Molecular Definitions of Acids and Bases: H 2 O (l)

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1 Molecular Definitions of Acids and Bases: Arrhenius Definition: An acid produces hydrogen ions (H + ) in an aqueous solution. For example: Consider hydrochloric acid, HCl, which when dissolved in water produces hydrogen ions (H + ): HCl (aq) H + (aq) + Cl - (aq) A base produces hydroxide ions (OH - ) in an aqueous solution. For example: Consider sodium hydroxide, NaOH, which when dissolved in water produces hydroxide ions (OH - ): NaOH (aq) Na + (aq) + OH - (aq) Under the Arrhenius definition, when acids and bases combine WATER is formed, and the acid s hydrogen ion (H + ) and the base s hydroxide ions (OH - ) neutralize each other in the process: H + (aq) + OH - (aq) H 2 O (l) Bronsted-Lowry Definition: Although the Arrhenius definition of acids and bases is useful in a variety of situations (and is one with which you are probably already familiar), it does not explain why some substances, such as ammonia (NH 3 ), act as bases even though they do not contain a hydroxide ion (OH - ). It also does not apply to non-aqueous solvents (meaning you can t use the Arrhenius definition for any solution for which water is NOT the solvent, although for our purposes we are in fact going to restrict ourselves to consideration of aqueous solutions ). The Bronsted-Lowry definition is applicable to a broader range of acids and bases because it focuses on the transfer of hydrogen ions (H + ) in an acid-base reaction. Note that a positively charged hydrogen ion (H + ) is a hydrogen atom that has lost its only electron, and therefore is comprised entirely of a single proton in its atomic nucleus. Therefore, hydrogen ions (H + ) are also referred to as protons. Under the Bronsted-Lowry definition: An acid is a proton (hydrogen ion, H + ) donor; while A base is a proton (hydrogen ion, H + ) acceptor. Thus, under the Bronsted-Lowry definition, the chemical equation shown above for hydrochloric acid (HCl) in an aqueous solution is written as follows: NOTE that the only difference between the two equations is that we are more clearly accounting for what happens to the proton (hydrogen ion, H + ) in this reaction, showing that it associates with a molecule of water to form a hydronium ion (H 3 O + ) The Bronsted-Lowry definition also works well with bases such as ammonia (NH 3 ), which do not contain hydroxide ions (OH - ), but which cause the production of hydroxide ions (OH - ) in solution as ammonia accepts a proton from water to form an ammonium ion : NH 3(aq) + H 2 O (l) NH 4 + (aq) + OH - (aq) Under the Bronsted-Lowry definition, acids (proton donors) and bases (proton acceptors) always occur together. Thus, in the reaction between hydrochloric acid and water, HCl is the proton donor (acid) and H 2 0 is the proton acceptor (base):

2 Now, imagine that the reaction above were to proceed in reverse. In that case the H 3 O + (aq) ion would donate a proton, and therefore is the conjugate acid of the original H 2 0 molecule. Similarly, the Cl - (aq) ion would now accept a proton, and is therefore the conjugate base of the original HCl molecule. conjugate conjugate base acid Under the Bronsted-Lowry definition, two substances that are related to one another by the transfer of a proton are called a conjugate acid-base pair. For example, in the equation above, HCl and Cl - are a conjugate acid-base pair (shown by the connecting bracket). Simlarly, H 2 O and H 3 O + are a conjugate acid-base pair. NOW YOU PRACTICE LABEL the acid-base reaction below to identify the acid, base, proton donor, proton acceptor, conjugate acid, and conjugate base and then DRAW brackets to connect the conjugate acid-base pairs. Try it then check the answer key at the bottom of the page. NH 3(aq) + H 2 O (l) NH 4 + (aq) + OH - (aq)

3 Water: A special case of an acid and base in one!!! Under the Bronsted-Lowery definition of acids and bases, many substances are amphoteric, meaning that they can act as either an acid or a base. Water is a very special example of such an amphoteric substance. Thus, water acts as a base (proton acceptor) when it reacts with HCl (hydrochloric acid): But, water acts as an acid (proton donor) when it reacts with NH 3 (ammonia) H 2 O (l) + NH 3(aq) OH - (aq) + + NH 3 (aq) Even more amazingly, in water at room temperature (25 degrees C), water acts simultaneously as an acid and a base, performing the following reaction: H 2 O (l) + H 2 O (l) OH - (aq) + H 3 O + (aq) conjugate conjugate base acid In pure water at room temperature (25 degrees C), this reaction occurs only to a very small extent, such that the concentration of OH - is equal to the concentration of H 3 O +, both of which are equal to ONLY molar! In scientific shorthand: [OH - ] = [H 3 O + ] = 1.0 X 10-7 M SIDEBAR: Given that the ph of a solution is calculated as ph = log[h + ] = log[h 3 O + ], we can see why it is that a neutral ph is = ph7. In other words, ph7 is neutral because this ph represents the concentration of hydrogen ions produced naturally by the reaction of water into hydroxide ions and hydrodium ions in pure water at room temperature (25 C). ALL samples of water contain some hydroxide ions (OH - ) and some hydronium ions (H 3 O + ). In fact, the product of the concentrations of these two ions in an aqueous solution is constant for all aqueous solutions at room temperature, and is known as the ion product constant for water (K w ). Stated mathematically: K w = [OH - ][H 3 O + ] As mentioned above, in pure water at room temperature, [OH - ] = [H 3 O + ] = 1.0 X 10-7 M Therefore, K w = [OH - ][H 3 O + ] = (1.0 X 10-7 M)(1.0 X 10-7 M) = 1.0 X M To summarize: In an aqueous solution at room temperature (25 C): The preceding equation holds true for all aqueous solutions at room temperature. Therefore, for any aqueous solution, the concentration of hydroxide ions [OH - ] may be calculated from the concentration of hydronium ions [H 3 O + ], and vice versa. This relationship will come in handy for our ph practice problems

