Chemistry

Name: _________________________

CALCULATIONS INVOLVING STRONG ACIDS & BASES 3.

Calculations involving pH, pOH, Kw,  H3O+

(aq) )

 and OH- (aq).

pH 

Indicates the concentration of hydronium (hydrogen) ions in solution and therefore the degree of acidity



Developed by Soren Sorenson, a Danish chemist, in 1909 who used the term pH to refer to the potenz (power) of hydrogen.



pH is based on the logarithmic scale, to the base ten, and uses the following formula: pH = -(log10 H+(aq) ) or



pH = -(log10 H3O+(aq) )

 H3O+(aq)  ranges from approximately 10 mol/L down to 1.0 x 10-15 mol/L in most aqueous solutions, which correspond to pH values of –1 and 15, respectively.

pH Scale:

(p.570)



shows the range of possible pH values  most are between 0 and 14, however pH values may be lower than zero and greater than 14  a solution with a pH=7.00 is neutral, less than 7.00 is acidic ([H3O+] > [OH-]) and greater than 7.00 is basic ([H3O+] < [OH-])



In general, most foods are acidic (pH < 7.00);most cleaners are basic (pH > 7.00)

Approximate pH of Some Common Substances Substance 1.0 mol/L HCl(aq) Gastric juice (humans) Lemons Vinegar Soft drinks Wine Beer Rainwater Milk (cow) Saliva Pure water Blood Household ammonia 1.0 mol/L NaOH(aq)

Typical pH 0.0 2.0 2.3 2.9 3.0 3.4 4.5 6.2 6.5 7.0 7.0 7.4 11.0 14.0

pH Range 0.0 1.0-3.0 2.2-2.4 2.4-3.4 1.8-4.0 2.8-3.8 4.0-5.0 4.0-6.5 6.3-6.6 6.5-7.5 7.0 7.35-7.45 10.6-11.6 14.0

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Chemistry



Name: _________________________

Since the pH scale is a logarithm scale, for each decrease of one pH unit, the acidity of a solution increases by a factor of ten. For example,  at pH 6.00, a solution has a [H3O+] of 1.0 x 10-6, which is ten times greater than [H3O+] at pH 7.00  at pH 5.00, [H3O+] is 100 times greater than at pH 7.00.

Note: For solutions where the concentration of the hydronium ion is 1 times some power of ten, the pH is the negative of the exponent.  Eg: If [H3O+] of 1.0 x 10-7, the pH is 7.00

pH Calculations Finding pH from  H3O+(aq)  or OH- (aq) Example: The hydronium ion concentration in a cola is 4.5 x 10-4 mol/L. Find the pH of this solution. Solution: a)

Using a scientific calculator:  input 4.5, display shows 4.5  press the exponent key (exp or EE), display shows 4.5 00  press the +/- key and input 4, display shows 4.5 - 04  press the log key, display shows -3.3467875  press the +/- key, display shows 3.3467875

Note: Some scientific calculators require that you select the log key first, then input the value. Rounding Rule: Round off the pH value so that its number of decimal places equals the number of significant digits in the hydronium ion concentration when expressed in scientific notation. Since 4.5 x 10-4 has 2 significant digits, the pH value has 2 decimal places. The pH of the solution is 3.35. b)

Using a graphing calculator:  press the negative key (not the subtraction sign)  press the log key (log)  Input 4.5 second function key comma key, negative sign, 4, close bracket button  press the enter key  the display should show 3.3467875  Follow the rounding rule as above.

2

Chemistry

Name: _________________________

Exercises: 1.

Determine the pH from the following  H3O+(aq)  or OH- (aq) and indicate whether each solution is acidic or basic.

a)

 H3O+(aq)  = 1.0 x 10-13 mol/L, pH = _________, acidic or basic_________

b)

 H3O+(aq)  = 1 x 10-2 mol/L, pH = _________, acidic or basic __________

c)

 H3O+(aq)  = 10-6 mol/L, pH = _________, acidic or basic ______________

d)

 H3O+(aq)  = 0.0010 mol/L, pH = _________, acidic or basic ____________

e)

OH- (aq) = 1.0 x 10-6 mol/L, pH = _________, acidic or basic ____________

2.

Find the pH of a lime that has a hydronium ion concentration of 0.0120 mol/L.

3.

Determine the pH of a blood sample that has a OH- (aq) of 2.6 x 10-7mol/L

4.

Find  H3O+(aq)  and pH of a solution made by dissolving 10.0 g of KOH in water to make 4.00 L of solution.

3

Chemistry

Name: _________________________

Finding H3O+(aq)  or OH- (aq) from pH Since pH = -(log H3O+(aq) ), then log H3O+(aq) = -pH and H3O+(aq) = antilog (-pH)  H3O+(aq)  = antilog (-pH) Example 1: Find the hydronium ion concentration in a bottle of pop that has a pH of 2.09. Solution: a)

Using a scientific calculator:  input 2.09, display shows 2.09  press +/- key, display shows -2.09  press the second function key (e.g. 2ndF or inv), display shows -2.09  press log key (its second function is 10x), display shows 0.0081283052  Convert this value to scientific notation and round it off.

