Equilibria Solutions

1) What is the hydronium concentration of 0.03M solution of C₃H₇COOH, butanoic acid?
      What is the percent ionization?  The K_a of butanoic acid is 1.52x10^-5.

       C₃H₇COOH    +   H₂O  <--->  C₃H₇COO^-    +   H₃O⁺

          K_a =  [C₃H₇COO^-][H₃O⁺ ]
                  [C₃H₇COOH]      

        1.52x10^-5 =  [x][x] 
                            0.03M

        4.56 x 10^-7 =  x²

        6.75 x 10^-4 M =  x  =   [C₃H₇COO^-]  =  [H₃O⁺ ]    

        % ionization =       [H₃O⁺ ]        =   6.75 x 10^-4 M  x   100   =   2.25%
                               [C₃H₇COOH]                0.03M

2) What is the K_a of  0.15M citric acid, C₄H₆O(COOH)₃ when [C₄H₆O(COOH)₂COO^-]
      is 0.011M?

        C₄H₆O(COOH)₃  +   H₂O  <--->  C₄H₆O(COOH)₂COO^-   +   H₃O⁺

          K_a =  [C₄H₆O(COOH)₂COO^-][H₃O⁺ ]
                             [C₄H₆O(COOH)₃]

         K_a =  [0.011M][0.011M]
                            0.15M

         K_a =  7.44 x 10^-4

 3) What is the K_b of  2.8M phosphate, PO₄^3- when [OH^-] is 0.198M?

      PO₄^3- +  H₂O  <--->  PO₄H^2-  +  OH^-

        K_b =  [PO₄H^2-][OH^- ]
                         [PO₄^3- ]

         K_b =  [0.198M][0.198M]
                            2.8M

         K_b =  1.4 x 10^-2       

4) What is the hydroxyl concentration of a 0.2M solution of ammonia, NH₃? 
     What is the percent ionization?  The K_b of ammonia is 1.74 x 10^-5. 

       NH₃  +   H₂O  <--->  OH^-    + NH₄⁺

          K_b = [OH^-][NH₄⁺ ] 
                       [NH₃]      

        1.74 x 10^-5 =  [x][x] 
                            0.2M

        3.48 x 10^-6 =  x²

        1.87 x 10^-3 M =  x  =   [OH^-]  =  [NH₄⁺ ]    

        % ionization =       [ OH^-]        =   1.87 x 10^-3 M  x   100   =   .93%
                                     [NH₃]                0.2M

COMMON ION PROBLEMS

5)  What is the hydronium ion concentration, [H₃O⁺], in a solution of 0.521M HKCO₃ and 
      0.024 M K₂CO₃?  Ka of  HKCO₃ is 4.37 x 10^-7.  

       HKCO₃  +   H₂O <-->  1H₃O⁺  +  KCO₃^-  (+ KCO₃^-  + KOH)         

       K_a = [H₃O⁺][ KCO₃^- + 0.024M KCO₃^-]  
                            [HKCO₃ ]

        4.37 x 10^-7 = [X][X + 0.024M KCO₃^-]  
                                           0.521M

        4.37 x 10^-7 = 0.024X  
                              0.521M

        2.28 x 10^-7 = 0.024X

        9.49 x 10^-6 = X =  [H₃O⁺]

6)  What is the hydronium ion concentration, [H₃O⁺], in a solution of  1.13M HBO₃^-2 and 
      0.02 M Na₃BO₃?  Ka of  HBO₃^-2 is 1.58 x 10^-14. 

      H BO₃^-2 +   H₂O <-->  1H₃O⁺  +  BO₃^-3   (+ BO₃^-3  + Na₃OH₃)

        K_a = [H₃O⁺][ BO₃^{- 3}+ 0.02 M BO₃^-3]  
                            [HBO₃^-2 ]

        1.58 x 10^-14 = [X][X + 0.02 M BO₃^-3]  
                                           1.13 M

        1.58 x 10^-14 = 0.02 X  
                               1.13 M

        1.79x 10^-14 = 0.02 X

        8.93 x 10^-13 = X =  [H₃O⁺]

TITRATION PROBLEMS

7) How many mL of  0.15 M KOH are needed to neutralize 25.00 mL of  .20 M HCl?

     HCl + KOH <--> KCl + HOH

  [25.00 mL HCl][        1 L HCl][.20 mol HCl][1 mol KOH][1L KOH][1000 mL KOH] =
                           [1000mL HCl][1 L HCl      ][1 mol HCl   ][.15mol KOH][1L KOH   ]

  33.33 mL KOH required to neutralize HCl

8) If 28.25 mL of 0.50 M NaOH are needed to neutralize 50.00 mL of  HNO₃, what
    is the concentration of HNO₃? 

    HNO₃ + NaOH <-->  NaNO₃ + HOH

    [28.25 mL NaOH][   1 L  NaOH][.50 mol NaOH][1 mol HNO₃]          [1000mL] =
                            [1000mL NaOH][1 L    NaOH][1 mol NaOH][50 mL HNO₃][1L]

   0.283 M HNO₃ is the concentration of the acid