>> Study Material
>> IIT JEE Physics
>> Thermal Physics
>> Solved Sample Problems Based on Thermodynamics
1. Why is the enthalpy of sublimation is equal to the sum of enthalpy of fusion and enthalpy of vaporization?
2. Under what conditions of ΔG, ΔH or ΔS, a reaction will be spontaneous at all temperatures?
3. Why is the heat of neutralisation of a strong acid by a strong base is constant as 57.0 kJ / mole?
4. When does entropy increases in a reaction.
5. Entropy of the solution is higher than that of pure liquid, why?
6. The ΔG at m.pt. of ice is zero.
7. At temperature T, the endothermic reaction A ——> B proceeds almost to completion. WhyΔS is + ve ?
8. Why standard heat of formation of diamond is not zero though it is an element?
9. Can the absolute value of internal energy be determined? Why or why not?
10. Same mass of diamond and graphite (both being carbon) are burnt in oxygen. Will the heat produced be same or different? Why?
11. Why in chemical reactions generally heat is either evolved or absorbed?
12. Why is the enthalpy of sublimation equal to the sum of enthalpy of fusion and enthalpy of vaporisation?
13. When an ideal gas expands in vacuum, there is neither absorption nor evolution of heat. Why?
14. Calculate the heat change for the following reaction:
CH4(g) + 2O2(g) ———> CO2(g) + 2H2O(l)
for CH4, H2O and CO2 are -17.89, -68.3 and -94.05 kcal/mole
15. The heat of reaction C(s) + 1/2 O2(g) ——> CO(g) at 17°C and at constant volume is -29.29 kcal. Calculate the heat of reaction at constant pressure.
16. Thermochemistry is the study of relationship between heat energy & ………………………..
17.Define Gibbs free energy.
18. Total energy for a reversible isothermal cycle is……………………………
19.Find out the value of equilibrium constant for the following reaction at 298 K.
2NH3 (g) + CO2(g) ——> NH2CONH2(aq.) + H2O (l)
Standard Gibbs energy change Δr G- at the given temperature is -13.6 kJ/mol.
20.What you can conclude from this graph
Level – I
1. Which of the following can be determined? Absolute internal energy, absolute enthalpy, absolute entropy
2. Why would you expect a decrease in entropy as a gas condenses into liquid? Compare it with the entropy decrease when a liquid sample is converted into solid.
3. Under what conditions will the reaction occur, if both ΔS and ΔH are positive?
4. Justify, the entropy of a substance increases on going from liquid to vapour state at any temperature.
5. One mole of an ideal gas is heated at constant pressure from 0°C to 100°C.
(a) Calculate work done.
(b) If the gas were expanded isothermally & reversibly at 0°C from 1 atm to some other pressure Pt, what must be the final pressure if the maximum work is equal to the work involved in (a).
6. Air contains 99% N2 and O2 gases. Then why do not they combine to form NO under the standard conditions? Given that the standard free energy of formation of NO(g) is
86.7 KJ mol-1.
7. Calculate the heat of following reaction
N2 + 3H2 —> 2NH3
Given the bond energies of N = N, H - H and N ¾ H bonds are 226, 104 and 93 kcal respectively.
8. When 2 moles of C2H6 are completely burnt 3129 KJ of heat is liberated. Calculate the heat of formation, ΔHf for C2H6; ΔHf for CO2 and H2O are -395 and -286 KJ respectively.
9. Calculate the heat of formation of ethane at 25°C. The bond enthalpies for H - H, C - C and C -H bonds are 104.2 kcal, 80 kcal and 99.5 kcal respectively. Heat of vaporization of carbon is 171.7 kcal.
10. Define the following terms:
(a) Internal energy (b) Endothermic reaction
(c) Hess law (d) Calorific value
11.5 mole of an ideal gas expand isothermally & reversibly from a pressure of 10 atm to 2 atm at 300 K. What is the largest mass which can be lifted through a height of 1 mitre in this expansion?
12. The equilibrium constant for the reaction:
CO2(g) + H2(g) ——> CO(g) + H2O at 298 K is 73. Calculate the value of the standard free energy change (R = 8.314 JK-1mol-1).
13. An insulated container contains 1 mole of a liquid molar volumes 100 ml at 1 bar. When liquid is steeply passed to 100 bar, volume decrease t0 99 ml, find ΔH & ΔU for the process.
14. AB, A2 & B2 are diatomic molecules. If the bond enthalpies of A2, AB & B2 are in the ratio 1:1:0.5 & the enthalpy of formation of AB from A2 & B2 is -100 KJ mol-1. What is the bond enthalpy of A2?
Level – II
1. Calculate the C ¾ H bond energy in methane at 25°C from the data. Heat of formation of methane is -17.9 kcal, heat of vaporization of carbon is 171.1 cal and heat of formation of hydrogen atoms is 52.1 kcal/mol.
