NCERT Solutions for Class 11 Chemistry Chapter 5 Thermodynamics

Question 5.1 Choose the correct answer. A thermodynamic state function is a quantity
(i) used to determine heat changes
(ii) whose value is independent of the path
(iii) used to determine pressure-volume work
(iv) whose value depends on temperature only.

Answer :

A state function refers to the equilibrium state of a system. A thermodynamic state function is a quantity whose value is independent of the path.
Like- $p, V, T$ depends on the state of the system, not on the path.

So, the correct option is (ii)

Question 5.2 For the process to occur under adiabatic conditions, the correct condition is:

(i) $\Delta T = 0$
(ii) $\Delta p = 0$
(iii) q = 0
(iv) w = 0

Answer :

A system is said to be under adiabatic conditions if there is zero exchange of heat between the system and its surroundings. Hence, under adiabatic conditions, $q$ = 0.
So, the correct option is (iii) $q$ = 0

Question 5.3 The enthalpies of all elements in their standard states are:
(i) unity
(ii) zero
(iii) < 0
(iv) different for each element

Answer :

The enthalpies of all elements in their standard states are zero. The standard state of an element refers to its most stable form under standard conditions, typically at a pressure of 1 bar and a temperature of 298 K.
So, the correct option is (ii)

Question 5.4 $\Delta U ^\ominus$ of combustion of methane is $- X KJ mol ^{-1}$ . The value of $\Delta H ^\ominus$ is
(i) $= \Delta U ^\ominus$
(ii) $> \Delta U ^\ominus$
(iii) $< \Delta U ^\ominus$
(iv) = 0

Answer :

Equation of combustion of methane-

$CH_4(g)+\:2O_2(g)\rightarrow CO_2(g)\:+\:2H_2O(l)$

Since, $\Delta H^o=\Delta U^o+\Delta n_gRT$ and $\Delta U^o=-X\:KJ\:mol^{-1}$

from the equation $\Delta n_g=(n_p-n_R)=1-3=-2$

$\Delta H^o=-X-2RT$

$\Delta H^o<\Delta U^o$

So the correct option is (iii).

Question 5.5 The enthalpy of combustion of methane, graphite, and dihydrogen at 298 K are $-890.KJ mol ^{-1} , -393.5 KJ mol ^{-1} \: \:$ and $-285 .8 KJ mol ^{-1}$ respectively. Enthalpy of formation of $CH_4 (g)$ will be

(i) –74.8 $kJ mol^{-1}$

(ii) –52.27 $kJ mol^{-1}$

(iii) +74.8 $kJ mol^{-1}$

(iv) +52.26 $kJ mol^{-1}$

Answer :

$CH_4+2O_{2}\rightarrow CO_{2}+2H_{2}O\ \Delta H$ ................. -890.3 kJ/mol
$C+2O_{2}\rightarrow CO_{2}$ $\Delta H$ ..................-393.5 kJ/mol
$2H_{2}+O_{2}\rightarrow 2H_{2}O$ $\Delta H$ ..................-258.8 kJ/mol

So, the required equation is to get the formation of $CH_4 (g)$ by combining these three equations-

Thus, $C+2H_{2}\rightarrow CH_{4}$

$\Delta _fH_{CH_{4}} = \Delta _cH_c+2\Delta _cH_{H_2}$
= [-393.5 + 2(-285.8) + 890.3]
= -74.8 kJ/mol

Therefore, the enthalpy of formation of methane is -74.8 kJ/mol. So, the correct option is (i)

Question 5.6 A reaction, A + B $\rightarrow$ C + D + q is found to have a positive entropy change. The reaction will be
(i) Possible at high temperature
(ii) possible only at low temperature
(iii) not possible at any temperature
(v) possible at any temperature

Answer :

For the reaction to be feasible, the $\Delta G$ should be negative
$\Delta G = \Delta H - T\Delta S$

According to the question,
$\Delta S$ = positive unit
$\Delta H$ = negative (as heat is evolved in the reaction)
Overall the $\Delta G$ is negative.

Therefore, the reaction is possible at any temperature. So, the correct option is (iv)

Question 5.7 In a process, 701 J of heat is absorbed by a system and 394 J of work is done by the system. What is the change in internal energy for the process?

Answer :

The first law of Thermodynamics states that,
$\Delta U = q+W$

where, $\Delta U$ = change in internal energy for the process
q = heat and W = work

Given that,
q = +701 J (heat is absorbed)
W = - 394 (work is done by the system)

Substituting the value in the equation of the first law we get,

$\Delta U = 701+(-394) =307J$

So, the change in internal energy for the process is 307 J

Question 5.8 The reaction of cyanamide, $NH_2 CN$ (s), with dioxygen was carried out in a bomb calorimeter, and $\Delta U$ was found to be $-742.7 KJ mol ^{-1}$ at 298 K. Calculate the enthalpy change for the reaction at 298 K.

