5.8.2 The pH Scale
A chemist prepares a stock solution of hydrochloric acid, HCl, for use in a series of experiments. The solution pH is 1.00. The graph below displays the relationship between pH and concentration of hydrogen ion, represented by [H+].
Use the graph to answer the following questions.
1. What is the hydrogen ion concentration, [H+] in moles/litre for a solution with:
a) pH = 1.5
b) pH = 3.0
c) pH = 2.5
2. If hydrogen ion concentration is a measure of the strength of an acid, how much stronger is the acid at pH 1.5 than 3.0?
3. Describe the relationship between pH and hydrogen ion concentration.
5.8.3 The pOH Scale
A lesser known measurement sometimes used in chemical laboratories is pOH, which is analogous to pH. The pOH of very dilute basic solutions provides a means of measuring small concentrations of hydroxide ion, OH-. The sum of the pH and pOH of a solution is 14 under standard laboratory conditions.
The graph below represents the relationship between hydroxide ion concentration, [OH-] and pH and pOH for a solution of sodium hydroxide, NaOH.
Use the graph to answer the following questions:
1. Determine the pH and pOH of a solution with hydroxide ion concentration of:
a) 0.05 mol/L b) 0.01 mol/L
c) 0.005 mol/L d) 0.001 mol/L
2. If hydroxide ion concentration is a measure of the strength of the base, how much stronger is the solution at
a) 0.05 mol/L than at 0.01 mol/L
b) 0.05 mol/L than at 0.005 mol/L
3. Determine the hydroxide ion concentration in mol/L of a solution have the following:
a) pH = 12.0
b) pH = 10.5
c) pOH = 2.5
d) pOH = 1.2
5.8.2 The pH Scale (Answers)
1. What is the hydrogen ion concentration, [H+] in moles/litre for a solution with:
a) pH = 1.5 Answer: 0.0325 mol/l
b) pH = 3.0 Answer: 0.001 mol/l
c) pH = 2.5 Answer: 0.003
2. If hydrogen ion concentration is a measure of the strength of an acid, how much stronger is the acid at pH 1.5 than 3.0?
Answer:
An acid with pH 1.5 is about 32.5 times stronger than an acid with pH 3.0.
3. Describe the relationship between pH and hydrogen ion concentration.
Answers may vary. Ideally, students will make reference to the shape of the curve and describe the curve as either exponential or logarithmic. In fact, the relationship between pH and hydrogen ion concentration is logarithmic.
5.8.3 The pOH Scale (Answers)
1. Determine the pH and pOH of a solution with hydroxide ion concentration of:
a) 0.05 mol/L Answer: pH =12. 7 pOH = 1.3
b) 0.01 mol/L Answer: pH = 12.0 pOH = 2.0
c) 0.005 mol/L Answer: pH = 11.7 pOH = 2.3
d) 0.001 mol/L Answer: pH = 10.7 pOH = 3.3
2. If hydroxide ion concentration is a measure of the strength of the base, how much stronger a base is the solution at
a) pOH 1.5 than at pOH 2.0?
Answer: 0.03 mol/l ÷ 0.01 mol/l = 3. It is about 3 times stronger a base.
b) pH 13.0 than at pH 11.7?
Answer: 0.11 mol/l ÷ 0.005 mol/l = 22. It is about 22 times stronger a base.
3. Determine the hydroxide ion concentration in mol/L of a solution have the following:
a) pH = 12.0 Answer: 0.01 mol/l
b) pH = 10.5 Answer: 0.0005 mol/l
c) pOH = 2.5 Answer: 0.003 mol/l
d) pOH = 1.2 Answer: 0.07 mol/l
5.8.4 Industrial Water Treatment
In industry, it is critical that system water be tested on a regular basis to prevent corrosion of machinery and equipment. One example is that of industrial boilers. Many boilers operate at extremely high temperatures and pressures and must be maintained to ensure their metal structures are not weakened by corrosion from water that is too acidic or basic.
The graph below is typical of that used to calculate the amount of free carbon dioxide in industrial feed water. The presence of free carbon dioxide is a concern because it ionizes in water to create corrosive carbonic acid, H2CO3. Industrial water treatment consultants recommend that high pressure boiler feed water contain less than 10 parts per million (ppm) of free carbon dioxide. Free carbon dioxide removal is accomplished by passing condensed steam through ion exchangers before reboiling it to evaporate any remaining gas.
