Calculate a pH

In everyday life, pH is a scale generally used to describe the neutrality, or lack of neutrality, in a household item. In science, pH is a measure of ions within a solution. If you’re taking a science or chemistry class, you may need to know how to calculate pH based off concentration instead. Calculate pH by using the pH equation: pH = -log[H3O+].

Steps

Understanding pH

1. Know what pH actually is. The pH is the concentration of hydrogen ions in a solution. A solution with a high concentration of hydrogen ions is acidic. A solution with a low amount of hydrogen ions is basic, or also known as alkaline. Hydrogen ions, also known as hydronium, are written shorthand as H+ or H30+.
   • Know the pH scale. The pH scale is from 1-13. The lower the number, the more acidic the solution. The higher the number, the more basic the solution. For example, orange juice would have a pH of 2 because it is quite acidic. In contrast, bleach has a pH of 12 as it is quite basic. Numbers in the middle of the scale are often neutral, such as water, with a pH of 7.
   • One level of pH is a 10x difference. For example, when comparing pH 7 to pH 6, pH 6 is ten times more acidic than pH 7. Furthermore, pH 6 would be 100 times more acidic than pH 8.
2. Define pH in an equation. The pH scale is calculated by a negative logarithm. A negative logarithm is simply how many times a number must be divided. The pH equation can be seen as follows: pH = -log[H3O+].
   • The equation can sometimes be seen as pH = -log[H+]. Know that whether the equation has H3O+ or H+, they are the same.
   • It is not vital to have a firm understanding of what a negative log is to calculate pH. Most calculators used at high school and post secondary level will have a log button.
3. Understand concentration. Concentration is the number of particles of a compound in a solution. Concentration is commonly described in molarity. That is, moles per unit of volume (m/v or M). If you’re using a solution in a lab, the concentration will be written on the bottle. When working on your chemistry homework, the concentration will usually be given to you.

Using the Concentration to Calculate pH

1. Remember the pH equation. The pH equation is as follows: pH = -log[H3O+]. Ensure you know what all terms in the equation represent. Look at which term is used for concentration.
2. Identify the actual concentration. Read over your chemistry question. Identify the concentration of the acid or base. Write down the entire equation on paper with the known values represented in the equation. Always include units to avoid confusion.
   • For example, if the concentration is 1.05 x 10^5 M, write the pH equation as: pH = -log[1.05 x 10^5 M]
3. Solve the equation. When solving the pH equation, you must use a scientific calculator. First, hit the “negative” button. It is usually written as “+/-”. Now key in the “log” button. Your screen should display “-log”. Now hit an open bracket and enter in your concentration. Don’t forget to add exponents when necessary. Follow with a closed bracket. At this point, you should see “-log(1.05x10^5). Hit solve. Your pH should be 5.

Using pH to Calculate a Concentration

1. Identify the known unknowns. First write out the pH equation. Next, identify the values you have by writing them directly below your equation. For example, if you know the pH is a value of 10.1, write it on the paper below the pH equation.
2. Rearrange the equation. Rearranging the equation will require a strong understanding of algebra. To calculate concentration from pH, you must recognize that concentration needs to be on one side of the equal sign alone. Start by moving the pH onto one side, and hydronium ion concentration to the other. Keep in mind that the negative sign with the log will travel together with the hydronium ion, making it an addition of hydronium on the opposite said.. Then subtract the pH from the left side and add it as an exponent to the right.
   • For example, pH = -log[H3O+] will mold into +[H3O+] = log^-pH. Note that the pH value has become an inverse log. pH can then be filled in as 10.1
3. Solve the equation. When working with inverse log, the calculator process is unique. Remember that log is a type of multiplication by 10. To enter your equation, key in 10. Next, hit the “EXP” exponent button. Key in the negative sign followed by the value. Hit solve.
   • For example we have a pH value of 10.1. Key in “10” followed by “EXP.” Now key in “-/+” to have our value be negative. Finally, key in the pH of “10.1”. Hit solve. You should get 1e-100. This means our concentration is 1.00 x 10^-100 M.
4. Think about your answer. Does the above answer make sense? If you have a pH of 10.1, you know the hydronium ions should be very small as 10.1 is a basic solution. Therefore, having such a miniscule number for concentration does infact, make sense.

Tips

• If calculating pH seems difficult to you, there are many sources available. Use your textbook and reach out to your teacher for further help.

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Sources and Citations

See also

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• Prepare Citric Acid Solution
• Distinguish Between Acids and Bases
• Dilute an Acid

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