$NH_2 CN ( g ) + \frac{3}{2} O_2 (g) \rightarrow N_2 + CO_2 ( g ) H_2 O ( l)$

Answer :

Given information,
$\Delta U = -742.7kJmol^{-1}$
T = 298 K
R = 8.314 $\times 10^{-3}$

$\Delta n_g =$ $n_g$ (products) $- n_g$ (reactants)
= (2 - 1.5)
= 0.5 moles

The enthalpy change for the reaction is expressed as;

$\Delta H = \Delta U+n_gRT$
where, $\Delta U$ = change in internal energy and
$\Delta n_g =$ change in no. of moles

By putting the values we get,
$\Delta H = (-742.7)+0.5(298)(8.314\times 10^{-3})$
$=-741.5 kJmol^{-1}$

Question 5.9 Calculate the number of kJ of heat necessary to raise the temperature of 60.0 g of aluminum from $35 ^\circ C$ to $55 ^\circ C$. Molar heat capacity of Al is $24 J mol ^{-1} K ^{-1}$

Answer :

We know that
$q = mc\Delta T$
m = mass of the substance
c = heat capacity
$\Delta T$ = change in temperature

By putting all these values we get,
$q = (\frac{60}{27}mol)(24 J/mol/K)(20K)$
= 1066.7 J
= 1.07 kJ

Question 5.10Calculate the enthalpy change on freezing of 1.0 mol of water at $10.0 ^\circ C$ to ice at $- 10.0 ^\circ C$.

$\Delta _{ fus }H = 6.03 KJ mol ^{-1}$ at $0 ^\circ C$ .

$Cp [H_2O(l)] = 75.3 J mol^{-1} K^{-1}\\\\.$

$\: \: \: \: Cp [H_2O(s)] = 36.8 J mol^ { -1}K^{-1}$

Answer :

Total enthalpy change is equal to the summation of all the energy required at three different stages-
(i) from $10^o C$ to $0^o C$ of 1 mol of water (water $\rightarrow$ water )
(ii) from $0^o C$ to $0^o C$ of 1 mol of ice (water $\rightarrow$ ice)
(iii) from $0^o C$ to $-10^oC$ of 1 mole of ice (ice $\rightarrow$ ice)

So, the total enthalpy change
$\Delta H = C_p[H_2O(l)](\Delta T)+$

$\Delta H_(freezing)+C_p[H_2O(s)]\Delta T$

$\\ = (75.3)(-10)+(-6.03\times 10^{3})+(36.8)(-10)\\$

$=-753-6030 - 368\\$

$=-7151 Jmol^{-1}\\$

$= -7.151kJ/mol$
Hence, the total enthalpy change in the transformation process is -7.151 kJ/mol

Question 5.11 Enthalpy of combustion of carbon to $CO_2$ is $-393.5 KJ mol ^{-1}$ Calculate the heat released upon formation of 35.2 g of $CO_2$ from carbon and dioxygen gas.

Answer :

Formation of carbon dioxide from carbon and dioxygen reaction is-

$C+O_{2}\rightarrow CO_{2}$ ............. $\Delta H_f$ = -393.5 kJ/mol

1 mole of $CO_2$ = 44 g
So, the heat released in the formation of 44g of $CO_2$ = -393.5 kJ/mol
therefore, In 35.5 g of $CO_2$ the amount of heat released =
$\frac{-393.5}{44}\times 35.2 $

$= -314.8 kJ/mol$

314.8 KJ/mol heat is released when 35.2 g of CO₂ is formed from carbon and dioxygen.

Question 5.12 Enthalpies of formation of $CO (g ) , CO_2 ( g ), N_ 2 O ( g ) \: \: and \: \: N_2 O_4 (g)$ are –110, – 393, 81 and 9.7 $KJ mol ^{-1}$ respectively. Find the value of $\Delta _ r H$ for the reaction:

$N_2O_4(g) + 3CO(g) \rightarrow N_2O(g) + 3CO_2(g)$

Answer :

Given,
Enthalpies of formation of $CO (g ) , CO_2 ( g ), N_ 2 O ( g ) \: \: and \: \: N_2 O_4 (g)$ are –110, –393, 81 and 9.7 $KJ mol ^{-1}$
$N_2O_4(g) + 3CO(g) \rightarrow N_2O(g) + 3CO_2(g)$
We know that the $\Delta _rH=\sum \Delta _fH$ (product) $-\sum \Delta _fH$ (reactants)

For the above reaction,

$\Delta _rH =[{\Delta _fH(N_{2}O)+3\Delta _fH(CO_{2})}]-$

$[\Delta _fH(N_{2}O_{4})+3\Delta _fH(CO)]$
Substituting the given values we get,
$\\= [81+3(-393)]-[9.7+3(-110)]\\ $

$=-777.7 kJ/mol$
Thus the value of $\Delta _ r H$ of the reaction is -777.7 kJ/mol

Question 5.13 Given $N_2(g) + 3H_2(g) \rightarrow 2NH_3(g) ;$

$\Delta rH = -92.4 kJ mol ^{-1}$ .What is the standard enthalpy of the formation of $NH_3$ gas?

