In this explainer, we will learn how to define pH as a logarithmic measure of acid concentration and use it to determine the relative acidity or basicity of a substance.
There are many ways to define an acid. According to the Arrhenius definition, acids are substances that release hydrogen ions, while bases are substances that release hydroxide ions.
Definition: Arrhenius Acid
A substance that produces hydrogen ions () or increases the hydrogen ion concentration when dissolved in water.
Definition: Arrhenius Base
A substance that produces hydroxide ions () or increases the hydroxide ion concentration when dissolved in water.
The acidity of a substance depends on the concentration of its hydrogen ions, written as . If we look at an arbitrary acid , it will dissociate to release hydrogen ions in water:
However, hydrogen ions do not usually exist alone in water. They combine with water molecules to form hydronium ions with the chemical formula . This idea is described by the Brønsted–Lowry definition, which states that acids are substances that can donate a hydrogen ion, while bases are substances that accept a hydrogen ion. The dissolution of an arbitrary acid according to the Brønsted–Lowry definition is as follows:
Rather than simply releasing hydrogen ions, the acid in this equation donates a hydrogen ion to a water molecule. When determining the acidity, we need to know the concentration of hydronium ions, .
Chemists often use  and  interchangeably. It is simpler to refer to hydrogen ions alone, but it is more accurate to refer to hydronium ions. Either way, it is important to recognize that the two models described here are different ways of describing the same chemical process.
If we compare any two acids, the one with the higher concentration of hydrogen or hydronium ions will be more acidic. Scientists wanted a way to refer to the acidity or basicity of a substance without including the specific concentration of the ion, which can sometimes be a difficult number to work with. We can elegantly describe the acidity or basicity of a solution with the pH scale.
An example of a pH scale is shown in the figure below. The pH scale runs from 0 to 14, where 0 is the most acidic and 14 is the most basic. Water with a pH of 7 is considered neutral. A substance with a pH value below 7 is acidic, while a substance with a pH value greater than 7 is basic.
The higher the concentration of hydronium ions, the more acidic the substance and the lower the pH value. Coffee has a pH of 5 and so is mildly acidic. Stomach acid has a pH of 1 and is extremely acidic. If we compared the two acids, we would find a much higher concentration of hydronium ions in stomach acid than in coffee.
For basic solutions, a higher pH means a higher concentration of hydroxide ions. Egg whites have a pH of 9 and are mildly basic, while a drain cleaner has a pH of 14 and is extremely basic. The drain cleaner has a much higher concentration of hydroxide ions in solution than the egg white.
When the concentration of hydronium ions and hydroxide ions are the same, the solution is neutral. Pure water is a neutral substance with a pH of 7. In the image above, it is directly between the acids to the left and the bases to the right.
It is worth noting that the pH scale described so far is most accurate at a temperature of . Changing the temperature of a solution affects the acid’s ability to form hydronium ions, therefore, affecting the pH and shifting the pH scale.
Example 1: Determining Whether a Solution of a Given pH is Acidic, Basic, or Neutral
Coffee has a pH of 5. Is it acidic, basic, or neutral?
To answer this question, we need to know what pH values correspond to acidic, basic, and neutral solutions. At , a neutral solution has a pH of 7, a basic solution has a pH greater than 7, and an acidic solution has a pH less than 7.
With a pH less than 7, coffee is acidic.
The pH scale is a logarithmic scale that indicates the concentration of hydrogen ions, .
In a logarithmic scale like pH, increasing or decreasing the pH by 1 corresponds to a change in hydrogen ion concentration by a magnitude of ten. A solution with a pH of 4 has a concentration of hydrogen ions ten times greater than a solution with a pH of 5. A solution with a pH of 6 has a concentration of hydrogen ions ten times less than a solution with a pH of 5, and a hundred times less than a solution with a pH of 4. The table below can help us visualize this difference.
To calculate the magnitude of concentration difference in larger jumps on the scale, we can simply use powers of 10. A pH change of 2 is a concentration change of or 100 times. A pH change of 3 is a concentration change of or 1 000 times. A pH change of 6 is a concentration change of or 1 000 000 times.
