A25.0 ml sample of a 0.2900 m solution of aqueous trimethylamine is titrated with a 0.3625 m solution of hcl. calculate the ph of the solution after 10.0, 20.0, and 30.0 ml of acid have been added; pkb of (ch3)3n = 4.19 at 25°c.

a) After adding 10 mL of HCl

first, we need to get moles of (CH3)3N = molarity * volume

                                                                 = 0.29 m * 0.025 L
                                                                 = 0.00725M moles
then, we need to get moles of HCl = molarity * volume

                                                          = 0.3625 m * 0.01L
                                                          = 0.003625 moles

so moles of (CH3)3N remaining    = moles of (CH3)3N - moles of HCl
                                                         = 0.00725 - 0.003625

                                                      = 0.003625 moles

and when the total volume = 0.01 L + 0.025L = 0.035 L

∴ [(CH3)3N] = moles remaining / total volume

                    = 0.003625 moles / 0.035L
                    = 0.104 M

when we have Pkb so we can get Kb :

pKb = - ㏒Kb
4.19 = -㏒Kb

∴Kb = 6.5 x 10^-5

when Kb = [(CH3)3NH+] [OH-] / [(CH3)3N]

and by using ICE table we assume we have:

[(CH3)3NH+] = X & [OH] = X 

and [(CH3)3N] = 0.104 -X

by substitution:

∴ 6.5 x 10^-5 = X^2 / (0.104-X)  by solving for X

∴X = 0.00257 M
∴[OH-] = X = 0.00257 M

∴POH = -㏒[OH]

           = -㏒0.00257
           = 2.5

∴ PH = 14 - POH
         = 14 - 2.5
         = 11.5
b) after adding 20ML of HCL:

moles of HCl = molarity * volume
                       = 0.3625 m * 0.02 L

                       = 0.00725 moles

  

the complete neutralizes of (CH3)3N we make 0.003625 moles of (CH3)3NH+ So, now we need the Ka value of (CH3)3NH+:

and when the total volume = 0.02L + 0.025 = 0.045L

∴ [ (CH3)3NH+] = moles / total volume

                          = 0.003625 / 0.045L
                          = 0.08 M
 
when Ka = Kw / Kb 

and we have Kb = 6.5 x 10^-5 & we know that Kw = 1 x 10^-14 

so, by substitution:

Ka = (1 x 10^-14) / (6.5 x 10^-5)

    = 1.5 x 10^-10

when Ka expression = [(CH3)3N][H+] / [(CH3)3NH+]

by substitution:

∴ 1.5 x 10^-10 = X^2 / (0.08 - X)  by solving for X

∴X = 3.5 x 10^-6  M

∴ [H+]= X = 3.5 x 10^-6 M

∴PH = -㏒[H+]

        = -㏒(3.5 x 10^-6)

       = 5.5

C) after adding 30ML of HCl:

moles of HCl = molarity * volume 

                       = 0.3625m * 0.03L

                       = 0.011 moles

and when moles of (CH3)3N neutralized = 0.003625 moles 

∴ moles of HCl remaining    = moles HCl - moles (CH3)3N neutralized

                                                = 0.011moles - 0.003625moles

                                                = 0.007375 moles
when total volume = 0.025L + 0.03L

                                = 0.055L

∴[H+] = moles / total volume

           = 0.007375 mol / 0.055L

            = 0.134 M

∴PH = -㏒[H+]

        = -㏒ 0.134

        = 0.87

You use the atomic number to find out how many protons and neutrons there are in the atom. you use the atomic mass to find out how many protons and electrons there are in the atom. 

Both models are effective because they show the valence electrons, and these valence electrons indicate the reactivity of an element.