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Sunday, April 26, 2015

Explanation Of S-Block (Group IA) Elements

S – Block
(Group IA Elements)

Group I A Elements:

Hydrogen (Atomic number-1)

Lithium (Atomic number-3)

Sodium (Atomic number-11)

Potassium (Atomic number-19)

Rubidium (Atomic number-37)

Strontium (Atomic number-55)

Francium(Atomic number-87)

  •  Elements of group IA and IIA are known as s – block elements.
  •  Except Hydrogen all elements are metals.
  •  Group IA consists of Hydrogen, Lithium, Sodium, Potassium, Rubidium, Cesium, Francium.
  •  Group IIA consists of Beryllium, Magnesium, Calcium, Stratium, Barium, Radium.
  •   IA elements (except Hydrogen) – Alkali metals.
  •   IIA Elements   Alkaline earth metals.
  •  Have one electron in the outermost orbit.
  •  By loosing the electron they form stable + 1 ion.
  •  They are univalent and show + 1 oxidation state.


General periodic trends:
  •  As we move from up to down the atomic radius increases.
  • Order of radius size = H < Li < Na < Rb < Cs < Fr
  • Ionization potential coming from top to bottom decreases.
  • Density generally increases with an increase in atomic mass.
  • Exception   Potassium is expected to have more density than sodium but actually has less than sodium.
  • Electronegativity from top to bottom decreases.
  • Alkali metals along their individual periods have largest atomic radius.
  • Mobility of ions increases down the group
               is the order of mobility of ions.
  • Hydration enthalpy decreases down the group.
                in case of hydration enthalpy.


 Ø   Heating effects of carbonates of IA elements. 
   
      

     

 Ø   All metal carbonates of IA except    have no effect on heating.

        Ø  Heating effect of nitrates of IA elements.
                          
                              
Flame Test :

     Crimson Red
   Yellow
     Violet
    Red Violet
    Blue


Friday, April 24, 2015

Indefinite Integrals

Explanation Of Indefinite Integrals.......
  •  A function   is called a primitive (or) an anti-derivative of a function f(x) of
  •                                                
                                 
                          
                           Here  f(x) = integrand                                                 
                                                           














Algorithm to solve integrals of form:
                            
                       
                                    where     
Step 1:    Find m,n
Step 2:
*   If m is odd i.e. power or index of sin x is odd, put cos x = t and reduced the integrand in terms of it.
*  If n is odd then put sin x = t and reduce the integrand.
*  If both are odd you can use any of above two methods.

  • To Evaluate integrals of form
    where      and m + n is negative even integer then put
  tan x = t.
  • To evaluate integrals of form    where m,n are positive even integers then.                   
                                Let Z = cos x + i sin x
                                   
                                   
                                   
                                   
                                   
  • Some important standard integrals :
                           
                             
                           
                               
                           
                           

      Integrals of form

               to evaluate this type of integrals
                                 
      Define        (or)      


      Depending on integral then find     in terms of     (or) 


       Now integrate both sides of expression to get required integral.

Integration by parts :

     


     Very IMP Note:  
                            Choose first function as the function which come first in word “ILATE”
      (1)  I – Inverse trigonometric
L – logarithmic functions
A – algebraic functions
T for Trigonometric functions
E for exponential functions.

 è   Integrals of the form
                   
          Note:
                         
           è    
           è    

Some Very Important Integrals :

                   
                   
                  

Reduction Formulae :