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Acids and Bases

“Acids get the reputation for being scary and corrosive, but a strong base can often do the same damage — or worse. In this GIF Coke cans are subjected to a strong base (sodium hydroxide) and a strong acid (hydrochloric acid). At the molecular level, bases are donating oxygen atoms, and acids are donating hydrogens. Corrosion results from this disruption of molecular structure.”

pH scale and powers of 10

pH chart

* some substances are acids, some are bases

* acids are defined by the amount of somethings – H+ ions – floating in solution

* concentration of H+ ions varies a lot!

* If we use a linear x and Y axis, we’d have to compress a huge range of into tiny regions of the graph. Or, we could draw the data uncompressed, but then one of the axes would be huge. We’d need a 50 foot long sheet of paper… Look at this example from Math Bench. Has data for 600 animals. Can you see them all? On a linear scale, many of these data points are very close to each other.

Both axes are linear – each increment steps up an equal amount. Let’s think about the size of most mammals. Are most small or big? How many different species of mice are there compared to, say, elephants? Like most organisms, there are lots of species that are small and only a few that are big. In the case of our 600 mammals, about 95% are smaller than 15,000 grams. That means that the vast majority of our 600 data points are smashed into that first little segment of the graph. It’s impossible to see whats going on! “

“Now look at the same graph with both axes scaled by factors of 10 (logarithmic axes)”  ->graph on the right

“What a difference. There’s still lots of points to look at – but they are now spread evenly along both axes – so you can really see what’s going on across all six orders of magnitude in size.”

{quotes from Math Bench Biology Modules http://mathbench.umd.edu/modules/misc_scaling/page10.htm }

Here we can see a linear plot, and then the same plot transformed onto a log scale.

linear versus log scales

*If we use a log scale, we don’t have to use those huge ranges of H+ numbers (from billions, own to billionths. ) Now we just need to use the number in the exponent of the equations. Much simpler number system, and easy to graph.

pH scale examples
Adapted from “Creating the pH Scale – Teacher’s Guide”,  The WaterCAMPWS Center for Advanced Materials for Purification of Water with Systems, University of Illinois at Urbana-Champaign

Visualizing acids and bases

water molecule = 2 hydrogen atoms and 1 oxygen atom.

H atoms are smaller than O, and have a positive charge.

O is bigger and has a negative charge.

Water molecule has a + end and a – end.


water molecule

These + and – charges give water special abilities. Molecules of water stick to each other, to form chains. These chains create surface tension.

Another quality of water is dissociation: when these molecules bump into each other, sometimes a H atom breaks away from the remaining OH.

H2O                      ↔     H+          +             OH

Water                                                  hydrogen ion                                       hydroxide ion

(neutral)                                               (positive)                                             (negative)

water decomposition hydrogen hydroxide

Consider the H+ ions, when they get near regular water molecules.

H+ ions are not stable: They bond with H2O molecules, to form H3O+   (hydronium ion).

H+ bond with H2O to form Hydronium

In the end, water breaks apart into hydroxide ions and hydronium ions.

2H2O          ↔      OH             +       H3O+

water               ↔      hydroxide   +       hydronium

neutral ph            basic pH              acidic pH


In neutral water there are an equal number of basic and acidic ions.

Ratio of acidic to basic ions determines whether it is neutral, an acid, or a base.

pH scale developed in 1920.
pondus hydrogenii” or the potential for hydrogen ions (H+).

pH ranges from 0 to 14

0 = very strong acid

7 = neutral solution (equal number of H+ ions and OH- ions)

14 = very strong base

Lemon juice has pH  =  2.  Seven-up soda has pH = 4

But lemon juice is not twice as acidic as Coca-Cola…it is 100 times more acidic than the Seven-up!

How is that? The pH scale is based on powers of ten.

Water              ->         pH = 7

Root Beer        ->         pH = 6

The one unit difference means there’s a ten times difference in strength.

So there are 10 times the number of H+ ions.

pH Powers of ten copy

External links

“When Should I Use Logarithmic Scales in my Charts and Graphs?”
Originally published by Naomi Robbins on blogs.forbes.com.



MathBench Biology Modules!
“Data for scaling studies are almost always displayed and analyzed using log-transformed data. We are going to show you why and how – and make sure you are comfortable looking at these kinds of data and graphs. To do this, we are going to use our full data set of 600 mammals, and you will see why it is easier to see and analyze patterns in the data. In fact, you can see it just by looking at this picture!”


11th grade Chemistry

from "An Introduction to Chemistry by Mark Bishop"


pH and Equilibrium

According to the Arrhenius theory of acids and bases, when an acid is added to water, it donates an H+ ion to water to form H3O+ (often represented by H+).

The higher the concentration of H3O+ (or H+) in a solution, the more acidic the solution is.

An Arrhenius base is a substance that generates hydroxide ions, OH, in water. The higher the concentration of OH in a solution, the more basic the solution is.

