PLUG-IN   LOGS   &   pH    Chapter 7

 

10³ = 1000
The log of 1000 is 3.

10^-2 = .01
The log of .01 is -2.
The log is the exponent of 10.

Drill

Write the log of
       10000
             10
               1
               0.1
               0.01
               0.001
               0.0000001 

We can do logs of numbers other than powers of 10. 

10⁰ = 1           log of 1 = 0 

10¹ = 10   

log of 10 = 1 

so the logs of numbers between 1 and 10 are decimals.

 

Where do we get them?
            (a) log tables
            (b) calculators with log functions

From Log Tables

  log of 6 = .7782
  log of 4 = .6621

Find the log of
            3
            7
            9
            2
            1

(a) 30
(b) 300
(c) 3000
(d) 35
(e) 350
(f) 3500
(g) 82
(h) 23
(i) 54

 

Plug in Logs - pH and pOH

Find the log of 0.002.

Find the log of 0.0083.

Drill

Find the log of
(a) .02
(b) .002
(c) .0002
(d) .0025
(e) .0000001
(f) .0000008 

pH and Hydrogen Ion Concentration

pH refers to the concentration of [H⁺].
pOH refers to the concentration of [OH]^-.
In pure water at 25^oC the concentration of [H⁺]and the concentration of hydroxyl ions [OH]^- in moles per liter equal and each is equal to 1 x 10^-7 moles/liter.

pH is the negative log of [H⁺].
    The log of the [H⁺] is -7.
    The negative log of [H⁺] is -(-7) = 7. 

pOH refers to the negative log of [OH]^-.
   p[OH]^-  +  p[H⁺] = 14

 If we know the pH we can find out the pOH.

The pH is 4. What is the pOH?
pH + pOH = 14
 4 + X   = 14
  pOH    = 10

The pOH is 3. What is the pH?

pH 7 is neutral
pH's below 7 are acid.
pH's above 7 are basic.
Scale goes from 0 to 14. 

Molarity of Acid                       H⁺ moles/liter                            pH 

   1                                           10⁰                               0
                         .1                                          10^-1                              1                         
                         .01                                        10^-2                              2
                         .001                                      10^-3                              3
                         .0001                                    10^-4                              4
                         .00001                                  10^-5                              5 

The molarity of a solution of HCl is .015 M. What is its pH? (Find the log of 0.015).

 

What is the pH corresponding to a hydrogen ion concentration of 5 x 10^-4?

 

The pOH is 8. (a) What is the pH?                  (b) What is the [H⁺]?
(a) pH + pOH = 14                                                     (b) pH is the neg log of H⁺
                x + 8   = 14                                                   pH 6 = neg log of [H⁺] concentration
                  x   = 6                                                                        6 is the log   
               pH   = 6                                                                        -6 is the neg. log.
                                                                                                              1 x 10^-6

 

Drill  Determine the pH of the following solutions:
 (1) pOH = 4
 (2) pOH = 3
 (3) pOH = 11
 (4) pOH = 5.6
 (5) pOH = 3.5

 (6) 1 x 10^-3 M H⁺
 (7) 1 x 10^-6 M H⁺
 (8) 1 x 10^-8 M H⁺
 (9) 1 x 10^-8 M [OH]^-
(10) 1 x 10^-2 M [OH]^-
(11) 1 x 10^-4 M[OH]^-
(12) .001 M HCl
(13) .0001 M HCl
(14) .01 M Na(OH)
(15) .001 M Na(OH)
(16) 1 x 10^-2 M HCl
(17) 1 x 10^-3 M Na(OH)
(18) a solution that contains 1 x 10^-5 mole [H⁺] per liter
(19) a solution that contains .001 M [H⁺] per liter
(20) a solution that contains 1 x 10^-5 mole OH^- per liter
(21) a solution that contains .00001 M NaOH
(22) 3 x 10^-3 M HCl
(23) 5 x 10^-2 M [H⁺]
(24) 7 x 10^-5 M HCl
(25) 1.5 x 10^-5 M HCl
(26) 3.2 x 10^-2 M HCl
(27) .004 M [H⁺]
(28) .0003 M HCl
(29) .015 M [H⁺]
(30) .075 M HCl
(31) .0000025 M [H⁺]
(32) 2 x 10^-8 M Na(OH)
(33) 4 x 10^-2  M [OH]^-
(34) 7 x 10^-10 M [OH]^-
(35) 2.5 x 10^-3 M K(OH)
(36) 7.5 x 10^-6 M Na(OH)
(37) .025 M Na(OH)
(38) .0075 M Na(OH)
(39) .000015 M Na(OH) 

To go from the pH to the concentration, we must reverse the steps.

To find the pH from the concentration of  2.3 x 10^-4 M HCl, the steps are

2.30  exp   4   +/-     log     +/-         Ans 3.64 

To go from the pH 3.64 to concentration, the steps are

3.64    +/-     inv or 2nd      log      Ans 2.30 x 10^-4    

On some calculators the steps are
2nd or inv     log      -       3.64

What is the H⁺ concentration in the following solutions:

pH 3                                                                           pOH 5
pH 7                                                                           pOH 7
pH 2                                                                           pOH 10
pH 5.2                                                                        pOH 2.8
pH 4.3                                                                        pOH 5.1