Example 2: Determining the Change in Concentration from the Change in pH
An acidic solution was found to have a pH of 1. Upon the addition of a small volume of a base, the pH changed to 3. By what factor has the concentration of ions changed?
To answer this question, we must be aware of the relationship between pH and hydrogen ion concentration. We must determine the factor of change as well as the direction of that change.
Since pH is a logarithmic scale, a one-unit change in pH means that the ion concentration changes by a factor of 10. A two-unit change in pH means the concentration changes by a factor of , or in other words, by a factor of 100.
We now need to determine the direction of change. Since the pH is increasing, the solution is becoming more basic and less acidic, meaning the concentration of hydrogen ions is decreasing.
Putting these two pieces of information together, we can write our final answer. The concentration of hydrogen ions has decreased by a factor of 100.
Up to this point, we have considered only hydrogen ion concentration or , but a similar scale can be constructed using the concentration of hydroxide ions or .
A solution with a high hydrogen ion concentration will have a low hydroxide ion concentration. A solution with a high hydroxide ion concentration will have a low hydrogen ion concentration.
We cannot have a solution with high concentrations of both ions because the hydrogen ions and hydroxide ions would react to form water molecules and move the pH toward neutrality.
To include the concentration of hydroxide ions, we can look at something called pOH. We calculate pOH the same way as pH, but using the concentration of hydroxide ions instead of hydrogen ions. The result is that the pOH scale is the mirror of the pH scale. At , the sum of a solution’s pH value and pOH value is equal to 14. If we want to calculate the pH but only have the concentration of hydroxide ions, we can calculate the pOH value and subtract it from 14.
Relationship: The Relationship between the pH and pOH of a Solution at 25∘C
The pH and pOH of a solution at are related through the following equation:
A high pOH value means a low concentration of hydroxide ions and therefore an acidic solution. A low pOH value means a high concentration of hydroxide ions and therefore a basic solution. Coffee, with a pH of 5 and a pOH of 9, is mildly acidic. A drain cleaner, with a pH of 14 and a pOH of 0, is extremely basic.
Example 3: Determining Whether a Solution of a Given pOH is Acidic, Basic, or Neutral
Orange juice has a pOH of 9.8. Is it acidic, basic, or neutral?
To answer this question, we must know the ranges of pOH values for acidic, basic, and neutral solutions.
The pOH scale is the reverse of the pH scale. Acidic solutions have a pOH above 7, while basic solutions have a pOH below 7. Neutral solutions have a pOH of 7.
With a pOH above 7, orange juice is an acidic solution.
To keep from getting confused between pH and pOH, we could calculate the pH of orange juice as well. A solution with a pOH of 9.8 will have a pH of 4.2, as at , the pH and pOH values sum to 14. A solution with a pH of 4.2 is acidic.
We can observe experimentally how the pH of an aqueous solution changes when we neutralize an acid with a base or vice versa. The graph below shows how the pH of a strong acid like changes upon the addition of a strong base like sodium hydroxide, .
Initially, the pH changes gradually as the hydroxide ions from the base react with the hydrogen ions from the acid to form water molecules. The effect of this is to slowly decrease the concentration of hydronium ions in the solution and so raise the pH.
Upon the further addition of base, the pH begins to change more rapidly as it approaches the point at which the concentration of hydronium ions will equal that of hydroxide ions. Eventually, this point will be reached and surpassed, leading to a greater number of hydroxide ions compared with hydronium ions. When that happens, the pH will suddenly increase and the solution will rapidly become more basic.
As the pH increases to become more and more basic, the same amount of solution added will increase the pH by less and less each time, resulting in a flattening of the pH curve.
Example 4: Identifying the Graph Showing Change in pH When Mixing an Acid with a Base
In an experiment, a solution of 1 M was placed into a beaker. solution was added to the beaker at regular intervals and the pH was continually measured. Which of the graphs shows how the pH would change during this experiment?
This question is asking us to identify which graph shows how the pH changes over the course of a reaction. We begin with an acid, , and slowly add a base, .