4 Mathematical Definitions of Acids and Bases: Using the ph scale!! The ph scale is commonly used to express how acidic or basic a solution is. At room temperature (25 C) the ph scale has the following characteristics: o The ph scale ranges from 0 to 14. o Pure water at room temperature is neutral and has a ph of 7. o Solutions with a ph of less than 7 are acidic. o Solutions with a ph of greater than 7 are basic. o The further from 7 you go the more acidic or basic something is. o The ph of a solution is often critical, for example as we have already discussed the enzymes in your body work only in a narrow ph range. o ph can be measured with ph paper, which contains indicator dyes that change color at different ph values. o ph can also be measured with a ph meter, which measures the electric charge of the ions in a acid/base solution and converts this measurement to a ph value. The ph scale is a quantitative scale based upon the hydrogen ion concentration, [H + ], of an aqueous solution. Note that in aqueous solutions, a hydrogen ion (H + ) combines with a molecule of water to yield a hydronium ion (H 3 O + ): H + + H 2 O (l) H 3 O + (aq) from the (from the proton donor) (proton acceptor) Thus, ph by definition also reflects the hydronium ion concentration, [H 3 O + ], since [H + ] = [H 3 O + ]. ph is calculated as follows: ph = -log 10 [H + ] = -log 10 [H 3 O + ] *Logarithm of base ten indicates a tenfold difference in [H + ] per unit of ph. Note that mathematically, the ph scale is a logarithmic scale, meaning that a change of 1 ph unit corresponds to a tenfold change in hydrogen ion (or hydronium ion) concentration. In other words, each change of 1 in ph equals a 10-fold change in hydrogen ion concentration. For example, a lime with ph2 is 10 times more acidic than a plum with ph3. Note also that we are taking the negative log and that in even the most acidic solutions we are dealing with relatively low concentrations of hydrogen ions. Thus, for example, our lime has only 0.01 M hydrogen ions (1 X 10-2 M hydrogen ions), which gives ph = -log 10 [H + ] = -log 10 [1 X 10-2 ] = -(-2) = 2 Our plum has a lower hydrogen ion concentration of M hydrogen ions (1 X 10-3 M H + ), which gives ph = -log 10 [H + ] = -log 10 [1 X 10-3 ] = -(-3) = 3 Therefore, in the ph scale o As hydrogen ion concentration goes UP, ph goes DOWN and a solution is MORE ACIDIC. o As hydrogen ion concentration goes DOWN, ph goes UP, and a solution is MORE BASIC.

5 The concentration of a strong acid allows you to calculate ph as follows: 1. Concentration is measured in Molarity (M), or the number of moles of the substance per liter of solution. 2. For example, the hydronium ion concentration, [H 3 O + ], of pure water at25 o C is mol/l, or 10-7 M. 3. Since ph = -log 10 [H + ] = -log 10 [1 X 10-3 ], the ph is basically the negative power of 10. So, for pure water at 25 o C having [H + ] = [H 3 O + ] = mol/l = 10-7 M, the ph = -log 10 [1 X 10-7 ]= -(-7), which gives ph7. 4. Conversely, the ph of apple juice is about 3, so the concentration of H 3 O + in apple juice is 1 X 10-3 M. 5. If you know the concentration of a solution of a strong acid, you can calculate the ph of the solution. For example: Consider an aqueous solution of M HCl (hydrochloric acid). Since hydrochloric acid is a strong acid it fully dissociates in water: HCl (aq) H + (aq) + Cl - (aq) Thus, this aqueous solution contains M hydrogen ions [H + ], or 1.0 X 10-4 M H +. Given ph = -log 10 [H + ] Substituting our known values gives ph = -log 10 [1.0 X 10-4 ] which = -(-4) Therefore ph = 4 As we would expect this solution is highly acidic, with ph4. Remember, because ph is a logarithmic scale, small differences in ph mean larger differences in acidity. For example: the ph of apple juice differs from the ph of coffee by two ph units, so apple juice is 10 2, or 100 times more acidic than coffee. As discussed in detail above, the ph scale is calculated based up the concentration of hydrogen ions [H + ]. However, as also discussed above, in an aqueous solution at room temperature, Using this relationship, ph values can also be used to calculate hydroxide ion concentrations, [OH - ]; and conversely hydroxide ion concentrations [OH - ] can be converted into ph values. For example: Consider an aqueous solution of 0.1 M NaOH (sodium hydroxide), a base. Since sodium hydroxide is a strong base it fully dissociates in water: NaOH (aq) OH - (aq) + Na + (aq) Thus, this aqueous solution contains 0.1 M hydroxide ions, or 1.0 X 10-1 M OH -. Given which we can express as [H 3 O + ] = 1.0 X M [OH - ] Substituting our known values gives [H 3 O + ] = 1.0 X M 1.0 X 10-1 M Therefore, [H 3 O + ] = 1.0 X M and [H + ] = 1.0 X M Substituting this hydrogen ion concentration, [H + ], into the formula for ph gives ph = -log 10 [H + ] = -log 10 (1.0 X M) = -(-13) = 13 As we would expect this solution is highly basic, with ph13.

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