Kaplan MCAT General Chemistry Review

Hence, in a 1 M solution of NaOH, complete dissociation gives 1 M OH^-. The pH and pOH for this solution can be calculated as follows:

pH = 14 - pOH = 14 - (-log[OH^-]) = 14 + log (1) = 14 + 0 = 14

Virtually no undissociated strong acid or base, such as NaOH, remains in solution, and we can consider the dissociation of strong acids and bases essentially as going to completion. In the NaOH example given above, you should note that in calculating the pH, we assumed that the concentration of OH^- associated with the auto-ionization of water is negligible compared to the concentration of OH^- due to the addition of the strong base. The contribution of OH^- and H⁺ ions to an aqueous solution from the auto-ionization of water can be neglected only if the concentration of the acid or base is significantly greater than 10^-7 M. Keeping this in mind as you solve acid-base problems on Test Day will help you avoid “silly” mistakes. For example, with your brain on “autopilot,” you might calculate the pH of a 1 × 10^-8 M solution of HCl (a strong acid) as 8, because -log (10^-8) = 8. But a pH of 8 can’t possibly describe an acidic solution (at least not at 298 K), because the presence of the acid will cause the hydrogen ion concentration to increase above 10^-7 and the pH must be below 7.

MCAT Expertise

Always be sure to think about the answer and whether it makes sense on Test Day. As seen in this paragraph, a basic pH for an acidic solution should make you think about what might be wrong with your answer.

So what went wrong in this case? The error was in not recognizing that the acid compound concentration is actually ten times less than the equilibrium concentration of hydrogen ions in pure water generated by water’s autodissociation. Consequently, the hydrogen ion concentration from the water itself is significant and can’t be ignored. Now, the addition of the acid results in the common ion effect (Le Châtelier’s principle in action in ionic solutions) and causes the water system to shift away from the side of the ions, thereby reducing the concentration of hydrogen ions and hydroxide ions. The reversal of auto-ionization is thermodynamically favored to return the water system to equilibrium, and we can express this mathematically as

K_w = [H₃O⁺][OH^-] = [x + (1.0 × 10^-8)](x) = 10^-14

where x = [H₃O⁺] = [OH^-] from the auto-ionization of water. Solving for x (using a calculator!) gives x = 9.5 × 10^-8 M. The total concentration of hydrogen ions is [H⁺]_total = 9.5 × 10^-8 + 1.0 × 10^-8 = 1.05 × 10^-7 M. Notice that this indeed is slightly less than what the value would be if the common ion effect were not acting here [(1.0 × 10^-7)+ (1.0 × 10^-8) = 1.1 × 10^-7]. The pH of this acid solution can now be calculated as pH = -log (1.05 × 10^-7) = 6.98. This value is slightly less than 7, as it should be expected for a very dilute acidic solution. The point of all of this is: Don’t put your brain on autopilot on Test Day. Be alert and keep thinking critically, no matter how familiar the problem setups might seem to you!

MCAT Expertise

The K_w (like all equilibrium constants) will change if the temperature changes and, in turn, will change the pH scale. So be careful on the MCAT because our pH scale of 1-14 is only valid at 25°C.

Strong acids commonly encountered in the laboratory and on the MCAT include HCl (hydrochloric acid), HBr (hydrobromic acid), HI (hydroiodic acid), H₂SO₄ (sulfuric acid), HNO₃ (nitric acid), and HClO₄ (perchloric acid). Strong bases commonly encountered include NaOH (sodium hydroxide), KOH (potassium hydroxide), and other soluble hydroxides of group IA and IIA metals. Calculation of the pH and pOH of strong acids and bases assumes complete dissociation of the acid or base in solution: [H⁺] = normality of strong acid and [OH^-] = normality of strong base.

WEAK ACIDS AND BASES

Before we go any further in our discussion of acids and bases as “strong” or “weak,” we want to ensure that you are making the mental distinction between the chemical behavior of an acid or base with respect to its tendency to dissociate (e.g., strong bases completely dissociate in aqueous solutions) and the concentration of acid and base solutions. Although we may casually describe a solution’s concentration as “strong” or “weak,” it is preferable to use the terms concentrated and dilute, respectively, because they are unambiguously associated with concentrations, not chemical behavior.

Continuing our focus on the chemical behavior of acids and bases, we now must consider those acids and bases that only partially dissociate in aqueous solutions. These are called weak acids and bases. For example, a weak monoprotic acid, HA, will dissociate partially in water to achieve an equilibrium state: