sign of ∆G and ∆H, ∆S, and T

Discuss the factor ∆H, ∆S and ∆G for the spontaneous and non spontaneous processes     

                              OR                                                                                                                        

 classify the reaction with respect to sign of ∆G and ∆H, ∆S, and T

The process is spontaneous and non spontaneous is can be explained by Gibb’s equation.

                                                            ∆G = ∆H - T∆S

Case 1- if ∆H and ∆S are both are negative than ∆G will be negative only when T ∆S < ∆H or temp is low (then this reaction is carried out at low temp) hence this reaction is spontaneous.

Case 2- if ∆H and ∆S both are positive, then ∆G will be negative if T ∆S > ∆H such reaction must be carried out at high temperature hence this reaction is spontaneous

Case3- if ∆H is negative (∆H< 0) and ∆S is positive (∆S>0) then for all temp ∆G will be negative and reaction is spontaneous.

Case 4- if ∆H is positive (∆H>0) and ∆S is negative (∆S<0) , ∆G is always positive ∆G >0 hence the reaction will non spontaneous at all temp.

This can be summarized in the following table

Nature of reaction	∆H	∆S	∆G	Spontaneity of reaction
Exothermic	-ve	-ve	-ve at low temp	spontaneous at low temp
Endothermic	+ve	+ve	-ve at high temp	spontaneous only at high temp
Exothermic	-ve	+ve	-ve at all temp	spontaneous at all temp
Endothermic	+ve	-ve	+ve at all temp	non spontaneous at all temp

  

Temperature of equilibrium (Cross over temp)

We know that   

∆G = ∆H - T∆S

At equilibrium,     ∆G=0

 0=∆H - T∆S

   ∆H = T∆S

  T =

T is the temp at which change over between spontaneous and nonspontaneous occur.

Relation between ∆G and ∆Stotal

Derive the relation between ∆G and ∆S_total

soln:-

          Gibb’s free energy G is defined as

                            G = H - TS

Where H= enthalpy of system

            S= entropy of system

            T= absorbed temp

G is state function because H, T, S are state functions and extensive property.

          The change in Gibb’s energy ∆G depends upon the initial and final state and does not depend upon path

Therefore the change on Gibb’s energy at const temp and pressure defined as

                                       ∆G = ∆H - T∆S

Free energy change = Total enthalpy change - Temp X (Total entropy change)

 Definition:-

          It is the energy which is measure of work that can be obtained from a system at const temp and pressure.

Unit; - The SI unit of ∆G is J or KJ (or J/mol/or KJ/mole)

            The C.G.S unit of ∆G is cal or Kcal (Cal/mol or Kcal/mole)

 Gibb’s Energy and Spontaneity:-

            The total entropy change for a system and its surrounding for the process is given by.

            ∆Stotal = ∆Ssystem + ∆S surr.

            ∆S total = ∆S + ∆S (surr)

By second law of thermodynamics’ for spontaneous process

            ∆S total > 0

            If + ∆H is the entropy increases for the process or reaction at const. temp (T) and pressure then enthalpy decreases for surrounding will be -∆H

            ∆S (surr) = - ∆H /T

            ∆S = ∆S system + ∆S surr

            ∆S total = ∆S system - ∆H /T

T ∆S total = T ∆S system - ∆H

-T ∆S total = ∆H  - T ∆S system -------------  1

By Gibb’s equation

            ∆G = ∆H - T∆S total -------------------2

Comparing above two equation

∆G = -T ∆S total

This equation indicate that ∆G and ∆S total are have opposite signs because T is always positive.

∆G increases and ∆S total decreases

 Signification of ∆G

i)      ∆G < 0 process is spontaneous

ii)    ∆G > 0 process is non - spontaneous

iii)   ∆G =  0 process is at equilibrium 

spontaneous process and entropy

Spontaneous process (Irreversible process)

 Definition:-

 The process which is take place on its own without the external influence known as Spontaneous process.

Ex. flow of heat from hot body to cold body

Ex. Water flow from higher level to lower level.

          i.e. all the example show that the process occur spontaneously in one direction and cannot occurs spontaneously in opposite direction.

          The spontaneous process is still continuous up to the equilibrium reached.

Ex.- example of spontaneous process which is endothermic.

          Generally spontaneous process is exothermic but the many process which is endothermic and spontaneous. 

Ex;- Dilution of NaCl_(s) in water is spontaneous and endothermic process in which heat absorbed from surrounding.