Free CO2 Content in Boiler Feed Water vs. pH for Varying Total Alkalinities
5.8.4 Industrial Water Treatment (Continued)
To determine the free carbon dioxide using the graph above, locate the intersection of the vertical line for the system pH with the curved line for the system total alkalinity. Read horizontally to the left to determine the free carbon dioxide content in parts per million (ppm).
Use the graph to answer the following questions:
1. Complete the following table:
Methyl Orange Total Alkalinity, ppm / System pH / Free CO2 Content, ppm100 / 6.75
20 / 7.25
20 / 130
50 / 6.50
6.88 / 75
50 / 5.75
20 / 6.00
5.63 / 230
100 / 7.50
2. In your role as water treatment consultant you are required to make recommendations about the levels of system pH and total alkalinity your client should aim for in the water treatment program. Using the graph and completed table above, provide recommendations for system pH and total alkalinity that will ensure a free carbon dioxide content of less than 10 ppm.
3. After reflecting upon your recommendations, what conclusions can you draw about the relationships among total alkalinity, pH, and safe levels of free carbon dioxide in this industrial boiler feed water example?
5.8.4 Industrial Water Treatment (Answers)
Use the graph to answer the following questions:
1. Complete the following table:
Methyl Orange Total Alkalinity, ppm / System pH / Free CO2 Content, ppm100 / 6.75 / 96-98
20 / 7.25 / 5
20 / 5.88 / 130
50 / 6.50 / 65-67
100 / 6.88 / 75
50 / 5.75 / 385
20 / 6.00 / 100
20 / 5.63 / 230
100 / 7.50 / 15-17
2. In your role as water treatment consultant you are required to make recommendations about the levels of system pH and total alkalinity your client should aim for in the water treatment program. Using the graph and completed table above, provide recommendations for system pH and total alkalinity that will ensure a free carbon dioxide content of less than 10 ppm.
Responses may vary. Ideally, students will recognize that there are three total alkalinities to be considered, therefore there will be three corresponding system pH recommendations to make as well.
Since the system must maintain a free carbon dioxide level below 10 ppm, we are only dealing with the extreme right hand portion of the curves.
Total Alkalinity 20 ppm : pH must be maintained above 7.00
Total Alkalinity 50 ppm: pH must be maintained above approximately 7.35
Total Alkalinity 100 ppm: pH must be maintained above approximately 7.75
3. After reflecting upon your recommendations, what conclusions can you draw about the relationships among total alkalinity, pH, and safe levels of free carbon dioxide in this industrial boiler feed water example?
Students should notice that as the total alkalinity increases, so does the required system pH. Therefore, total alkalinity must have a negative effect on free carbon dioxide levels.
5.8.5 Home Activity
Sample Response
This graph compares linear and exponential growth. As you can see, the linear relation is labelled “arithmetic growth” and the exponential relation is labelled “geometric growth.” The graph of exponential growth was copied from an article about population growth. Population growth is caused by increases in the birth rate and immigration and is offset by the death rate of a population. The article points out that the reason population growth is exponential is because as time elapses, the size of the “pool” of subjects able to reproduce keeps increasing.
Elapsed time / Year / Human Population~2,000,000 / 10,000,000 BC / 5 - 10 million
10,000 / 1 A.D. / 170 million
1,800 / 1800 / 1,000,000,000
1930 / 2,000,000,000
1960 / 3,000,000,000
1975 / 4,000,000,000
1987 / 5,000,000,000
1999 / 6,000,000,000
2050 / 8,500,000,000
The table to the right was included in the same article. It is interesting because it shows a comparison of world human population over time. From the table, we can predict that the world’s population will be an estimated 8.5 billion people by the year 2050. Of course, that prediction only holds true if the rate of growth demonstrated by the table of values holds true.
If we calculate the average and instantaneous rates of growth for human population at a given point in time, we can easily see that they will not be the same.
5.8.5 Home Activity (Continued)
Since there is an inverse relationship between exponential and logarithmic functions, even though this is a graph showing exponential growth, it could be looked at in the context of logarithms. For example, if the equation for growth was given as where a is the base for the exponential function and t represents time, we could rearrange it to show the inverse, and find that .
Source: Indiana University – Purdue University Indianapolis, Department of Biology Course Notes, N100H, Population Ecology, April 17, 2000. Retrieved August 4, 2007 from http://www.biology.iupui.edu/biocourses/N100H/ch39pop.html