Chemistry: The pH Scale

The pH Scale

As you might imagine, it's useful to be able to measure the acidity of solutions. For example, the shaving cream I use in the morning has an acid listed on the ingredient label. Clearly, I would have a less enjoyable shaving experience if my shaving cream were as acidic as battery acid!

Scientists have come up with the pH scale for determining the concentration of acid in a solution so we can distinguish between solutions with varying acidity. The pH of a solution can be determined using the following equation:

• pH = -log[H⁺]

where [H⁺] is the concentration of H+ ions, in mol/L. The value of pH itself is unitless, so you can get away with saying that "the pH of this solution is 4.54" without any trouble.

Solutions with a pH less than seven are acidic. Solutions with a pH greater than seven are basic. If a solution has a pH exactly equal to seven, it is neutral.

The following figure shows the acidity of some common substances you may be familiar with:

It's possible to discover the pH of a solution by using compounds known as "indicators." Indicators are compounds that change colors as the pH of the solution changes. Probably the two most commonly used indicators are litmus (red in acid and blue in base) and phenolphthalein (pronounced "fee-no-thay-leen," colorless in acid, pink in base).

Finding the pH of a Strong Acid

Strong acids are acids that very nearly completely dissociate when you put them into water. That is, almost every molecule of the acid HA that's placed into water breaks up completely to form H⁺ and A^- ions. Some common strong acids include HCl, HBr, HI, HNO₃, and HClO₄.

Because strong acids completely dissociate in water, the concentration of H⁺ in solution is the same as the concentration of the acid you started with. For example, the pH of a 0.00500 M HCl solution would be:

• -log(0.00500 M) = 2.30

Finding the pH of a Weak Acid

Weak acids are acids that stay mostly undissociated in water. As a result, their dissociation is an equilibrium with the following general form:

• HA ⇔ H⁺ + A^-

The equilibrium constant for this expression is given the symbol K_a, which stands for acid-dissociation constant. Some common weak acids include acetic acid and formic acid.

As a result, when we place weak acids in water, the H⁺ concentration is not the same as the original concentration of the acid. Fortunately, we can use our knowledge of aqueous equilibria (Solution Chemistry/emical Equilibria) to find the acid concentration.

Example: What's the pH of a 0.500 M acetic acid solution? K_a (C₂H₃O₂H) = 1.75 × 10^-5.

Solution: The equilibrium formed when acetic acid dissociates in water is expressed by the following equation:

• C₂H₃O₂H ⇔ C₂H₃O₂^- + H⁺

To determine the concentration of both, we need to set up the expression for the equilibrium constant (go back to Solution Chemistry/emical Equilibria if this doesn't make sense):

• ^{[C₂H₃O₂-][H+]}⁄_[C2H3O2H]

Initially, the concentration of acetic acid is 0.500 M. However, at equilibrium, some of the acetic acid will have dissociated, so the concentration of the acetic acid will have decreased. Since we don't yet know how much acetic acid will have dissociated, we'll express this quantity as "x." As a result, the equilibrium concentration of acetic acid is "0.500 - x" M.

For every molecule of acetic acid that dissociates, one acetate ion and one hydronium ion will be formed. Subsequently, the quantity of each ion formed will be equal to "x." Replacing the quantities in the expression above, we get:

• 1.75 × 10^-5 = ^[x][x]⁄_{[0.500 - x]}
• x = 0.00296 M

Because acetic acid is a weak acid with a low equilibrium constant, we'll assume that "x" is a small value compared to 0.500 M. We can then simplify the equation above as:

The concentration of H⁺ and C₂H₃O₂^- ions is 0.00296 M. To find the pH, we'll place this value for [H⁺] into the equation for pH to get:

• pH = -log[H⁺]
• pH = -log(0.00296)
• pH = 2.53

Finding the pH of Basic Solutions

What's the pH of a 0.0500 M NaOH solution? This is kind of a funny question because when NaOH breaks up in water, it doesn't form H⁺ ions. Instead, it forms Na⁺ and OH^- ions, which makes it a basic solution.

This poses a problem. After all, the equation for finding pH requires that you have the concentration of H⁺ ions, and, as far as we can tell, there are no H⁺ ions in a basic solution!

Hey, not so fast there, buddy. As it turns out, there are a very small number of H⁺ ions in basic solutions. These H⁺ ions are formed when water dissociates in the following way:

• H₂O ↔ H⁺ + OH^-

As a result, whenever water is present (as it must be in an aqueous solution), there will be a few H⁺ and OH^- ions—not many, but a few. The equilibrium constant for the dissociation of water has the symbol "K_w". K_w is equal to 10^-14.

This turns out to be handy for those of us wanting to find the pH of a basic solution. The reason for this is that the previous equation yields the following equilibrium expression:

• K_w = [H⁺][OH^-]

So if we know the concentration of base, we can use this expression to find the concentration of acid.

Example: What is the pH of a 0.0500 M NaOH solution?

Solution: Using the equilibrium expression for water and replacing the values with what we know, we get:

• K_w = [H⁺][OH^-]
• 1.00 × 10^-14 = [H⁺][0.0500]
• [H⁺] = 2.00 × 10^-13 M

To find pH, we simply use the equation:

• pH = -log[H⁺]
• pH = -log[2.00 × 10^-13]
• pH = 12.7

This answer indicates a very basic solution, which is what we would expect from a 0.0500 M NaOH solution.