How to Find pH for a Given Molarity

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It's hard to live in the modern world without hearing references to acids, which are often portrayed in pharmaceutical and other advertisements as liquid aggressors bent on erasing and damaging all sorts of things, from skin to clothing to furniture. You've no doubt seen ads for products called antacids, which are designed to deal with the effects of acid produced in the stomach.

Acids have varying degrees of strength, or acidity. The quirky but fundamentally simple scale known as the pH scale is a measure of how acidic an aqueous solution is, or, in a different framing of the same chemical scenario, how basic or alkaline it is.

To determine the pH of an aqueous solution (that is, a substance dissolved in water), you need to only know the concentration of hydrogen ions (H+) in that solution, or its molarity. But apart from pH, what are moles, molarity and acids all about, anyway?

Facts About Acids and Bases

Acids are molecules that can donate protons. A simple example is hydrochloric acid, HCl. This molecule readily gives up its H+ component in aqueous solution and is a strong acid. Other acids, such as carbonic acid (H2CO3), give up their protons more reluctantly and are called weak acids. When an acid (HA) donates a proton (H+), it is said to be ionized, with the products being H+ and whatever is left (generically A; in the case of carbonic acid, HCO3).

Strong acids have low pH values. Water is neutral, with a pH of 7; strong bases, or proton acceptors (such as sodium hydroxide, NaOH) have high pH values, some close to 14.0.

Moles and Molarity

For acid-base chemistry purposes, it is more appropriate to measure solute concentration in moles, or individual particles (e.g., atoms, molecules), per unit volume rather than mass per unit volume. This is because atoms react with each other in known proportions in a way unrelated to atomic mass.

One mole (1 mol) of anything is 6.02 × 1023 particles; 1 mol in a volume of 1 L has a molarity of 1.0. Thus 6 mol of NaCl in 8 L of aqueous solution has a molarity of 6 mol/8 L = 0.75; 6 mol of the much more massive molecule adenosine triphosphate dissolved in 8 L has more mass but has the same molarity, 0.75 M.

What Is the pH Formula?

The pH equation is most often written in the form

pH = -log_{10}[H^{+}]

Here, the quantity in brackets is the molarity of H+ ions in the solution. Thus, if you know the molarity, you can get the pH value and conversely.

Examples of pH Calculations

To go from molarity to pH, use your calculator or a similar tool to take the logarithm to the base 10 (the default base) of the molarity, reverse the sign to get a positive value, and you're done!

Example: If the molarity of an aqueous solution is 6.3 × 10-5 M, what is the pH?

pH = −log[6.3 × 10-5] = 4.2.

You can also calculate concentration from pH and pKa, the latter being derived from the acid dissociation constant Ka. The higher the Ka for a particular acid, the stronger the acid it is. The pKa for any acid is the pH at which half of the acid has been ionized (that is, when half of the "acidic" protons have been offloaded into the solution).

The equation of interest is known as the Henderson-Hasselbach equation and is written:

pH = pKa + log_{10}\dfrac{[A^{-}]}{[HA]}

This means that given an acid's pKa and the relative concentration of anion and "intact" acid, you can determine the pH. Ka values can be easily looked up online, and you can find the pKa using the same operation as for pH if it is not listed as well.

Online pH and pOH calculator

See the Resources for a web tool that allows you to determine the pH of various acidic and basic solutions. You can use this to gain a feel for the relationships between different individual acid strengths, concentration and pH.

References

Resources

About the Author

Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.

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