{F}_2$ cooled $1.25 \mathrm{~g}$ sample at constant atmospheric pressure of $1 \mathrm{~atm}$ from $320 \mathrm{~K}$ to $293 \mathrm{~K}$. During cooling the sample volume decreased from $274$ to $248 \mathrm{~mL}$. Calculate $\Delta {H}$ for the $\mathrm{CCl}_2 \mathrm{F}_2$ for this process. $\left(C_p=80.7 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)$.

For $A \rightarrow B, \Delta H=4 \mathrm{~kcal} \mathrm{~mol}^{-1}, \Delta S=10 \mathrm{~cal} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}.$ Reaction is spontaneous when temperature will be

Heat of formation of two moles of $\mathrm{NH}_3(\mathrm{~g})$ is $-90 \mathrm{KJ}$. Bond energies of $\mathrm{H}-\mathrm{H}$ and $\mathrm{N}-\mathrm{H}$ bonds are $435 \mathrm{KJ}$ and $390 \mathrm{KJ} \mathrm{mol}^{-1}$ respectively. The value of the bond energy of $N=N$ will be

Determine whether or not, it is possible for sodium to reduce aluminium oxide to aluminium at $298 {~K}$. Also calculate equilibrium constant. Given that $G_f^{\circ}$ of ${Al}_2 {O}_3$ at $298 {~K}=-1582 {~kJ} {~mol}^{-1} ; G_f^0$ of ${Na}_2 {O}(s)$ at $298 {~K}$ $=-377 {~kJ} {~mol}^{-1}$.

Two moles of an ideal gas $\left(C_{v, m}=\frac{5}{2} R\right)$ was compressed adiabatically against constant pressure of $2 \mathrm{~atm},$ which was initially at $350 \mathrm{~K}$ and $1 \mathrm{~atm}.$ The work done on the gas in this process is

The temperature coefficient of e.m.f. of a cell can be given by:

In the following reactions,

I. $30 \mathrm{~mL}$ of $0.1 \mathrm{~M} \mathrm{~Ba}(\mathrm{OH})_2(a q)+30 \mathrm{~mL}$ of $0.1 \mathrm{~M} \mathrm{~H}_2 \mathrm{SO}_4(\mathrm{aq})$, rise in temperature $=\Delta T_1$

II. $90 \mathrm{~mL}$ of $0.1 \mathrm{~M} \mathrm{~Ba}(\mathrm{OH})_2(\mathrm{aq})+90 \mathrm{~mL}$ of $0.1 \mathrm{~M} \mathrm{~H}_2 \mathrm{SO}_4(a q)$, rise in temperature $=\Delta T_2$. Thus,

An ideal gas was subjected to a reversible adiabatic expansion then its initial volume was restored by reversible, isothermal compression. If ' $q$ ' denotes the heat added to the system and $w$ the work done on the system for the overall process then

Assertion :- At constant pressure of the change $\mathrm{H}_2 \mathrm{O}(\mathrm{s}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g})$ work done is negative.

Reason :- During phase transition work done is always negative.

Work done by a sample of an ideal gas in a process ${A}$ is double the work done in another process ${B}.$ The temperature rises through the same amount in the two processes. If $C_{{A}}$ and $C_{{B}}$ are the molar heat capacities for the two processes, then

The standard state Gibbs free energies of formation of $C$ (graphite) and C (diamond) at $T=298 {~K}$ are

$\begin{aligned} & \Delta_f G^{\circ}[{C} \text { (graphite) }]=0 {~kJ} {~mol}^{-1} \\ & \Delta_f G^{\circ}[{C} \text { (diamond) }]=2.9 {~kJ} {~mol}^{-1} \end{aligned}$

The standard state means that the pressure should be 1 bar, and substance should be pure at a given temperature. The conversion of graphite [C(graphite)] to diamond $\left[C\right.$ (diamond)] reduces its volume by $2 \times 10^{-6} {~m}^3 {~mol}^{-1}$. If ${C}$ (graphite) is converted to ${C}$ (diamond) isothermally at ${T}$ $=298 {~K}$, the pressure at which ${C}$ (graphite) is in equilibrium with ${C}$ (diamond), is :

$[\text{Useful information:}$ $1 {~J}=1 {~kg} {~m}^2 {~s}^{-2}$;
$\left.1 {~Pa}=1 {~kg} {~m}^{-1} {~s}^{-2} ; 1 {bar}=10^5 {~Pa}\right]$

Enthalpy change in the formation of $\mathrm{Cl}^{+} \mathrm{Cl}^{-}$(imaginary) lattice from $\mathrm{Cl}_2$ based on following data is $\mathrm{Cl}-\mathrm{Cl}$ bond energy= $x_1$, ionisation energy of $\mathrm{Cl}=x_2$ electron affinity of $\mathrm{Cl}=x_3$, lattice energy of $\mathrm{Cl}^{+} \mathrm{Cl}^{-}=x_4$

The heat of combustion of ethanol into carbon dioxides and water is $- 327\,\,kcal$ at constant pressure. The heat evolved (in cal) at constant volume and ${27^\mathrm{o}}\,\,C$ (if all gases behave ideally) is ($R = 2$ cal $mo{l^{ - 1}}\,{K^{ - 1}}$ )……

Calculate the standard internal energy change for the following reaction at $25^{\circ} \mathrm{C}$.

$\begin{aligned} & 2 \mathrm{H}_2 \mathrm{O}_2(\mathrm{l}) \longrightarrow 2 \mathrm{H}_2 \mathrm{O}(\mathrm{l})+\mathrm{O}_2(\mathrm{g}) \\ & \mathrm{H}_2 \mathrm{O}_2(\mathrm{l})=-188.0 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ & \mathrm{H}_2 \mathrm{O}(\mathrm{l})=-286.0 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ & \left(\mathrm{R}=8.314 \mathrm{~J~K}^{-1} \mathrm{~mol}^{-1}\right) \end{aligned}$