Entropy

Entropy is a measure of randomness or disorder of the system.

The greater the randomness, the higher is the entropy. Evidently, for a given substance, the crystalline solid state has the lowest entropy, the gaseous state has the highest entropy and the liquid state has the entropy in-between the two. Thus, the order of randomness or entropy of solid, liquid and gas is :

Gas > Liquid > Solid

Like internal energy and enthalpy, entropy is a state function. The change in its value during a process, called the entropy change (represented by ∆S) is given by

∆S = S₂ - S₁ = ∑ S_Products – ∑S_Reactants

Quantitatively, the degree of disorder, i.e., expression for the entropy change may be arrived at as follows:

(i) When a system absorbs heat, the molecules start moving faster because kinetic energy increases.

Hence, the disorder increases. More the heat absorbed, greater is the disorder.

(ii) For the same amount of heat absorbed at low temperature, the disorder is more than at higher temperature. This shows that entropy change is inversely proportional to temperature.

Thus, AS is related to q and T for a reversible reaction as :

∆S =

Hence,

Entropy change during a process is defined as the amount of heat (q) absorbed isothermally and reversibly (infinitesimally slowly) divided by the absolute temperature (T) at which the heat is absorbed.

Units of Entropy Change

As ∆S = and it is an extensive property, therefore, the units of entropy change are calories/K/mol (cal K^-1 mol^-1) in C.G.S. system and joules/K/mol (J K^-1 mol^-1) in SI units.

At the end of the cyclic process, the entropy of the system remains the same as it originally had. This proves that entropy is a state function.

Problems

1. The entropy values (in JK^-1 mol^-1) of H₂ (g) = 130.6, Cl₂ (g) = 223.0 and HCl(g) = 186.7 at 298 K and 1 atm pressure. Then entropy change for the reaction H₂ (g) +Cl₂ (g) →2HCl (g) is

A. + 540.3 

B. + 727.3

C. - 166.9 

D. + 19.8

Solution:

ΔS°=2S°HCl−(S°H₂+S°Cl2)

=2×186.7− (130.6+223.0)

= 19.8JK⁻¹mol⁻¹

2.  Which of the following is zero during adiabatic expansion of the gas

A. ∆T

B. ΔS

C. ΔE

D. None of these

Solution:

For adiabatic expansion q=0 then according to following relation 

ΔS=qT, ΔS=0

3. In which state, the matter have highest entropy

A. Solid     

B. Liquid

C. Gas       

D. Equal in all

Solution:

Entropy of gases is highest.

4. The ΔS for the vaporisation of 1 mol of water is 88.3 J/mole K. The value of ΔS for the condensation of 1 mol of vapour will be

A. 88.3 J/mol K       

B. (88.3)2 J/mol K

C. - 88.3 J/mol K   

D. 188.3 J/mol K

Solution:

For reverse reaction sign will be change.

5. For which reaction from the following, ΔS will be maximum

A. Ca(s)+12O₂(g)→CaO(s)

B. CaCO₃(s)→CaO(s)+CO₂(g)

C. C(s)+O₂(g)→CO₂(g)

D. N₂(g)+O₂(g)→2NO(g)

Solution:

Solid → Gas, 

ΔS is maximum.

6. The occurrence of a reaction is impossible if

A. ΔH is +ve; ΔS is also + ve but ΔH<TΔS

B. ΔH is - ve; ΔS is also - ve but ΔH>TΔS

C. ΔH is - ve; ΔS is + ve

D. ΔH is + ve; ΔS is - ve

Solution:

+ve ΔH and –ve ΔS both oppose the reaction.

7. For chemical reactions, the calculation of change in entropy is normally done

A. At constant pressure

B. At constant temperature

C. At constant temperature and pressure both

D. At constant volume

Solution:

Calculation of change in entropy is done at constant temperature and pressure both.

8. When the value of entropy is greater, then the ability of work

A. Is maximum      

B. Is minimum

C. Is medium          

D. None of these

Solution:

When the value of entropy is greater, then ability of work is maximum.

9. When a solid is converted into liquid, entropy

A. Becomes zero  

B. Remains the same

C. Decreases          

D. Increases

Solution:

Solid→Liquid, 

ΔS increases

10. In a spontaneous process, the entropy of the system and its surroundings

A. Equals zero

B. Decreases

C. Increases            

D. remains constant 

Solution:

ΔS=+ve than process is spontaneous.

11. The positive value of ΔS indicates that

A. The system becomes less disordered

B. The system becomes more disordered

C. The system is in equilibrium position

D. The system tends to reach at equilibrium position

Solution:

ΔS=+ve than the system is more disordered.

12. The entropy of a perfectly crystalline solid at absolute zero is

A. Positive               

B. Negative

C. Zero      

D. Not definite

Solution:

According to III law of thermodynamics. The entropy of a perfectly crystalline solid at absolute zero is Zero.