Answer :

the standard enthalpy of formation of any compound is the required change in enthalpy of formation of 1 mole of a substance in its standard form from its constituent elements.

Thus we can re-write the reaction as;
$\frac{1}{2}N_{2}+\frac{3}{2}H_{2}\rightarrow NH_{3}$

Therefore, standard enthalpy of formation of ammonia is = $\frac{1}{2}\Delta _rH^\Theta$
= 1/2 (-92.4)
= -46.2 kJ/mol

Question 5.14 Calculate the standard enthalpy of the formation of CH3OH(l) from the following data:

$CH_3OH (l) + 3/2 O_2(g) \rightarrow CO_2(g) + 2H_2O(l) $

$\Delta _r H = -726 kJ mol^{-1}\\\\ .$

$\: \: \: \: C(graphite) + O_2(g) \rightarrow CO_2(g) ;$

$\Delta_ cH = -393 kJ mol ^ {-1}\\\\ .$

$\: \: \: H_2(g) + 1/2 O_2(g) \rightarrow H_2O(l) ; $

$\Delta_ f H = - 286 kJ mol^{-1}.$

Answer :

for the formation of $CH_3OH$ the reaction is ,

$C+2H_{2}O+\frac{1}{2}O_{2}\rightarrow CH_3OH$
This can be obtained by the following expressions-
required eq = eq (ii) + 2 (eq iii) - eq (i)

$\Delta _fH[CH_{3}OH] = \Delta _cH^\Theta +$$2\Delta _fH[H_{2}O]-\Delta _rH^\Theta$
$=(-393) + 2(-286)-(-726)$
$=-239 kJmol^{-1}$

Therefore, $\Delta_{\mathrm{f}} \mathrm{H}^\theta\left[\mathrm{CH}_3 \mathrm{OH}(\ell)\right]=-239 \mathrm{kJmol}^{-1}$

Question 5.15 Calculate the enthalpy change for the process $CCl_4(g)\rightarrow C(g) + 4 Cl(g)$ and calculate bond enthalpy of $C-Cl$ in $CCl_4(g)$
$\Delta _{vap} H ^{\ominus }(CCl_4) = 30.5 kJ mol^{-1}.\\\\ .$

$\: \: \: \: \: \Delta _f H ^\ominus (CCl_4) = -135.5 kJ mol^{-1}.\\\\.$

$\: \: \: \: \Delta _ a H ^ \ominus (C) = 715.0 kJ mol ^{-1} , $

$where \: \: \Delta_ a H ^\ominus \: \: is\: \: enthalpy \: \: of \: \: atomisation\\\\.$

$\: \: \: \: \Delta _ a H ^\ominus (Cl_2) = 242 kJ mol ^{-1}$

Answer :

We have the following chemical reaction equations-

$(1)\ CCl_{4}(l)\rightarrow CCl_{4}(g)$ ................ $\Delta _{vap}H^o = 30.5kJ/mol$
$(2)\ C(s)\rightarrow C(g)$ ........................ $\Delta _{a}H^o =715.0kJ/mol$
$(3)\ Cl2(g)\rightarrow 2Cl(g)$ .................. $\Delta _{a}H^o =242kJ/mol$
$(4)\ C(g)+4Cl\rightarrow CCl_4(g)$ ............ $\Delta _{f}H =-135.5kJ/mol$
The enthalpy change for the process $CCl_4(g)\rightarrow C(g) + 4 Cl(g)$ by the above reaction is calculated as;

$\Delta H =\Delta _aH^o(C)+2(\Delta _aH^o(Cl_{2}))-$

$\Delta _{vap}H^o-\Delta _fH$
$= [(715)+2(242)-(30.5)-(-135.5)] kJ/mol$
$=1304 kJmol^{-1}$

And the bond enthalpy of C-Cl bond in $CCl_4$ (g) = 1304/4 = 326 kJ/mol

Question 5.16 For an isolated system, $\Delta U = 0$, what will be $\Delta S$?

