Hydroxide ion concentration: How to find the concentration of hydroxide ion from pH and pOH

Sample Problem 1 : What are the concentrations of hydronium and hydroxide ions in a beverage whose pH =3.05 ?

Solution:

Step1 : To convert from pH to ion concentrations,first apply equation 17-1 to calculate [H3O+]. Then make use of water equilibrium to calculate [OH-]

Step 2 : We must rearrange equation  pH = -log [H+]  , in order to solve for concentration

Step 3 : log [H+] = -pH and [H+] = 10 -pH   

Step 4 ; Now substitute and evaluate:

[H+] = 10-3.05 = 8.9 x 10-4 M

Step 5: To determine the hydroxide ion concentration,we need to rearrange the water equilibrium expression:

Kw = 1.0 x 10 -14 = [H3O+]eq [OH-]    and           [OH-]eq = 1.0 x 10- 14 / [H3O+]

now susbtitute and evaluate:

       = 1.0 x 10- 14 / 8.9 x 10-4  = 1.1 x 10-11 M   

 

Sample protblem 2 : What is the  OH- ion concetraion of a solution of NaOH with pH 13.40 ?

Solution:

Step 1 : First find pOH from the given pH:

     pH + pOH = 14 

      pOH = 14 - 13.40 = 0.60

Step 2 : As you have now the value of pOH you can find the OH- ion concentration using formula

pOH = -log [OH-]

[OH- ]  =  10 - pOH =  10 - 0.60 = 0.25 M

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