ChemTalk

# What Is pH? The pH Formula & Equation

pH is a measure of how acidic or basic a substance is. In our everyday routine, we encounter and drink many liquids with different pH. Water is a neutral substance. Soda and coffee are often acidic. The pH is an important property, since it affects how substances interact with one another and with our bodies. In our lakes and oceans, pH determines what creatures are able to survive in the water. Read on to learn vocabulary associated with pH, how to use the pH formula, how to calculate pH, and why pH is an important measurement!

## What is pH?

pH is a measure of how basic or acidic a substance is. pH has a range of 0-14. A pH greater than 7 means the substance is basic. A pH less than 7 means the substance is acidic. When the pH is exactly 7 that indicates that the substance is neutral.

An acidic substance is anything that will give up a proton. A basic substance will accept a proton. For more on acids and bases see this article.

The pH formula is:

pH = -log ([H+])

This formula for pH is discussed in more detail in a section below, including how to use the pH formula.

## What Is the pH Scale?

The pH scale starts from the number 0 and ends at the number 14. These numbers allow the classification of substances based on their pH; the most acidic substances will be close to 0, while the most basic or alkaline substances will be close to 14. The lower the pH, the more H+ ions will be present and the stronger the acid. The most basic or alkaline substances will have a classification between 7 and 14.

## pH Formula

pH = −log ([H+])

The formula for pH is shown above. pH is defined as the negative log base 10 of the hydronium concentration.

The pH is a logarithmic measure of the concentration of hydrogen ions in a solution. Because pH is on a log scale that means that increasing the pH by 1 corresponds to multiplying the concentration of H+ ions by 10! So even though the difference between pH 6 and pH 7 might sound small, it’s actually quite sizeable. For the pH equation, the concentration of hydrogen ions is always a molar concentration, that is, moles of H+ per liter.

## How to calculate pH

If you know the concentration of hydrogen ions, then calculating the pH is just plugging in to the pH equation. Sometimes, a problem will tell you that an acid completely dissociates into ions in solution. In this, knowing the hydrogen ion concentration is straight forward.

For example: Assume a 0.2 molar solution of HCl completely dissociates in solution. This means for each mole of hydrochloric acid, there is 1 mole of H+ ions. (HCl is a strong acid, so completely dissociates). So the concentration of hydrogen ions is 0.2 M. The pH formula tells us that the pH is the negative log of the hydrogen ion concentration – which is 0.2 molar. Then use a calculator to plug the 0.2 M into the pH formula.

pH = -log ([H+]) = – log (0.1) = 0.699

Now if the acid does not completely dissociate, and they give you the Ka of the acid, you need to calculate pH from Ka, which is covered in this article.

## pH Equation – Converting pH to H+

In some situations, we know the pH and need to convert to the molar concentration of H+ ions. For this, we need to invert the logarithm from the first equation, by raising 10 to the power of the negative pH.

[H+] = 10-pH

Using this equation, we find that if the pH of a solution is 7, then [H+] = 10-7 M. If the pH of a solution is 0, then [H+] = 10-0 M = 1M (a one molar solution), and if the pH of a solution is 14, then [H+] = 10-14 M.

## Measuring pH

There are several ways to measure the pH of a substance in the laboratory, at home, or in the field.

1. pH Probe: A pH probe is an instrument that has an arm with two small electrodes in it. The arm is placed in a substance and the electrodes respond to the pH of the solution. The pH is typically displayed on a small screen. There are both large and small portable models of this instrument.

2. Litmus paper: Litmus paper is a thin strip of paper that changes color based on the pH of the solution it is dipped in to. This pH indicator can be found at some pet supply stores to test the pH of aquariums.

3. Chemical Indicators: Chemical indicators are chemicals you can place into solution that will change the color of the solution as the pH changes. Some common ones are phenolphthalein, bromthymol blue, and litmus. Although theses won’t give you the exact pH they are a great way to tell about what pH a substance is.

4. Many Others: There are many other chemicals that can act as indicators in different ways. One easy one to test at home is using cabbage juice. Instructions for making your own cabbage juice indicator can be found here. Another great activity for exploring the pH of different substances can also be found here.

## pOH

The term pOH is similar to pH, but refers to alkalinity or basicity, that is, the concentration of hydroxide ion (OH-) in a solution. The two scales function identically, except that the scale is reversed. A neutral substance has both pH and pOH of 7. However in the pOH scale a basic substance will have a pOH of less than 7. The equation for pOH is the same as that for pH except using the concentration of hydroxide instead of H+:

pOH = −log [OH]

## Water and its pH

Pure water has a pH of 7 on the pH scale, meaning that it is neutral. In pure water, the concentration of hydrogen ions, and hydroxide ions, are both the same – 10-7 M.

However, dissolved acids, bases, or salts can make it either acidic or basic. For example, ocean water tends to have a pH of about 8. Even a glass of water won’t have a pH of exactly 7 due to the carbon dioxide from the atmosphere that dissolves into it. Pollutants can also change the pH of water, so water pH is frequently monitored in many situations for both safety and research.

## Kw in Chemistry

Kw is the dissociation constant or ionization constant of water.

When water ionizes, it splits into a hydrogen ion (H+) and a hydroxide ion (OH). H+ is unstable in water on its own and prefers to form a hydronium ion (H3O+), but for convenience we usually still refer to it as H+.

The ionization constant of water represents the degree to which it exists as ions versus together as a molecules and equals the concentration of H+ times the concentration of OH:

Kw = [H+][OH]

pKw = -log Kw

At room temperature, Kw = 10-14 and pKw = 14. We can use this constant to convert between the pH and pOH via the equation below:

pH + pOH = pKw

## Why is pH important?

Some chemical reactions only take place under certain pH conditions. Sometimes this is because H+ or OH acts as a reactant in the reaction. In other cases, acid or base can catalyze a reaction, meaning that they affect the rate of the reaction.

Living organisms rely on a wide variety of biochemical reactions and processes, most of which require specific pH ranges. As a result, ecosystems like lakes and rivers thrive under the pH conditions that are favorable to the biochemistry of the local flora and fauna.

Like an ecosystem, the human body has a certain pH that allows the proper functioning of the different tasks that our body performs. We require one value in our blood, and a totally different one (much more acidic) in our digestive fluids. Otherwise, normal biochemistry could break down, causing serious health issues. Luckily, humans and many other creatures have blood that is buffered, so that the pH cannot change easily. This is why if you drink a bottle of alkaline water or acidic soda, your blood will stay nearly the same, keeping you safe from the effects of imbalance!

Another consequence of this safety net built into your blood is that the common health benefits associated with alkaline water are mostly made-up. Even if your blood were somehow too acidic, drinking some water with pH 8 would barely change it!

## Fun Facts About the pH Scale

• Acids often have a sour taste to them, like lemons
• Bases tend to taste bitter
• Søren Peder Lauritz Sørensen devised the pH formula and pH scale in 1909. Sørensen was a Danish chemist working at the Carlsberg Laboratory.
• Many cleaners are very basic (pH > 10). Some examples include drain cleaner, bleach and ammonia solution. Always be careful working with very basic or very acidic substances.
• Due to the increase in carbon dioxide in the air, our oceans are currently decreasing in pH which means they are getting more acidic. The change in pH has cascading effects on the creatures in the ocean. For background and activities on this topic, see this article.