Note: Some scientific calculators require that you enter inverse/second function and log key first, then the value. Rounding Rule: Round off the concentration so that the final answer has the same number of digits as those to the right of the decimal in the pH value. The hydronium ion concentration is 8.1 x 10-3 mol/L b)

Using a graphing calculator:  press the 2nd function key  press the log key (it has 10x written over it)  press the negative sign  input 2.09  press enter  Round-off the answer as per the rule above.

Example 2: Find the hydroxide ion concentration in a solution with a pH of 2.92. First, solve for  H3O+(aq) :

Then, solve for OH- (aq):

 H3O+(aq)  = antilog (-pH)

OH- (aq) = 1.00 x 10-14 (mol/L)2 1.2 x 10-3 mol/L

= antilog (-2.92) = 1.2 x 10

-3

= 8.3 x 10-12 mol/L

mol/L

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Chemistry

Name: _________________________

Exercises: 1.

For each of the following, determine the  H3O+ (aq)  from the given pH, and indicate whether each solution is acid or basic or give the OH- (aq).

a)

pH = 9.00

 H3O+

(aq)

 = ________________acidic or basic___________

b)

pH = 5.0

 H3O+

(aq)

 = ________________acidic or basic ___________

c)

pH = 8.00

 H3O+

(aq)

 = ________________ OH- (aq) ______________

d)

pH = 6.00

 H3O+

(aq)

 = ________________ OH- (aq) ______________

2.

A sample of seawater was tested and found to have a pH of 8.64. Find  H3O+(aq) ) and OH- (aq).

3.

Consider a sample of stomach contents which has a pH of 1.40. Find  H3O+ (aq) ) and OH- (aq).

5

Chemistry

Name: _________________________

pOH CALCULATIONS The pOH refers to the alkalinity of a solution. The pOH scale is based on a logarithm scale, such that the lower the pOH value the greater the hydroxide ion concentration and therefore the more basic the solution. pOH = - ( log10OH- (aq)) Finding pOH from OH- (aq) Example: Calculate the pOH of a solution whose OH- (aq) is 3.94 x 10-3 mol/L. pOH

= - (log(3.94 x 10-3 mol/L)) = - ( - 2.405) = 2.405

Exercises: 1.

For each of the following hydroxide ion concentrations given, find the pOH value, and indicate whether the solution is acidic or basic.

a)

OH- (aq) = 2.0 x 10-11 mol/L

pOH = ________, acidic or basic _______

b)

OH- (aq) = 4.4 x 10-2 mol/L

pOH = ________, acidic or basic _______

c)

OH- (aq) = 1 x 10-14 mol/L

pOH = ________, acidic or basic _______

d)

OH- (aq) = 10-8 mol/L

pOH =________, acidic or basic _______

2.

Determine the pOH of a sample of blood that has a  H3O+(aq)  of 3.2 x 10-8 mol/L.

3.

Find the pOH of a solution prepared by dissolving 5.00 g of barium hydroxide in 2.00L of water.

4.

What is the pH of the solution in Question #3 above?

6

Chemistry

Name: _________________________

Finding OH- (aq) or  H3O+(aq)  from pOH Example 1: Find the hydroxide ion concentration in a solution with a pOH of 8.05.  OH-aq)  = antilog (-pOH) = antilog (- 8.05) = 8.9 x 10-9mol/L Example 2: Find the hydronium ion concentration in a solution that has a pOH of 12.06. NOTE: There are 2 ways to solve this problem: (1)

First, solve for  OH-aq) :

then, solve for  H3O+(aq) :

 OH-aq)  = antilog (-12.06)

 H3O+(aq)  = 1.00 x 10-14 mol/L)2 8.7 x 10-13 mol/L

= 8.7 x 10-13 mol/L

(2)

= 1.1 x 10-2 mol/L

First, find pH:

then, find  H3O+(aq) :

pH = 14.00 – pOH = 14.00 - 12.06 = 1.94

 H3O+(aq)  = antilog (-1.94) = 1.1 x 10-2 mol/L

Exercises: 1. For each of the following pOH values find the  OH-aq)  and indicate whether each solution is acidic or basic or give the pH value. a)

pOH = 8.76  OH-aq)  = __________________, acidic or basic __________

b)

pOH = 2.45  OH-aq)  = __________________, acidic or basic __________

c)

pOH = 7.0

d)

pOH = 8.00  OH-aq)  = __________________, pH = ______________

e)

pOH = 4.00  OH-aq)  = __________________, pH = ______________

2.

Find the hydronium concentration in a solution that has a pOH of 4.30.

 OH-aq)  = __________________, pH = ______________

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