# How to calculate ph Abstract: pH is a unit of measurement often used in fundamental chemistry concepts. “How to Calculate pH” explains it’s categories the scientific mathematics and role pH has in our lives.

### Terms to Be Familiar With:

• pH
• pOH
• Hydrogen ion
• Hydroxide ion
• Acid
• Base

## The pH Scale: Acidic, Neutral, and Basic

The pH scale describes the acidity of the solution: acidic, neutral, or basic A solution with a pH less than 7 is an acid, exactly 7 is a neutral solution, and above 7 is a base. Bases have less hydrogen ions but more hydroxide ions, represented by the pOH or “potential of hydroxide ions.”

Table 1. The pH Scale

 Acidic Neutral Basic Less than 7 7 Greater than 7

Many other scientists studied the proprieties of acids and bases from the ideas of Sorensen and Arrhenius and came up with their own definitions. A notable theory is known as the Bronsted-Lowry Theory. The Bronsted-Lowry Theory is a concept involving acid and bases which suggest that acids act as proton donors. Since neutral hydrogen atoms are usually made of one proton and one electron, a positive hydrogen ion is often referred to as a proton. These protons carry a positive charge and are given away to the bases. Bases, with that logic, are proton acceptors. Bases, carrying lone pairs of electrons, attract positive hydrogen ions (protons).

In the lab, pH can be determined by a pH indicator such as pH paper. pH paper usually contains a weak acid or a weak base which will respond by changing color at a specific pH. This method is used frequently as a cheap, quick way to determine pH rather than using pH meters which need frequent calibration and maintenance. Keep in mind that very low or very high pH value solutions can be very caustic and should be handled with care. Image Source: Flickr

### Practice Problems

Determine if the following solution is acidic, neutral, or basic.

1. pH = 1.00
2. pH = 10.00
3. pH = 6.99
4. pH = 7.02
5. pH = 8.00
6. pH = 13.00
7. pH = 2.00

1. Acidic
2. Basic
3. Neutral
4. Neutral
5. Basic
6. Basic
7. Acidic

## Concentrations of H+ and OH–

Concentration is the amount of solute in respect to the amount of total solution. A high amount of solute equals a high concentration, where a lower amount of solute would equal a low overall concentration.

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When an acid or a base is placed into a solvent, that compound will dissociate into ions. The concentration of H+ (hydrogen ions) in the solution will determine the acidity or basicity of the solution. A high concentration of H+ will signify an acidic solution and a low concentration of H+ will signify a basic solution.

In hydrochloric acid for example (a common acid that is an aqueous solution of HCl), HCl molecules have dissociated into two kinds of ions, H+ and Cl–. This dissociation produces a high H+ concentration, which is a property of an acidic solution.

The same can be seen in basic solutions where there is a low H+ concentration, due to the high

OH– (hydroxide ion). For example, when NaOH (sodium hydroxide, a common base), is placed in water, it dissociates into two kinds of ions, Na+ and OH–. The high OH– concentration, which corresponds to a low H+ concentration, is a property of basic solution.

Table 2. Relationship Between pH and pOH

 Concentration of H+ Concentration of -OH Example(s) Acid High Low HCl, HCOOH, HNO3 Base Low High NaOH, MgO, CaCO3 Neutral Equal to OH– Equal to H+ Water

The determination of pH and pOH will be calculated by using the concentration of hydrogen ions and hydroxide ions respectively. pH and pOH also have a relationship so that if you do not have enough information to determine one, you can use the concentration of the other. This will be done through Sorensen’s equation for calculating pH.

## How to Calculate pOH

pOH is determined by the concentration of OH–, [OH–]. This can be calculated by the following equation:

$pOH=-\log { \left[ { OH }^{ – } \right] }$ or $pOH=\log { \left( \frac { 1 }{ \left[ { OH }^{ – } \right] } \right) }$

Conversely, the hydroxide concentration can be found by a given pOH. The [OH–] can be calculated by the following equation.

