1 CALCULATIONS INVOLVING STRONG ACIDS & BASES 1. Finding H 3 O + (aq) ) from strong acid concentrations and OH - (aq) from strong base concentrations 2. Finding H 3 O + (aq) and OH - (aq) using K w. 3. Calculations involving ph, poh, K w, H 3 O + (aq) ) and OH - (aq). 4. Dilution Problems Finding H 3 O + (aq) from strong acid concentrations and OH - (aq) from strong base concentrations Step 1 Step 2 Write the ionization equation (strong acid) or dissociation equation (strong base) Use the mole ratio to calculate the ion concentration in solution Examples: 1. Find the H 3 O + (aq) ) in a 0.467 mol/l solution of hydrochloric acid. 2. Find the OH - (aq) in a 0.0356 mol/l magnesium hydroxide solution. 1. Find the H 3 O + (aq) ) in a 0.497 mol/l solution of nitric acid. 2. Find the OH - (aq) in a 0.0272 mol/l strontium hydroxide solution.
2 Background Information: Finding H 3 O + (aq) and OH - (aq) using K w Pure water has a very slight conductivity that can only be measured with very sensitive equipment, therefore water can form ions: H 2 O (l) H + (aq) + OH - (aq) Auto-ionization of water water molecules in a pure sample of water will collide with each other, some of which will react to produce ions: H 2 O (l) + H 2 O (l) H 3 O + (aq) + OH - (aq) reverse reaction is favored since the most prevalent species present is water reaction is at a maximum when there are no other chemical species present ie. in pure water K w, the Equilibrium Constant of Water Also called ionization constant or ion-product constant The expression for the equilibrium constant = products reactants In pure water, the equilibrium concentration for both H 3 O + (aq) and OH - (aq) = 1.00 x 10-7 mol/l, at 25 0 C. Thus K w = H 3 O + (aq) OH - (aq) = 1.00 x 10-14 (mol/l) 2 (Recall that water is not included in the expression since it is a liquid) Addition of an acid or base will increase the H 3 O + (aq) or OH - (aq) and shift the equilibrium in such a way as to reduce the concentration of the other ion. Since K w will not change with changes in concentration (unless there is a temperature change), the value of K w can be used to find the unknown concentration of H 3 O + (aq) or OH - (aq). Example: If 1.00 x 10-3 mol of NaOH (aq) is added to 1.00 L of water, at 25 0 C, find the H 3 O + (aq). Since H 3 O + (aq) OH - (aq) = 1.00 x 10-14 (mol/l) 2, then H 3 O + (aq) = 1.00 x 10-14 (mol/l) 2 = 1.00 x 10-14 (mol/l) 2 = 1.00 x 10-11 mol/l OH - (aq) 1.00 x 10-3 mol/l Thus addition of OH - to the water: - increased OH - (aq) from 1.00 x10-7 mol/l to 1.00 x 10-3 mol/l - decreased H 3 O + (aq) from 1.00 x10-7 mol/l to 1.00 x 10-11 mol/l
3 Diagram to illustrate that the product of H 3 O + (aq) OH - (aq) is a constant H 3 O + (aq) = 10-1 10-4 10-7 10-10 10-13 OH - (aq) = 10-13 10-10 10-7 10-4 10-1 1. 2. Write the answers to the following questions in the blank spaces provided above. 1. What is the product of H 3 O + (aq) OH - (aq) in each situation in the above figure? 2. Label each situation above as to whether the aqueous solution is acidic (A), basic (B) or neutral (N). Conclusion: In any solution of an acid or a base both H 3 O + (aq) and OH - (aq) are present but their concentrations will vary (and their product, at 25 o C, will always be 1.00 x 10-14 mol/l) ACID: H 3 O + (aq) OH - (aq) BASE: H 3 O + (aq) OH - (aq) In pure water, NEUTRAL: H 3 O + (aq) = OH - (aq)
4 Examples: 1. Find the H 3 O + (aq) in a cleaning solution that is 0.00400 mol/l KOH. 2. Find the OH - (aq) of a solution of apple juice in which H 3 O + (aq) = 6.0 x 10-3 mol/l. 3. A recipe for lye soap calls for 3.40g of NaOH to be dissolved in water to produce a 15.0 ml NaOH solution. Find the OH - (aq) and H 3 O + (aq) Assume standard conditions of 25 0 C and 101 kpa for all questions below. 1. Find the H 3 O + (aq) in milk of magnesia that has a OH - (aq) = 1.43 x 10-4 mol/l. 2. Find the OH - (aq) in lime juice where H 3 O + (aq) = 1.3 x 10-2 mol/l 3. Find the OH - (aq) and H 3 O + (aq) in a solution of aluminum hydroxide prepared by dissolving 2.50g of the ionic compound in water to produce a 150.0 ml solution.
