pH Scale Soren Sorensen (1868 - 1939) The pH scale was invented by the Danish chemist Soren Sorensen for a brewery to measure the acidity of beer. Soren Sorensen (1868 - 1939)

Hold up! First we need to review! Acids – Arrhenius Definition Produce Hydronium ions (H3O+1) in water H O water H O +1 H +1 Hydronium ion By this definition, if an acid is to give a H+1 to water, then all acids will have hydrogen as the cation (first element written). Bases – Arrhenius Definition Bases produce the hydroxide ion in water H O -1 Hydroxide ion

Ok, here we go… the pH Scale It is a scale to measure the acidity of a sample. It measures the concentration of hydronium (H3O+1)ions in the solution. 1 14 Highly acidic Very basic (not acidic) neutral 7

pH of Common Substances vinegar 2.8 water (pure) 7.0 soil 5.5 gastric juice 1.6 carbonated beverage 3.0 drinking water 7.2 bread 5.5 1.0 M NaOH (lye) 14.0 orange 3.5 potato 5.8 blood 7.4 1.0 M HCl milk of magnesia 10.5 apple juice 3.8 urine 6.0 detergents 8.0 - 9.0 bile 8.0 lemon juice 2.2 tomato 4.2 milk 6.4 ammonia 11.0 seawater 8.5 coffee 5.0 bleach 12.0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 acidic neutral basic [H+] = [OH-] Timberlake, Chemistry 7th Edition, page 335

Each step on pH scale represents a factor of 10. How does the scale work? pH scale : measures acidity/basicity Søren Sorensen (1868 - 1939) ACID BASE 10x 10x 10x 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 NEUTRAL Each step on pH scale represents a factor of 10. pH is defined as the negative base-10 logarithm of the hydrogen ion concentration pH = – log [H+] or [H+] = 10-pH Hydrogen ion concentration in pure water is 1 x 10-7 M at 25ºC; the pH of pure water is – log [1.0 x 10-7] = 7.00. pH decreases with increasing [H+] — adding an acid to pure water increases the hydrogen ion concentration and decreases the hydroxide ion concentration. Adding a base to pure water increases the hydroxide ion concentration and decreases the hydrogen ion concentration—pH increases with decreasing [H+]. pH scale runs from pH = 0 (corresponding to 1 M H+) to pH 14 (corresponding to 1 M OH–). Relationships between acidity, basicity, and pH: If pH = 7.0, the solution is neutral. If pH < 7.0, the solution is acidic. If pH > 7.0, the solution is basic. A change of 1,0 in the pH of a solution corresponds to a tenfold change in the hydrogen ion concentration because the pH scale is logarithmic. pH 5 vs. pH 6 (10X more acidic) pH 3 vs. pH 5 (100X different) pH 8 vs. pH 13 (100,000X different)

Richter Scale - Earthquakes 6 5 7 Area Radius Richter Scale Diameter pH [H+] 1000000 564 7 1128 mm 1 0.1 M 100000 178.4 6 356.8 2 0.01 M 10000 56.4 5 112.8 3 0.001 M 1000 17.8 4 35.6 4 0.0001 M 100 5.64 3 11.28 5 0.00001 M 10 1.784 2 1.128 6 0.000001 M 1 0.564 1 ------ 7 0.0000001 M . 4 3 2 1

radius = 112.8 cm radius = 35.7 cm radius = 11.3 cm radius = 3.6 cm pH = 2 pH = 3 pH = 1 Area Radius Richter Scale Diameter pH 1000000 564 7 1128 mm 1 100000 178.4 6 356.8 2 10000 56.4 5 112.8 3 1000 17.8 4 35.6 4 100 5.64 3 11.28 5 10 1.784 2 1.128 6 1 0.564 1 ------ 7 . pH = 4 5 6