Answer :

Since $\Delta U = 0$
Means change in internal energy $\Delta$U for an isolated system is zero, it does not exchange any energy with the surroundings. But entropy tends to increase in case of spontaneous reaction. Therefore, $\Delta$S > 0 or positive.

Question 5.17 For the reaction at 298 K,
2A + B $\rightarrow$ C
$\Delta H = 400 kJ mol^ {-1 }\: \: and \: \: $

$\Delta S = 0.2 kJ K ^{-1} mol^{-1}$
At what temperature will the reaction become spontaneous considering $\Delta H$ and $\Delta S$ to be constant over the temperature range?

Answer :

From the equation,

$\Delta G = \Delta H-T\Delta S$
Suppose the reaction is at equilibrium, So the change in temperature is given as;

$T=\frac{\Delta H -\Delta G}{\Delta S}$
$= \frac{400}{0.2} $

$=2000K$ ( $\Delta G$ at equilibrium is zero)
To reaction should be spontaneous, $\Delta G$ should be negative. So, for the given reaction T should be greater than 2000 K

Question 5.18 For the reaction, $2 Cl (g) \rightarrow Cl_2 ( g)$ , what are the signs of $\Delta H \: \: and \: \: \Delta S$?

Answer :

The given reaction represents the formation of a chlorine molecule from its atom. Bond formation taking place, therefore the energy is released during this. So, $\Delta H$ is negative.

Two moles of an atom have more randomness than one mole of chlorine. So, spontaneity is decreased. Hence $\Delta S$ is negative.

Question 5.19 For the reaction
$2 A (g) + B ( g ) \rightarrow 2 D ( g)$
$\Delta U ^ \ominus = -10.5 KJ \: \: and \: \: \Delta S ^\ominus = - 44.1 JK^{-1}$
Calculate $\Delta G ^ \ominus$ for the reaction, and predict whether the reaction may occur spontaneously.

Answer :

Given reaction is $2 A (g) + B ( g ) \rightarrow 2 D ( g)$

We know that, $\Delta G^o = \Delta H^o-T\Delta S^o$
and $\Delta H^o = \Delta U^o+\Delta n_{g}RT$
here $\Delta n_{g}= 2 - (3) = -1$

and $\Delta U ^ \ominus = -10.5 KJ \: \: and \: \: \Delta S ^\ominus = - 44.1 JK^{-1}$

Substituting the given values in equations-
$\Delta G = (-10.5+8.314\times 10^{-3}\times 298)-$

$298(-44.1)$
$\\\Delta G = (-12.98 +13.14 )kJ\\$

$\Delta G= +0.16 kJ$

Hence the reaction will not occur spontaneously because the $\Delta G ^ \ominus$ value is positive for this reaction.

Question 5.20 The equilibrium constant for a reaction is 10. What will be the value of

$\Delta G ^ \ominus ? R = 8.314 JK ^{-1} mol ^{-1} , T = 300 K$

Answer :

Given values are,
$R = 8.314 JK ^{-1} mol ^{-1} , T = 300 K$
and equilibrium constant = 10

It is known that,
$\Delta G^o = -2.303\ RT \log K_{eq}$
$\\=-2.303(8.314)(300)\log 10\\ $

$=-5744.14 Jmol^{-1}\\ $

$=-5.744 kJmol^{-1}$

Hence the value of $\Delta G^o$ is -5.744 kJ/mol

Question 5.21 Comment on the thermodynamic stability of NO(g), given

$1/2 N_2(g) + 1/2 O_2(g)\rightarrow NO(g) ; $

$\Delta _ rH ^ \ominus = 90 kJ mol ^{-1}\\\\ .$

$\: \: \: NO(g) + 1/2 O_2(g) \rightarrow NO_ 2(g) : $

$\Delta _ r H^ \ominus = -74 kJ mol ^{-1}$

Answer :

The formation of $NO$ is unstable because $\Delta _rH$ is positive which means heat is absorbed during the reaction. So, $NO$ (g) has higher energy than its reactants $N_{2}$ and $O_{2}$.
On the other hand, $NO_{2}$ is stable because $\Delta _rH$ is negative means heat is released during the formation of $NO_{2}$. It is established with minimum energy. Hence unstable $NO$ changes to stable $NO_{2}$.

Question 5.22 Calculate the entropy change in surroundings when 1.00 mol of $H_2 O (l)$ is formed under standard conditions. $\Delta _f H ^ \ominus = -286 KJ mol ^ { -1}$

Answer :

-286 kJ/mol heat is evolved when 1 mol of the water molecule is formed. It means the same amount of energy is absorbed by the surrounding also.

$q_{surr}= +286$ kJ/mol
We know that,
Entropy changes for the surrounding is = q(surr)/ temp.
= 286000/ 298

= 959.73 J/mol/K