Concepts:
H⁺ and OH^- Ions, pH, K_a, K_b, and K_w

~ H⁺ and OH^- Ions

The presence of both the H⁺ and the OH^- ions are what gives acids and bases their individual characteristic properties. These include, for acids, a sour taste and the ability to corrode metals. Bases, or substances that are alkaline (another term for basic substances), often have a slippery texture and a bitter taste. What's interesting about these two types of substances, and what intrigued scientists of old, was the fact that, when brought into contact with each other, both acids and bases lose these characteristic properties.

Acids and Bases: What are they?
Acid: a substance that increases the H⁺ ion concentration in an aqueous solution
Base: a substance that increases the OH^- ion concentration in an aqueous solution

When either an acid or a base is in pure water, they dissociate. This means that they separate into their respective ions and their conjugate acid or base. An acid will dissociate into H⁺ ions and its conjugate base. A base dissociates into OH^- ions and its conjugate acid. For example, sodium hydroxide (NaOH), a very strong base, dissociates to OH^- and Na⁺. Na⁺ is the conjugate acid of the base NaOH. When HCl is added to water, it separates into H⁺ and Cl^-, where Cl^- is the conjugate base of the acid HCl.

Neutralization
When an acid and a base are mixed together, instead of increasing the H⁺ or OH^- ion concentrations, the ions combine to form our old friend, H₂O. Look familiar? By this process, the acid and base form a mixture of water and their respective conjugates, effectively neutralizing each other. When someone has an upset stomach, there might be an excess of stomach acid. Swallowing an antacid tablet from the medicine cabinet might help them feel better because the tablet is an alkaline substance that reacts with the stomach acid to neutralize it.

~ pH

The pH scale is simply a way for us to express the concentration of H⁺ ions without using very small numbers or exponents. By taking the opposite of the log (base-10) of the concentration of the H₃O⁺ ions in moles per liter, you can determine the pH of a substance.

pH = ^_ log [H₃O⁺]

The pH scale ranges from 1 to 14. A substance with a pH of 1 is extremely acidic, and a substance with a pH of 14 is very basic. Those of you out there with fish tanks probably already know this, as the pH of the water in a fish tank can determine the health of the fish. If the pH reaches extreme levels (especially if it gets too low), the fish will die.

If the concentration of H₃O⁺ is unknown, another way to determine the pH of a substance is through the use of pH paper strips. The H⁺ ions change the color of the paper strip. When compared to a key, it can be seen that dark blues and greens indicate the substance is alkaline (high pH). Reds and dark oranges means it is acidic (low pH). A pH of 7 is considered neutral, and the color for this is light orange. Basic Lye (pH 13) and ammonia (ph 12) would turn the strip blue. Human blood (pH 7.5) and milk (pH 6.7) would turn the strip a neutral orange. Battery acid (pH 1.2) and lemon juice (pH 2.5) would turn the paper dark orange and red.

Another way to express acidity is the pOH scale, also ranging from 1 to 14. The pOH can be determined by finding the opposite log of the hydroxide (OH^-) ion concentration.

pH = ^_ log [OH^-]

The sum of the pH and the pOH of a solution is always equal to 14.

pH + pOH = 14

~ K_a, K_b, and K_w

K_a is the dissociation constant for an acid in water. For example, for acid HA in water,

HA (aq) + H₂O (l) H₃O⁺ (aq) + A^- (aq)

K_a = ( [H₃O⁺] [A^-] ) / ( [HA] )

K_b is the dissociation constant for a base in water. For base in water,

B (aq) + H₂O (l) BH⁺ (aq) + OH^- (aq)

K_b = ( [BH⁺] [OH^-] ) / ( [B] )

Both K_a and K_b are constants that express the acidity of a substance. Large values for either K_a or K_b indicate a strong acid or base. If the K_a for an acid is very high, the K_b for its conjugate base is very small, and vice versa. The same is true for the K_b of a base and the K_a of its conjugate acid.

K_w is the special symbol given to the auto ionization constant for water. Water autoionizes--it separates into H⁺ ions and OH^- ions. From the following equation, we can derive the equilibrium constant, K. (See the Chemical Reactions chapter.)

2 H₂O (l) H₃O⁺ (aq) + OH^- (aq)

K = ( [H₃O⁺] [OH^-] ) / ( [H₂O]² )

Remember the [H₂O] is already included in the constant K, so

K [H₂O]² = [H₃O⁺] [OH^-]

K_w = [H₃O⁺] [OH^-]

In pure water, the concentrations of H₃O⁺ and OH^- are equal. In fact, electrical conductivity measurements show that both concentrations are equal to 1.0 x 10^-7 moles per litre. We can thus conclude that K_w is equal to 1.0 x 10^-14. When either an acid or a base is added to water, this equilibrium changes, and thus the equations for K_a and K_b must be used to find the new constant.

One way K_w is useful is in finding either K_a or K_b. If either K_a or K_b is known, the following equation can be used to find the other:

K_a x K_b= K_w

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