pH Scale: Identification of Acids and Bases

pH Scale Lab Script: Identification of Acids and Bases. An Interdisciplinary Lab Script for Allied Health, Biology, Chemistry, Environmental, Food Technology and Applied Math Courses.

Instructions

To the Instructor

• Discuss with students all theory relevant to the experiment.
• Feel free to modify the experiment title, description and any required observation.
• Use results to perform any statistical analysis or further computations.

Theory

The simplified reaction equation for the dissociation equilibrium of water is

H₂O === H ⁺ + OH ^-

For pure water

[H ⁺] = [OH ^-]

where brackets are used to indicate equilibrium concentrations (Eq/liter). The "===" expression indicates that the reaction proceeds in both directions. H ⁺ and OH ^- are the hydrogen and hydroxide ions, whose concentrations can be represented in logarithmic notation of base ten as

pH = - log[H ⁺] and pOH = - log[OH ^-]

where the dissociation equilibrium constant of water is defined as

K = [H ⁺] [OH ^-] / [H₂O]

The water dissociation constant, K, is temperature dependent. Its value is 1.8 x 10 ^-16 Eq/liter at 25 degrees C and 4.3 x 10 ^-16 Eq/ liter at 37 degrees C.

In many chemistry textbooks [H ⁺] is replaced by [H₃O ⁺] and the "w" subscript is appended to the K constant. This is actually done to account for the autoionization of water.

H₂O + H ⁺ === H₃O ⁺ + OH ^-

The net (overall) reaction is

2H₂O === H₃O ⁺ + OH ^-

where [H ⁺] = [H₃O ⁺]. Since [H₂O] is over 55 Eq/liter and can be considered constant, it can be combined with K into a new constant called the ion product for water, Kw = 10 ^-14.

Applying the Law of Logarithms

Kw = [H ⁺] [OH ^-] = 10 ^-14

pKw = pH + pOH = 14

pOH = pKw - pH = 14 - pH

Therefore,

[H₃O ⁺] = [H ⁺] = 10 ^{- pH} and [OH ^-] = 10 ^{- pOH} = Kw/[H ⁺]

Consequently, the pH scale should run from pH = 0 to pH = pKw = 14 and one should be able to classify systems as

• Neutral if the measured pH = pKw/2 = pOH.
• Acidic if the measured pH < pKw/2.
• Basic if the measured pH > pKw/2.

Finally, given the fact that pH = -log[H ⁺] it must follow that

pH = (-1/2.303) (ln[H ⁺])

and the dpH/d[H ⁺] derivative is simply

dpH/d[H ⁺] = (-1/2.303[H ⁺])

which approximated by finite increments gives

ΔpH/Δ[H ⁺] = (-1/2.303[H ⁺])

This result can be used in pH calculations involving absolute and relative errors.

Notes

It should be pointed out that these definitions ignore activity coefficients. Furthermore, pKw is not necessarily 14 at other temperatures nor the pH scale will run from 0 to 14 at other temperatures. For instance, in blood plasma at body temperature (37 Celsius), pKw = 13.4 and neutral means pH = 6.7. Since "standard" arterial blood plasma has pH around 7.4 (7.35 - 7.45) and greater than pKw/2, it is classified as an alkaline fluid.

In general, for non aqueous solutions the pH scale is determined by the ion product constant of the corresponding solvent. Still for most highly diluted aqueous systems and where activity effects can be neglected, the above definitions hold and can be used to classify systems as neutral, acidics or basics (alkalines or alkalotics) by measuring its pH with a pH probe.

A pH probe can be

1. electronic; e.g., an electrode or a computer-interfaced sensor.
2. visible; e.g., with pH paper or an acid-base indicator.
3. light; e.g., using light absorbance methods.

If a strong monobasic acid of molar concentration Ca, such as hydrochloric acid (HCl), is dissolved in water the measured pH is then determined by the contribution of [H ⁺] coming from Ca and from water

[H ⁺] = [OH ^-] + Ca = Kw/[H ⁺] + Ca

Evidently,

[H ⁺] = (Kw + Ca[H ⁺])^1/2

This equation can be solved using successive approximations (iterations), for example, by initially guessing [H ⁺] at the right side of the expression as [H ⁺] = Kw^1/2, calculating a new [H ⁺] value and using the result as the next guessed value. The process can be repeated until the computed [H ⁺] value does not change significatively or a boundary (tolerance) value is achieved. The calculated and measured pH values should be the same.

Possible Experiments

1. Allied Health: pH Determinations of Physiological Samples.
2. Chemistry: pH Determinations of Weak and Strong Electrolytes in Water.
3. Food Samples: pH Determinations of Milk, Vinegar and Wine Samples.
4. Environmental: pH Determinations of Rainfall Samples.
5. Applied Math: Derivative Methods in Acid-Base Equilibrium Calculations.

Suggested Exercises

1. Generate pH scales with pKw = 13, pKw = 14 and pKw = 16. How would you define neutral, acidic, and basic systems in each case and why?
2. What is the pH value of pure water at 100 Celsius and why?
3. Calculate pH, pOH, hydrogen and hydroxide concentration values for a non aqueous system. Generate its pH scale, accordingly.
4. What is the expected pH of a hypothetical 10 ^{- 7} M solution of a strong monobasic acid at 25 and 37 Celsius, respectively?
5. Generate a pH scale whose pH increments best describe the conditions known as acidosis and alkalosis in respiratory therapist and similar allied health disciplines.
6. Determine the pH of the following household chemicals: bleach, soap, detergent, ammonia and tap water.
7. Determine the pH of the following samples: urine, saliva, vomit, and blood.
8. Determine the pH of the following food samples: raw egg, coffee, lemon juice, onion, apple juice, salsa and soda pop.
9. Rainfall in the U.S. generally has a pH between 4.5 and 6.0. Determine the pH of rainfall collected from urban and rural areas and areas of high traffic in your state or territory.
10. CO₂, NO₂ and SO₂ form carbonic acid, nitrous acid, nitric acid and sulfurous acid in rain dropplets (acid rainfall). Propose reaction equations for the formation of these acids in water. If individually dissolved in pure water samples at 25 Celsius, which gas or gases cause the largest change in pH and why? Justify your answer with reaction equations and calculations.
11. Show that the absolute and relative errors in pH readings are given by ΔpH = (-1/2.303) (Δ[H ⁺]/[H ⁺]) and by ΔpH/pH = (1/ln[H ⁺]) (Δ[H ⁺]/[H ⁺])
12. Derive an explicit expression for the dCa/d[H ⁺] derivative. Evaluate this derivative when [H ⁺] ² = Kw and when [H ⁺] ² >> Kw. Ca is the molar concentration of a strong acid such as HCl. What is the chemical significance of these conditions?

References

1. Analytical Chemistry: Practice John Kennedy; Saunders, 1990.
2. Concepts & Calculations in Analytical Chemistry Henry Freiser; CRC, 1992.

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