As we are beginning with a solution of an acid, then the pH is likely to be low. Adding a basic solution to an acidic solution can only increase the pH. Choices B and C show a decreasing pH, so we can discount these as being the correct answer.
As we add the basic solution to the acid, the hydroxide ions will neutralize the hydrogen ions, eventually neutralizing all of them to create a basic solution.
At the beginning of this process, the pH will increase slowly, as there is a very high concentration of hydrogen ions. Eventually, a point will be reached where the pH will change more quickly. At this point, the solution is neutralized. Once the solution is neutralized and there are more hydroxide ions relative to hydrogen ions, the pH will continue to increase, but at a more gradual rate.
This process of an initial slow increase, followed by a rapid increase, followed by an ending slow increase is the exact shape of the curve we see in choice D. The correct answer is choice D.
Definition: pH Indicator
A pH indicator is a substance that changes color within a certain range of pH values.
We can use a variety of chemicals known collectively as indicators to approximate the pH of a solution. An indicator will change color within a certain pH range. For example, methyl orange is red up to a pH of 3.0, orange from 3.0 to 4.4, and yellow at pH values above 4.4. The colors associated with pH values of several common indicators are included in the graph below.
If we add methyl orange to a solution with an unknown pH and the indicator turns yellow, we will know that the pH of the solution is between 4.4 and 14. These indicators give a range of values for the pH of the solution, but not a precise measurement.
In order to provide more precision, scientists developed a mix of indicators called the “universal indicator” that provides a spectrum of colors across the pH scale.
The colors of the universal indicator are shown in the image below, with red representing a pH of 0-1, green representing a pH of 7, and purple representing a pH of 14. Using the universal indicator gives a narrower range of possible pH values than other indicators, allowing us to approximate the pH of the solution to the nearest whole number. While even universal indicators are imprecise, they are easier to use and less expensive than digital pH probes for everyday uses such as pool maintenance and gardening.
Example 5: Estimating pH Values of Solutions with Added Universal Indicator
A few drops of universal indicator were added to four flasks containing unknown solutions. Which of the following values provide the best estimate for the pH of each solution?
- A = 11, B = 1, C = 3, and D = 7
- A = 3, B = 7, C = 11, and D = 1
- A = 3, B = 1, C = 11, and D = 7
- A = 1, B = 11, C = 7, and D = 3
- A = 7, B = 11, C = 3, and D = 1
This question is asking us to match pH values to the solutions in the beakers based on their colors. The easiest way to solve this problem would be to look at a reference table for the colors and pH values of the universal indicator, but there is a way to solve it intuitively.
The colors for the universal indicator follow a rainbow, with the most acidic solutions turning red and the most basic solutions turning purple. Among the four answer choices, the red solution, D, will have the lowest pH, followed by yellow, A, then green, B, and finally blue, C.
Only two answer choices have the red solution, D, as the lowest pH, choice B and choice E. Only choice B has yellow as the next lowest pH. Checking the last two values, we find that choice B indeed has the blue solution as the highest pH and the green solution as the second highest.
Looking at a reference table confirms our answer that red solutions have a pH of 1, yellow solutions have a pH of 3, green solutions have a pH of 7, and blue solutions have a pH of 11.
The correct answer is choice B.
Let us summarize what has been learned in this explainer.
- The pH scale tells us the acidity or basicity of a solution. At , a pH of 7 represents a neutral solution. Values greater than 7 are basic, while values lower than 7 are acidic.
- More specifically, the pH value of a solution is an indication of the concentration of hydrogen ions or hydronium ions within it.
- The pH scale is a logarithmic scale, meaning that a change in 1 unit of pH represents a change in hydrogen ion concentration.
- The inverse of the pH scale is the pOH scale, which indicates the concentration of hydroxide ions.
- In the reaction of an acid with a base, the pH changes as hydronium and hydroxide ions react. The changes in pH can be used to follow the reaction and determine the point at which the solution shifts from acidic to basic.
- Chemicals called “indicators” change color within certain pH ranges. They can be useful for approximating the pH of a solution.