         NaCl_(s) + aq  ---------->     Na⁺_(aq) + Cl^-_(aq)      ∆_soluH⁰ = +3.9 Kj/mol 

Ex. conversion of ice into water  

            Ice (H₂O_(s)) ---------->    water (H₂O_(l))      ∆_fusH⁰ = + 6.01KJ/mol

Entropy

  The molecular disorder or randomness is measured by thermodynamic property called entropy.

   It is denoted by S. greater is the randomness higher is the entropy.

          It is a state function and extensive property and unit is J/K

Ex.- When solid I₂  dissolved in water

                    I_2(s) ----------->     I_2(aq)               ∆S = positive

     Order state               disorder state                

Ex.- When H_2(g)  is converted in H_(g)

                 H_{2(g)---------------->}   2H_(g)                  ∆S = positive

         Disorder state           more disorder state 

Ex        H_{2 (g)} + O_{2 (g)}  ----------------> 2 H₂O_(l)   ∆S = Negative

More disorder state                       less disorder state

Quantitative definition of entropy (Entropy change):-        

          The entropy change (∆S) of a system in a process is equal to heat transferred to it in reversible manner divided by the absolute temperature (T) at which transfer takes placed. 

Entropy change = heat transfer reversibly/ absolute temp. of heat transfer

                          ∆S = qrev/T    

          Unit of entropy are JK^-1 in SI unit and cal K^-1 in C.G.S. system

Note: - The disorder of the system increases entropy increases i.e. solid has less entropy than liquid which has less entropy than vapour.absolute temp. of heat transfer

Entropy and spontaneity (second law of thermodynamics)

                    The total entropy of system and its surrounding increase in a spontaneous process.

                   ∆S_universe = ∆S _total = ∆S_sys + ∆S_surr >0

                             

Significance of ∆S

i)            ∆S total  >0 , process is spontaneous

ii)           ∆S total  <0 , process is non spontaneous

iii)         ∆S total  =0 , process is equilibrium

HESS'S LAW OF CONSTANT HEAT SUMMATION

HESS’S LAW OF CONSTANT HEAT SUMMATION

                                                        Hess’s law stated that if the chemical reaction takes place in one step or in several step then amount of heat absorbed or evolved during any chemical reaction is always remain same                                                                     

                                                                       OR

                                                  ‘’The law stated that the change in enthalpy in a chemical reaction depend upon initial state of reactant and final state of product and it does not depend on a path by which reaction is brought about”.

Explanation: -

                                       Let consider a reaction in which substance change from A to D this reaction takes place by two methods

1)     Direct Method

            2)     Indirect Method

 Direct Method:-

                In this method A is directly converted to D

                          A        ----------------->     D           ΔH = H_D- H_A           ----------------------------       1 

Where H_D is enthalpy of product D   AND H_A is enthalpy of reactant A

Indirect Method:-

                                    In this method the A is converted into D in several step

                        Step (i):-         A ---------------->    B                    ΔH₁ = H_B –H_A

                       Step (ii):-        B   ----------------->  C                     ΔH₂ = H_C- H_B

                       Step (iii):-       C  -------------------> D                    ΔH₃ = H_D -H_C

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                  Add i+ii+iii            A ------------------->  D       ΔH₁ + ΔH₂+ ΔH₃ = H_D – H_A ------------   2

From equation 1 and 2

                                    ΔH = H_D- H_A

                                    ΔH₁ + ΔH₂+ ΔH₃ = H_D – H_A

       In general      ΔH = ΔH₁ + ΔH₂+ ΔH₃+-----------+ ΔH_n

    Illustration: Consider the formation of Methylene chloride. This reaction is carried out by two ways.

Method I: - Direct method

                            Methylene chloride can be prepared directly by the reaction of CH₄ with Cl₂ gas

CH₄(g) + Cl₂ (g) + Heat ----------->  CH₂ Cl₂ (g) + 2HCl(g) ∆H₁ = -202.3 KJ ------1

Method II: - Indirect method

 Step I -  CH₄(g) + Cl₂(g)--------> CH₃Cl (g) + HCl(g)     ∆H₂ =  -98.3KJ  ------  1                                                                                                                            

Step II - CH₃Cl(g)+ Cl₂(g)---------> CH₂Cl₂ (g) + HCl(g)  ∆H₃  = -104.0KJ  ---  2

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   CH_4(g) + 2Cl_{2(g)------------->}  CH₂Cl_2(g) + 2HCl_(g)∆H = ∆H₂ + ∆H₃ =-202.3 KJ ---3

From equation 1 & 2

                             ∆H₁ = ∆H₂   +∆ H₃

Therefore, whether the reaction take placed in one step or in two or more step enthalpy of Reaction is always same