5 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 = -(log 10 H + (aq) ) or ph = -(log 10 H 3 O + (aq) ) H 3 O + (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 of 7.00 is neutral, less than 7.00 is acidic ([H 3 O + ] > [OH - ]) and greater than 7.00 is basic ([H 3 O + ] < [OH - ]) In general, most foods are acidic (ph < 7.00) and most cleaners are basic (ph > 7.00) 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 [H 3 O + ] of 1.0 x 10-6, which is ten times greater than [H 3 O + ] at ph 7.00 at ph 5.00, [H 3 O + ] 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 [H 3 O + ] of 1.0 x 10-7, the ph is 7.00
6 ph Calculations Finding ph from H 3 O + (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: If using a graphing calculator (e.g. TI-83, TI-84, etc): 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. If using a non-graphing 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. Solution: The ph of the solution is 3.35. 1. Determine the ph from the following H 3 O + (aq) or OH - (aq) and indicate whether each solution is acidic or basic. a) H 3 O + (aq) = 1.0 x 10-13 mol/l, ph =, acidic or basic b) H 3 O + (aq) = 1 x 10-2 mol/l, ph =, acidic or basic c) H 3 O + (aq) = 10-6 mol/l, ph =, acidic or basic d) H 3 O + (aq) = 0.0010 mol/l, ph =, acidic or basic e) OH - (aq) = 1.0 x 10-6 mol/l, ph =, acidic or basic
7 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 10-7 mol/l 4. Find H 3 O + (aq) and ph of a solution made by dissolving 10.0 g of KOH in water to make 4.00 L of solution.
8 Finding H 3 O + (aq) or OH - (aq) from ph Since ph = -(log H 3 O + (aq) ), then log H 3 O + (aq) = -ph and H 3 O + (aq) = 10 -ph Example 1: Find the hydronium ion concentration in a bottle of pop that has a ph of 2.09. Solution: If using a graphing calculator (e.g. TI-83, TI-84, etc): press the 2nd function key press the log key (it has 10 x written over it) press the negative sign input 2.09 press enter Round-off the answer as per the rule above. If using a non-graphing 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 10 x ), 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. Solution: The hydronium ion concentration is 8.1 x 10-3 mol/l Example 2: Find the hydroxide ion concentration in a solution with a ph of 2.92. First, solve for H 3 O + (aq) : Then, solve for OH - (aq):
9 1. For each of the following, determine the H 3 O + (aq) from the given ph, and indicate whether each solution is acid or basic or give the OH - (aq). a) ph = 9.00 H 3 O + (aq) = acidic or basic b) ph = 5.0 H 3 O + (aq) = acidic or basic c) ph = 8.00 H 3 O + (aq) = OH - (aq) d) ph = 6.00 H 3 O + (aq) = OH - (aq) 2. A sample of seawater was tested and found to have a ph of 8.64. Find H 3 O + (aq) ) and OH - (aq). 3. Consider a sample of stomach contents which has a ph of 1.40. Find H 3 O + (aq) ) and OH - (aq).
10 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 = - ( log 10 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 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 H 3 O + (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?
11 Finding OH - (aq) or H 3 O + (aq) from poh Example 1: Find the hydroxide ion concentration in a solution with a poh of 8.05. OH- aq) = 10 -poh = 10-8.05 = 8.9 x 10-9 mol/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 H 3 O + (aq) : OH- aq) = 10-12.06 H 3 O + (aq) = 1.00 x 10-14 mol/l) 2 = 8.7 x 10-13 mol/l (2) First, find ph: then, find H 3 O + (aq) : 8.7 x 10-13 mol/l = 1.1 x 10-2 mol/l ph = 14.00 poh H 3 O + (aq) = 10-1.94 = 14.00-12.06 = 1.1 x 10-2 mol/l = 1.94 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 OH- aq) =, ph = 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.
12 ACID & BASE DILUTION PROBLEMS Most solutions bought for laboratories are done so in concentrated form. Some solutions are prepared in concentrated form in the laboratory for later use. The purchased or prepared concentrated solutions are then diluted to give solutions of known concentration as required. When a solution is diluted, only the amount of solvent is increased. Therefore, the number of moles of solute in the initial (concentrated) solution is equal to the number of moles in the final (diluted) solution. Since n = Cv and n i = n f, then C i v i = C f v f, where i = initial and f = final. Examples: 1. Nitric acid, with an initial concentration of 0.256 mol/l, is used to prepare 100 ml of a diluted acid solution. If 15 ml of the concentrated acid is used, what will be the ph of the diluted solution? 2. Calculate the poh of a 0.150 L solution of sodium hydroxide that is prepared by adding 25 ml of a more concentrated sodium hydroxide solution with a poh of 1.12 to water.
13 1. Calculate the ph of a dilute solution of hydrobromic acid if the initial solution has a ph of 2.40 and 34 ml of this concentrated acid is diluted to a final volume of 2.56 L. 2. Find the poh of a 3.45 L solution of KOH if the poh of the concentrated solution is 2.70 and 49 ml of it is diluted. 3. Find the volume of a dilute solution of sulfuric acid when 10.0 ml of 5.50 mol/l sulfuric acid is added to water to prepare a final solution with a concentration of 0.34 mol/l. 4. In many high school chemistry laboratories acids and bases are used at a concentration of 0.10 mol/l. If a student wants to prepare 100 ml of 0.10 mol/l hydrochloric acid from a more concentrated solution of this acid (1.0 mol/l), what volume of the original acid must be used?