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Tuesday 23 December 2014

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 ∆Stotal

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
                    I2(s) ----------->     I2(aq)               ∆S = positive
     Order state               disorder state                
Ex.- When H2(g)  is converted in H(g)
                 H2(g)---------------->   2H(g)                  ∆S = positive
         Disorder state           more disorder state 
Ex        H2 (g) + O2 (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.
                   ∆Suniverse = ∆S total = ∆Ssys + ∆Ssurr >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

Monday 22 December 2014

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 = HD- HA           ----------------------------       1 
Where HD is enthalpy of product D   AND HA is enthalpy of reactant A
Indirect Method:-
                                    In this method the A is converted into D in several step
                        Step (i):-         A ---------------->    B                    ΔH1 = HB –HA
                       Step (ii):-        B   ----------------->  C                     ΔH2 = HC- HB
                       Step (iii):-       C  -------------------> D                    ΔH3 = HD -HC
---------------------------------------------------------------------------------------------------------------------------------------------------
                  Add i+ii+iii            A ------------------->  D       ΔH1 + ΔH2+ ΔH3 = HD – HA ------------   2
From equation 1 and 2
                                    ΔH = HD- HA
                                    ΔH1 + ΔH2+ ΔH3 = HD – HA
       In general      ΔH = ΔH1 + ΔH2+ ΔH3+-----------+ ΔHn

    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
-------------------------------------------------------------------------------------------------------
   CH4(g) + 2Cl2(g)------------->  CH2Cl2(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