2. The heats of combustion of hydrogen, ethane and ethylene are 68.4, 370.4 and 393.5 kcal per molecule respectively. Calculate the energy when ethylene is reduce to ethane.
3. The molar heat of formation of NH4NO3 is 367.54 KJ and those of N2O(g) and H2O are 81.46 KJ and -285.78 KJ, respectively at 25°C and 1.0 atm pressure. Calculate ΔH and ΔE for the reaction.
NH4NO3(s) ———> N2O (g) + 2H2O(l)
4. Given that
N2(g) + l2 (g) ———> 2Hl(g) ΔH = –12.46 kcal
l2(g) ———> 2l(g) ΔH = 35.8 kcal
H2(g) ———> 2H(g) ΔH = 103.7 kcal
Calculate the bond energy of H – I
5. Calculate the maximum work done when pressure on 10 g of hydrogen is reduced from 20 to 1 atm at a constant temperature of 273 K. The gas behaves ideally. Calculate Q.
6. Standard heat of formation of HgO(s) at 298 K and at constant pressure is -90.8 kJ / mole. Excess of HgO(s) absorbs 41.84 kJ of heat at constant volume, calculate the amount of Hg that can be obtained at constant volume and 298 K, Atomic weight of Hg = 200.
7. Calculate the heat of formation of anhydrous Al2Cl6 from
2Al(s) + 6HCl (aq) ——> Al2Cl6(aq) + 3H2(g), ΔH = –239.76 kcal
H2(g) + Cl2 ——> 2HCl(g) ΔH = –44.0 kcal
HCl(g) + Aq ——> HCl(aq.) ΔH = –17.32 kcal
Al2Cl6(s) + Aq ——> Al2Cl6(aq.) ΔH = –153.69 kcal
8. Calculate the heat of formation of Ag2O from following data:
9. Calculate resonance energy of from the following data if the observed heat of formation of is -439.7 kJ.
Bond Energy Heat of atomisation (kJ)
C – H = 413 C = 716.7
C – C = 348 H = 218.0
C = O = 732 O = 249.1
C – O = 351
O – H = 463
10. For a reaction, ΔH = 30 KJ mol-1 and ΔS = 0.07 KJ K-1 mol-1 at 1 atm. Calculate upto which temperature, the reaction would not be spontaneous.
Solutions of Level – I
1. Absolute entropy
2. In liquid, the molecules have much less freedom of motion as compared to the molecules of the gas. When a liquid changes into solid the entropy becomes very low because in a solid the molecular motion almost stops (except vibrational motion)
3. ΔG = ΔH – TΔS. For a reaction to occur, ΔG should be negative.
If both ΔH and ΔS are positive, ΔG can be negative only if TΔS > ΔH in magnitude. Thus either ΔS has large positive value so that even if T is low, TΔS is greater than ΔH or if ΔS is small, T should be high so that TΔS > ΔH.
4. The molecules in the vapour state have greater freedom of movement and hence greater randomness than those in the liquid state. Hence entropy increases in going from liquid to vapour state.
5. (a) Work done during heating of gas form 0°C to 100°C is
W = -PΔV = -P(V2 - V1) = -P[(nRT2/P)-(nRT1/P)]
= –nR (T2–T1) = –1 × 1.987 × (373 – 273)
= -198.7 cal
(b) If work equivalent to 198.7 cal is used for gas at 0°C, causing its isothermal expansion, from 1 atm to pressure Pt
WR = -2.303nRTlog(P1/P2)
–198 = –2.303 × 1.987 × 273log (1/Pt)
∴ Pt = 0.694 atm
6. Standard free energy of formation (ΔG°f) for the reaction 1/2 N2 (g) + 1/2 O2(g) is positive (= +86.7 KJ mol-1). Hence the reaction is non – spontaneous under the standard conditions.
7. -20 kcal/mol
8. -83.5 KJ
9. -21 kcal
11. Work done by the system
= –nRT loge P1/P2 = –2.303 nRT log10 P1/P2
= –2.303 × 5 × 8.314 × 300 log 10/2 = –20.075 × 103 J
Let M be the mass
Work done in lifting the mass
= Mgh = M × 9.8 × 1 J
M × 9.8 = 20.075 × 103
M = 2048.469 kg
12. ΔGo = –2.303 nRT log Kc
ΔGo = –2.303 × 8.314 × 298 log10 73
= -10.632 kJ
13. ΔH = 9900 bar ml
ΔU = 100 bar ml
14.400 KJ mol-1
Solutions of Level – 2
1. 99.35 kcal 2. +91.5 kcal
3. -857.64 KJ, -860.1175 KJ 4. 75.98 kcal
5. 8180 cal 6. 93.37 gm
7. -321.99 kcal
8. 68 cals
9. -110.3 kJ / mole
10. T < 428.57 K