Can a pH value be negative?

Yes! While the standard scale goes from 0 to 14, highly concentrated strong acids (greater than 1 M) will yield a negative pH. For example, a 2.0 M solution of HCl has a pH of -0.30.

How do I find pH if I am only given the OH- concentration?

First, calculate the pOH using the exact same style of formula: $pOH = -\log[OH^-]$. Then, assuming the solution is at room temperature (25 degrees Celsius), subtract the pOH from 14 to find your pH, because $pH + pOH = 14$.

How do I work backwards from pH to find concentration?

You need to do the inverse math. Since $pH = -\log[H^+]$, you can find the concentration by taking 10 to the power of negative pH. The formula is $[H^+] = 10^{-pH}$.

How do you calculate pH?

The pH of a solution is calculated using the formula $pH = -\log[H^+]$ , where $[H^+]$ is the concentration of hydrogen ions in moles per liter. This simple mathematical operation translates incredibly tiny concentrations into a manageable scale from 0 to 14. Think of pH like a Richter scale for earthquakes. Just as a magnitude 6 earthquake is ten times stronger than a magnitude 5, a solution with a pH of 4 has ten times more hydrogen ions than a solution with a pH of 5. The lowercase 'p' in chemistry just means 'take the negative logarithm of', and 'H' stands for hydrogen.

What the formula means

To calculate pH, you need to know the molar concentration of hydrogen ions, written as $[H^+]$ or sometimes $[H_3O^+]$ for hydronium. Because these concentrations are usually very small numbers like 0.00001, chemists use logarithms to make them easier to read. The base-10 logarithm asks '10 to what power gives this number?'. By taking the negative log, we turn a tiny decimal into a neat, positive number.

How to use your calculator

When you have your concentration, type the negative sign, hit the 'log' button (make sure it is base 10, not 'ln' which is natural log), enter the concentration, and press equals. If your concentration is written in scientific notation like $2.0 imes 10^{-4}$ , be careful to use parentheses around the whole number so the calculator performs the math in the correct order.

Where students slip up

The most common mistake is forgetting the negative sign at the beginning of the formula. Without it, you will end up with a negative pH for normal solutions, which should immediately flag that something went wrong. Another common slip is trying to use the concentration of a weak acid directly in the formula. Weak acids only partially break apart, so you have to use an equilibrium constant to find the actual $[H^+]$ first.

Worked through

Calculate the pH of a 0.0025 M solution of hydrochloric acid (HCl).

First, recognize that HCl is a strong acid, meaning it breaks apart completely in water. Therefore, the concentration of hydrogen ions $[H^+]$ is equal to the concentration of the acid, which is 0.0025 M. Next, plug this value into the pH formula: $pH = -\log(0.0025)$ . Using your calculator, you will find that $\log(0.0025)$ is approximately -2.60. Finally, apply the negative sign from the formula: $-(-2.60) = 2.60$ . The pH of the solution is 2.60.

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Where this comes from: OpenStax Chemistry 2e: Acid-Base Equilibria · Khan Academy: Acids and bases unit