# How to Find pH for a Given Molarity

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Molarity is the number of moles of a solute in a liter of solution. A mole is a measure of how many particles are present, which means that molarity is a very specific way to measure concentration. If you know the molarity of an acidic or basic solution, you can use this number to calculate the pH of that solution. pH is a logarithmic measure of how many free hydrogen ions are in a solution. High pH solutions are basic and low pH solutions are acidic. The calculation of pH from molarity is somewhat complicated by the existence of weak acids and bases. Strong acids, such as hydrochloric acid, almost always give up a hydrogen ion, but in weak acids, such acetic acid, only some of the molecules give up a hydrogen ion. Put another way, weak acids will have a higher pH than strong acids at the same molarity because not all of the particles have given up their hydrogen ions. The same is true for strong and weak bases.

## Calculating pH

Look up the ionization constant for your acid or base, abbreviated Ka. The ionization constant is the likelihood that a solute will release an ion in a solution at room temperature.

Calculate the concentration of hydrogen ions that dissociate into your solution. If the ionization constant listed is “very large” you can assume that it is 100 percent ionized or dissociated. To calculate the molarity of hydrogen ions, multiply the ionization constant by the initial molarity of your solution and take the square root of the result.

Determine if you need to calculate normality. If you have an acid such as hydrogen fluoride -- formula HF -- it only has one hydrogen ion to donate, but an acid such as sulfuric acid -- formula H2SO4 -- has two hydrogen ions that can dissociate. If there is only one hydrogen ion, you do not have to determine normality.

Run the ionization equation again for the second hydrogen ion in order to determine normality, which is based on molarity. After calculating the concentration of hydrogen ions for your acid, you need to look up the ionization constant for the acid without the first hydrogen, such as HSO4- in the case of sulfuric acid. Take the concentration you calculated before and use this as your initial concentration and recalculate for the second acid using the new ionization constant. Add the result of the first concentration calculation and to the result of this calculation to determine your total hydrogen ion concentration.

Calculate the pH. To do this, you will simply take the negative log, or inverse log of your hydrogen ion concentration.

#### Tips

• If the ionization constant of your acid is close to your initial molarity, the calculation becomes much more complicated and you will need to solve the following formula for x : Ka = x2 / (Initial molarity – x).

#### Warnings

• If you are dealing with strong acids and bases in the laboratory while you are calculating pH, be sure to use appropriate protective gear, such as lab coats, protective eye wear and corrosion-resistant gloves.