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Acid and Base Concentrations
 
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Acids and Bases

An Arrhenius acid produces hydrogen ions when it is dissolved in water:

HA + H2O → H+(aq) + A-(aq)

Here, HA is the non-dissociated acid, H+ is the hydrogen cation, and A- is the solvated anion — called the conjugate base. An Arrhenius base produces hydroxide ions when dissolved in water:

BOH + H2O → B+(aq) + OH-(aq)

Here, BOH is the non-dissociated base, OH- is the hydroxide ion, and B+ is the solvated cation — called the conjugate acid. A conjugate base is formed when an acid loses a hydrogen ion and has the potential to gain a hydrogen. The same follows for a conjugate acid, which is formed when a base loses a hydroxyl group and has the potential to regain it. Every acid has a conjugate base, and every base has a conjugate acid.

pH

pH is the degree of acidity of the solution and is a measure of the amount of hydrogen ions in a solution. The pH scale is logarithmic and runs from 0 to 14; aqueous solutions with a pH below 7 are described as acidic, and aqueous solutions with a pH above 7 are described as alkaline or basic. Solutions at pH 7 are considered neutral.

The pH of a solution is equal to the negative log base ten of the concentration of hydrogen ions in solution.

Water interacts strongly with the hydrogen ion because its strong positive charge attracts the negative pole of surrounding water molecules. In fact, they interact so strongly that they form a covalent bond and the H3O+ cation, called hydronium. The above equation is rewritten to reflect this.

For simplicity, we’ll refer to the concentration of hydrogen ions instead of hydronium ions when discussing pH. The lower the pH value of a solution, the more hydrogen ions that are present, and by extension, the more acidic the solution. For example, the pH of 1 mM of sulfuric acid is 2.75, whereas the pH of 1 mM of hydrochloric is 3.01. The concentration of hydrogen ions in the sulfuric acid solution is calculated as 1 × 10-2.75, whereas the concentration of hydrogen ions in the hydrochloric acid solution is 1 × 10-3.01. Thus, there are more hydrogen ions present in sulfuric acid, and it is more acidic. Remember, even though the pH of two solutions may vary by as little as half a pH value, due to the logarithmic nature of the pH scale, the amount of hydrogen varies greatly.

Strength of Acids and Bases

An acid’s strength is affected by the electronegativity of the conjugate base and the polarity of the acidic hydrogen. Strength, therefore, refers to how readily the hydrogen cation (H+) disassociates from the anion. Strong acids and bases dissociate entirely in aqueous solutions, whereas weak acids and bases only dissociate partially into their conjugate ions.

The dissociation constant, Ka, represents acid strength. Ka is calculated using the concentrations of the non-dissociated acid HA, and the concentrations of the hydrogen cations and the conjugate base, A-. Higher Ka values represent stronger acids, whereas smaller Ka values represent weaker acids.

Ka is numerically very small, and it is often reported in the form of pKa, which is the negative log base ten of Ka. Lower pKa values correspond to a stronger acid, whereas higher pKa values correspond to a weaker acid.

Some acids dissociate only one hydrogen ion and therefore have one pKa value. These acids are called monoprotic. However, some acids can dissociate more than one hydrogen ion and are called polyprotic. These acids have a pKa value for each hydrogen ion dissociation.

pKa can also be used to calculate the equilibrium pH of an acid-base reaction, as shown in the Henderson-Hasselbalch equation.

The Henderson-Hasselbalch equation is used to calculate pH, when the concentrations of the conjugate base and the weak acid are known, or to calculate the pKa if the pH and concentrations are known.

Titration

Acid-base reactions are quantitatively studied using titration. In a titration experiment, a solution of a known concentration, called a standard solution, is used to determine the concentration of another solution. For acid-base titrations, a standardized solution of base is slowly added to an acid of unknown concentration (or the acid is added to the base). The acid-base reaction is a neutralization reaction, which forms a salt and water. When the moles of hydrogen ions in the acid are equal to the moles of hydroxyl ions added from the base, the solution reaches neutral pH.

To perform an acid-base titration, the standardized base is slowly added to a stirring flask of the unknown acid using a burette, which enables the measurement of volume and the dropwise addition of base. The pH of the solution is closely monitored throughout the titration using a pH indicator added to the acid. Typically, phenolphthalein is used as the solution remains colorless until it becomes basic, turning a light pink.

As the titration approaches the equivalence point, which is when the moles of hydrogen ions equal the moles of hydroxyl ions added, the pH indicator temporarily changes color due to an excess of hydroxyl ions. When the flask is swirled, the pH indicator’s acidic color returns. The titration is complete and has reached its endpoint when a tiny excess of hydroxyl ions changes the indicator permanently to its basic color.

The titration curve is a plot of the pH of a solution versus the volume of standardized base added. The equivalence point is located at the inflection point of the curve, and it is calculated as the second derivative of the titration curve.

If an acid is polyprotic, it will have multiple equivalence points, one for each hydrogen ion dissociation. The pH at the halfway point to the equivalence point for monoprotic acids, or between equivalence points in the case of polyprotic acids, is equal to the pKa of the acid.

References

  1. Kotz, J.C., Treichel Jr, P.M., Townsend, J.R. (2012). Chemistry and Chemical Reactivity. Belmont, CA: Brooks/Cole, Cengage Learning.
  2. Silberberg, M.S. (2009). Chemistry: The Molecular Nature of Matter and Change. Boston, MA: McGraw-Hill.
  3. Harris, D.C. (2015). Quantitative Chemical Analysis. New York, NY: W.H. Freeman and Company.

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