Pure water undergoes a reversible reaction in which both H+ and OH are generated.

H2O(l)        H+(aq)  +  OH(aq)

The equilibrium constant for this reaction, called the water dissociation constant, Kw, is 1.01 × 10-14 at 25 °C.

Kw  =  [H+][OH]  =  1.01 × 10-14   at 25 °C

Because every H+ (H3O+) ion that forms is accompanied by the formation of an OH ion, the concentrations of these ions in pure water are the same and can be calculated from Kw.

Kw  =  [H+][OH]  =  (x)(x)  =  1.01 × 10-14

x  =  [H+]  =  [OH-]  =  1.01 × 10-7 M
(1.005 × 10-7 M before rounding)

The equilibrium constant expression shows that the concentrations of H+ and OH in water are linked. As one increases, the other must decrease to keep the product of the concentrations equal to 1.01 × 10-14 (at 25 °C).

If an acid, like hydrochloric acid, is added to water, the concentration of the H+ goes up, and the concentration of the OH goes down, but the product of those concentrations remains the same.

An acidic solution can be defined as a solution in which the [H+] > [OH].

The example below illustrates this relationship between the concentrations of H+ and OH in an acidic solution.

EXAMPLE 1 – Determining the Molarity of Acids and Bases in Aqueous Solution:  Determine the molarities of H+ and OH in a 0.025 M HCl solution at 25 °C.


Kw  =  [H+][OH]  =  1.01 × 10-14   at 25 °C

We assume that hydrochloric acid, HCl(aq), like all strong acids, is completely ionized in water. Thus the concentration of H+ is equal to the HCl concentration.

[H+] = 0.025 M H+

We can calculate the concentration of OH by rearranging the water dissociation constant expression to solve for [OH] and plugging in 1.01 × 10-14 for Kw and 0.025 for [H+].

Note that the [OH] is not zero, even in a dilute acid solution.

If a base, such as sodium hydroxide, is added to water, the concentration of hydroxide goes up, and the concentration of hydronium ion goes down. A basic solution can be defined as a solution in which the [OH] > [H+].

EXAMPLE 2 – Determining the Molarity of Acids and Bases in Aqueous Solution:    Determine the molarities of H+ and OH in a 2.9 × 10-3 M NaOH solution at 30 °C.


Kw  =  [H+][OH]  =  1.47 × 10-14   at 30 °C    (From Table)

Sodium hydroxide is a water-soluble ionic compound and a strong electrolyte, so we assume that it is completely ionized in water, making the concentration of OH- equal to the NaOH concentration.

[OH] = 2.9 × 10-3 M OH

Note that the [H+] is not zero even in a dilute solution of base.

Typical solutions of dilute acid or base have concentrations of H+ and OH between 10-14 M and 1 M. The table below shows the relationship between the H+ and OH concentrations in this range.

Concentrations of H+ and OH in Dilute Acid and Base Solutions at 25 °C

[H+] [OH]
1.0 M 1.0 × 10-14 M
1.0 × 10-3 M 1.0 × 10-11 M
1.0 × 10-7 M 1.0 × 10-7 M
1.0 × 10-10 M 1.0 × 10-4 M
1.0 × 10-14 M 1.0 M

We could describe the relative strengths of dilute solutions of acids and bases by listing the molarity of H+ for acidic solutions and the molarity of OH for basic solutions. There are two reasons why we use the pH scale instead.

The first reason is that instead of describing acidic solutions with [H+] and basic solutions with [OH], chemists prefer to have one scale for describing both acidic and basic solutions. Because the product of the H+ and OH concentrations in such solutions is always 1.01 × 10-14 at 25 °C, when we give the concentration of H+, we are indirectly also giving the concentration of OH.

For example, when we say that the concentration of H+ in an acidic solution at 25 °C is 10-3 M, we are indirectly saying that the concentration of OH in this same solution is 10-11 M.

When we say that the concentration of H+ in a basic solution at 25 °C is 10-10 M, we are indirectly saying that the OH concentration is 10-4 M.

The pH concept makes use of this relationship to describe both dilute acid and dilute base solutions on a single scale.

The next reason for using the pH scale instead of H+ and OH concentrations is that in dilute solutions, the concentration of H+ is small, leading to the inconvenience of measurements with many decimal places, such as 0.000001 M H+, or to the potential confusion associated with scientific notation, as with 1 × 10-6 M H+.

In order to avoid such inconvenience and possible confusion, pH is defined as the negative logarithm of the H+ concentration.

pH  =  -log[H+]

Instead of saying that a solution is 0.0000010 M H+ (or 1.0 × 10-6 M H+) and 0.000000010 M OH (or 1.0 × 10-8 M OH), we can indirectly convey the same information by saying that the pH is 6.00.

pH  =  -log[H+]  =  -log(1.0 × 10-6)  = 6.00

When  taking  the logarithm of a number, report the same number of decimal positions in the answer as you had significant figures in the original value.