The pH Scale Acid Base pH = 7 Acidic Basic [H+] [OH-] [H+] = Neutral

pH of Common Substance 14 1 x 10-14 1 x 10-0 0 13 1 x 10-13 1 x 10-1 1 pH [H1+] [OH1-] pOH 14 1 x 10-14 1 x 10-0 0 13 1 x 10-13 1 x 10-1 1 12 1 x 10-12 1 x 10-2 2 11 1 x 10-11 1 x 10-3 3 10 1 x 10-10 1 x 10-4 4 9 1 x 10-9 1 x 10-5 5 8 1 x 10-8 1 x 10-6 6 6 1 x 10-6 1 x 10-8 8 5 1 x 10-5 1 x 10-9 9 4 1 x 10-4 1 x 10-10 10 3 1 x 10-3 1 x 10-11 11 2 1 x 10-2 1 x 10-12 12 1 1 x 10-1 1 x 10-13 13 0 1 x 100 1 x 10-14 14 NaOH, 0.1 M Household bleach Household ammonia Lime water Milk of magnesia Borax Baking soda Egg white, seawater Human blood, tears Milk Saliva Rain Black coffee Banana Tomatoes Wine Cola, vinegar Lemon juice Gastric juice More basic 7 1 x 10-7 1 x 10-7 7 More acidic

pH pH = -log [H1+] Kelter, Carr, Scott, Chemistry A World of Choices 1999, page 285

Acid – Base Concentrations 10-1 pH = 3 pH = 11 H3O+ OH- pH = 7 10-7 concentration (moles/L) H3O+ OH- OH- H3O+ 10-14 [H3O+] > [OH-] [H3O+] = [OH-] [H3O+] < [OH-] acidic solution neutral solution basic solution Timberlake, Chemistry 7th Edition, page 332

pH Calculations pH pOH [H3O+] [OH-] pH + pOH = 14 pH = -log[H3O+] [H3O+] = 10-pH [H3O+] [OH-] = 1 x10-14 The pH scale is a concise way of describing the H3O+ concentration and the acidity or basicity of a solution • pH and H+ concentration are related as follows: pH = –log10[H+] or [H+] = 10–pH • pH of a neutral solution ([H3O+] = 1.00 x 10–7 M) is 7.00 • pH of an acidic solution is < 7, corresponding to [H3O+] > 1.00 x 10–7 • pH of a basic solution is > 7, corresponding to [H3O+] < 1.00 x 10–7 • The pH scale is logarithmic, so a pH difference of 1 between two solutions corresponds to a difference of a factor of 10 in their hydronium ion concentrations There is an analogous pOH scale to describe the hydroxide ion concentration of a solution; pOH and [OH–] are related as follows: pH = –log10[OH–] or [OH–] = 10–pOH • A neutral solution has [OH–] = 1.00 x 10–7, so the pOH of a neutral solution is 7.00 • The sum of the pH and the pOH for a neutral solution at 25ºC is 7.00 + 7.00 = 14.00 pKw = –log Kw = –log([H3O+] [OH–]) = (–log[H3O+]) + (–log[OH–]) = pH + pOH • At any temperature, pH + pOH = pKw, and at 25ºC, where Kw = 1.01 x 10–14, pH + pOH = 14.00; pH of any neutral solution is just half the value of pKw at that temperature [OH-] pOH = -log[OH-] [OH-] = 10-pOH

pH + pOH = 14 pH pOH pH + pOH = 14 This is true because 1 to 14 is the whole range of the scale. Therefore, what ever part is not hydronium ions is composed of hydroxide ions.

Auto-ionization of Water [H3O+] Water will split into ions 2 H2O  H3O+1 + OH-1 Water will do this to make sure that they come to equilibrium and this is true: [H3O+1] × [OH-1] = 1 × 10-14 Therefore, if you know the concentration of one you always know the concentration of the other! How handy! [H3O+] [OH-] = 1 x10-14 [OH-]

Example Problems !! Example: Find the pH of an acid if the pOH is 12

Example Problems !! Example: Find the pH if the concentration of [H3O+1] is 0.25 M Is the pH acidic or basic?

Example Problems !! Example: Find the [H3O+1] if the pH is 2.7

Example Problems !! Example: Find the [OH-1] if the pH is10.7 ***Keep in mind there is more than one way to go about this***