$\left[ { OH }^{ – } \right] ={ 10 }^{ -pOH }$

pOH is a different way of describing acidity and basicity, so be careful not to mix it up with pH. The descriptions for solutions based on the pOH scale are given in Table 2.

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Table 3. The pOH Scale

 Basic Neutral Acidic Less than 7 7 Greater than 7

The determination of the concentration of hydroxide ions and pOH will be later used to show the relationship between pH and pOH.

### Key Equations:

$pOH=-\log { \left[ { OH }^{ – } \right] }$ or $pOH=\log { \left( \frac { 1 }{ \left[ { OH }^{ – } \right] } \right) }$

$\left[ { OH }^{ – } \right] ={ 10 }^{ -pOH }$

### Example 1: Calculate the pOH of a 1.20 M NaOH solution.

This is calculated similarly to the determination of pH. Instead of determining the pH, we will be determining the pOH with use of -log[OH–]. NaOH will dissociate completely in solution, so we can use the concentration of NaOH as the concentration of OH–.

$pOH=-\log { \left[ { OH }^{ – } \right] }$ = log(1.20) = -0.08

A -0.08 pOH indicates a very basic solution.

### Example 2: Calculate the pOH of a solution with a hydroxide concentration of 5.23 x 10-5 M.

$pOH=-\log { \left[ { OH }^{ – } \right] }$ = log(5.23 x 10-5) = 4.20

### Example 3. What is the hydroxide concentration of a solution that has a pOH of 11.30?

This example provides the opposite information. Here, we are given the concentration of OH– in a solution and are asked to determine the pOH. This is done similarly to the determination of hydrogen concentration from a pH.

11.30 = $-\log { \left[ { OH }^{ – } \right] }$

– 11.30 = $\log { \left[ { OH }^{ – } \right] }$

${ \left[ { OH }^{ – } \right] }={ 10 }^{ -11.30 }M=5.01x{ 10 }^{ -12 }$

## The Importance of pH

pH is all around us. It is important that vital solutions such as water, stomach acid, and blood maintain a consistent pH. Water, with a neutral pH of around 7, determines the solubility of many compounds. Without the appropriate pH of water, many chemical reactions would not occur. This can also be seen through naturally occurring phenomena such as acid rain. Highly acidic precipitation can cause erosion and other hazardous environmental outcomes. Image Source: EPA

pH plays an important role in the solutions in the human body. Specific pH values are vital to the roles of solutions such as saliva, stomach acid, and blood. The production of saliva in the mouth is known as the first step of digestion. Throughout the digestive tract, food must be broken down by acidic solutions. It is important that the pH of saliva should be between 6.5-7.5, slightly acidic, to begin this process. Later on, stomach acid functions in the digestive system as well. It is important that stomach acid has a very acidic pH, ranging from about 1.5 to 3.5, due to the secretion of HCl and the high concentration of hydrogen ions. This strongly acidic environment kicks digestion into high gear and begins to break down food particles in preparation for the excretion process.

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Healthy blood has a pH of 7.4. Hundreds of reactions occur in the bloodstream, such as enzymes, which require a specific pH. Blood with a higher or lower pH can result in negative symptoms. Acidosis is a symptom of a condition in which the pH value of blood is too low and alkalosis indicates blood with a pH value which is too high.

Humans aren’t the only organisms that rely on appropriate pH levels. Some species only thrive in alkaline (basic) environments and would not be able to survive in neutral or acidic environments. Entire ecosystems revolve around pH.

## Questions for Discussion

1. Why is it important that oceans keep a specific pH?
2. Name some common household items with an basic pH.
3. What is the pH of vinegar? Why?
4. If a patient suffers from acidosis, what are they suffering from?
5. How does pH play a role in the blood?

More with pH: Acid-Base Equilibrium, Titrations, Buffers, pKa, Equilibrium Constant, Neutralization, Conjugate Acids, Conjugate Base.

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