Because 1.0 × 10-6 has two significant figures, we report 6.00 as the pH for a solution with 1.0 × 10-6 M H+.

The table below shows a range of pH values for dilute solutions of acid and base.

pH of Dilute Solutions of Acids and Bases at 25 °C

[H+] [OH-] pH
1.0 1.0 × 10-14 0.00
1.0 × 10-1 1.0 × 10-13 1.00
1.0 × 10-2 1.0 × 10-12 2.00
1.0 × 10-3 1.0 × 10-11 3.00
1.0 × 10-4 1.0 × 10-10 4.00
1.0 × 10-5 1.0 × 10-9 5.00
1.0 × 10-6 1.0 × 10-8 6.00
1.0 × 10-7 1.0 × 10-7 7.00
1.0 × 10-8 1.0 × 10-6 8.00
1.0 × 10-9 1.0 × 10-5 9.00
1.0 × 10-10 1.0 × 10-4 10.00
1.0 × 10-11 1.0 × 10-3 11.00
1.0 × 10-12 1.0 × 10-2 12.00
1.0 × 10-13 1.0 × 10-1 13.00
1.0 × 10-14 1.0 14.00

This table illustrates several important points about pH. Notice that

  • When the solution is acidic ([H+] > [OH), the pH is less than 7.
  • When the solution is basic ([OH] > [H+]), the pH is greater than 7.
  • When the solution is neutral ([H+] = [OH]), the pH is 7. (Solutions with pH’s between 6 and 8 are often considered essentially neutral.)

Also notice that

  • As a solution gets more acidic (as [H+] increases), the pH decreases.
  • As a solution gets more basic (higher [OH]), the pH increases.
  • As the pH of a solution decreases by one pH unit, the concentration of H+ increases by ten times.
  • As the pH of a solution increases by one pH unit, the concentration of OH increases by ten times.
  • The pH, [H+], and [OH] of some common solutions are listed in the figure below. Notice that gastric juice in our stomach has a pH of about 1.4, and orange juice has a pH of about 2.8. Thus, gastric juice is more than ten times more concentrated in H+ than orange juice.

The pH difference of about 4 between household ammonia solutions (pH about 11.9) and milk (pH about 6.9) shows that household ammonia has about ten thousand (104) times the hydroxide concentration of milk.

pH of Common Substances     Acidic solutions have pH values less than 7, and basic solutions have pH values greater than 7. The more acidic the solution is, the lower its pH. The more basic a solution is, the higher the pH.

The corresponding H+ and OH concentrations are shown in units of molarity. Notice that a decrease of one pH unit corresponds to a ten-fold increase in [H+], and an increase of one pH unit for a basic solution corresponds to a ten-fold increase in [OH].

EXAMPLE 3 – pH Calculations:  In Example 1, we found that the H+ concentration of a 0.025 M HCl solution was 0.025 M H+. What is its pH?


pH = -log[H+]  =  -log(0.025) =  1.60

EXAMPLE 4 – pH Calculations:  In Example 2, we found that the H+ concentration of a 2.9 × 10-3 NaOH solution was 5.1 × 10-12 M H+. What is its pH?


pH = -log[H+]  =  -log(7.5 × 10-12) =  11.29

We can convert from pH to [H+] and [OH] using the following equations, as demonstrated in Examples 5 and 6.

[H+]  =  10-pH

EXAMPLE 5 – pH Calculations:  What is the [H+] in a glass of lemon juice with a pH of 2.12?


[H+]  =  10-pH  =  10-2.12  =  7.6 × 10-3 M H+

EXAMPLE 6  – pH Calculations: What is the [OH] in a container of household ammonia at 25 °C with a pH of 11.900?


[H+]  =  10-pH  =  10-11.900  =  1.26 × 10-12 M H+

Learning Standards

2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS1-9 (MA). Relate the strength of an aqueous acidic or basic solution to the extent of an acid or base reacting with water, as measured by the hydronium ion concentration (pH) of the solution. Make arguments about the relative strengths of two acids or bases with similar structure and composition.

Science and Engineering Practices

Mathematical and computational thinking in 9–12 builds on pre-K–8 and experiences and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data.

Benchmarks for Science Literacy, AAAS

Most cells function best within a narrow range of temperature and acidity. At very low temperatures, reaction rates are too slow. High temperatures and/or extremes of acidity can irreversibly change the structure of most protein molecules. Even small changes in acidity can alter the molecules and how they interact. 5C/H7

The temperature and acidity of a solution influence reaction rates. Many substances dissolve in water, which may greatly facilitate reactions between them. 4D/M4



ACS Middle School Chemistry Lessons

From middleschoolchemistry.com, contact staff at ACS. Copyright 2015 American Chemical Society

Online textbook: Chapter 5: Acids Bases and their reactions



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