ACIDS AND BASES
Acid/Base reactions are sometimes simple double displacement reactions that form water. Additionally, unless an acid or base is extremely strong, their reactions are further applications of your understanding of systems in equilibrium.
Definitions of Acids and Bases
Arrhenius Acids and Bases
By the Arrhenius definition, acids and bases are determined by what they donate to a solution when they dissolved in water. An Arrhenius base is a substance that, when dissolved in water, donates hydroxide ions (OH-). NaOH is a classic example of this. When this ionic compound dissociates in water, hydroxide ions are released and the increased OH- concentration in the solution turn litmus paper blue. Arrhenius acids on the other hand, are substances that increase the concentration of hydrogen ions (H+) in a solution. HCl is an example of this. When it dissociates in water, H+ ions are released, and this type of solution turns litmus paper red. Its important to note that not all acids and bases dissociate to the same extent.
Bronsted-Lowry Acids and Bases
The focus of Brønsted-Lowry acids and bases is what happens to only H+ in solution. As a sidenote, it’s important to understand that there are lots of different names and notations for H+ that get used in the context of acid/base chemistry, and they all mean the same thing. A hydrogen atom consists of one proton and one electron. If hydrogen gives up it’s electron, it is now just a proton and hydrogen ions are sometimes named as such. Hydronium ions are another name given to H+. When hydrogen ions are released into solution, they don’t just float around unclaimed. They are usually picked up by water (H2O). When this happens, the water becomes H3O+, or hydronium. So, when you are measuring the concentration of acidic protons in solution, the notation is either [H+] or [H30+], and you can refer to this as either a proton, hydrogen ion, H+, H3O+, or hydronium ion concentration. They all mean the same thing.
Bronsted-Lowry acids are defined as substances that donate protons to solution, while bases are defined as substances that can accept protons in solution. Because the definition of an acid is the same by both the Arhhenius and Bronsted-Lowry definitions (something that donates H+), it is pretty easy to remember. Bases are where things differ. Consider the reaction of NH₃ and HCl. In this case, ammonia acts as a Brønsted-Lowry base by accepting the proton released by HCl. HCl can be considered an acid by both definitions. However, so far, NH3 can only be a base by the Bronsted definition. It accepts a proton and becomes NH4+, but it does not donate OH- to solution.
Lewis Acids and Bases
The Lewis definition is the last of the three acid/base definitions, and it is usually used in the context of organic chemistry. Where the Bronstead-Lowry definition focuses on where protons go, the Lewis definition is more concerned with how they get there., or more generally, how bonds form. A Lewis base is a substance that can donate a pair of electrons to another chemical species, forming a coordinate covalent bond, Lewis bases are also referred to as nucleophiles. Lewis acids are substances that can accept a pair of electrons, and they are referred to as electrophiles.
There’s a lot to unpack here. First, a coordinate covalent bond is a bond formed by an electron pair that its donated from one atom (vs. two atoms that each donate one electron to form a bond).
A classic example of a Lewis base is ammonia (NH₃). In a reaction with boron trifluoride (BF₃), ammonia acts as a Lewis base by donating a pair of electrons to form a coordinate covalent bond with the boron atom in BF₃, resulting in the formation NH₃·BF₃. While Lewis bases usually dontate their electon pairs to reach out and bond to new hydrogens, this example strengthens the point that no hydrogen transfer is needed for something to be classified as a Lewis acid or base. It’s all about the electron pairs, what is donating them, and what is accepting them.
The Strength of Acids and Bases
Not all acids and bases perform their jobs to the same extent. This means that sometimes while molecules technically have the ability to donate H+ or OH- to solution, they don’t like doing it. When these types of “reluctant” acids or bases are added to solution, they’ll do what they have to do, just not very much. Because of this range in dissociation, the extent to which an acid or base donates/accepts protons to/from water molecules determines its strength. In general, stronger acids release more protons into solution, leading to a higher concentration of hydrogen (or hydronium) ions and a lower pH. Stronger bases accept protons from water more readily and increase the concentration of OH- left in solution.
Strong acids completely ionize in solution, meaning all of their molecules donate protons. Examples of strong acids include hydrochloric acid (HCl) and sulfuric acid (H₂SO₄). On the other hand, weak acids only partially ionize, resulting in a lower concentration of hydrogen ions and a higher pH.
Strong bases, like strong acids, react completely with water in solution leaving a high concentration of hydroxide ions. Examples include sodium hydroxide (NaOH) and potassium hydroxide (KOH). In contrast, weak bases only partially ionize water, leading to a lower concentration of hydroxide ions and a higher pH. Ammonia (NH₃) is an example of a weak base.
A conjugate is what the acid or base becomes after it has done it’s job. When an acid donates a proton, what is left over is its conjugate base. When a base accepts a proton, the new molecule is it’s conjugate acid. In this way, conjugate pairs are an acid and its conjugate base, or a base and its conjugate acid. The strength of a conjugate pair is inversely related; a strong acid or base has a weak conjugate. A good way to think about “weak” is stable, or unreactive. Furthermore, the strength of an acid or base is determined by the stability of its conjugate. Think about it, would a molecule give away a proton if it would be extremely unstable without it? No. Just like a molecule wouldn’t accept a proton if doing so made it unstable. This means that the happier (weaker, less reactive, more stable) the conjugate is, the more likely an acid or base is to do its job and become one.
The pH Scale
"pH" stands for "power of hydrogen”, and the pH scale is a logarithmic measurement system used to express the acidity or basicity of a solution. The scale ranges from 0 to 14, with 7 being considered neutral. Solutions with a pH less than 7 are acidic, while those with a pH greater than 7 are basic or alkaline. The pH of a solution is determined by the concentration of hydrogen ions (H+) in the solution. The lower the pH, the higher the concentration of hydrogen ions, and the more acidic the solution is. Conversely, a higher pH indicates a lower concentration of hydrogen ions, resulting in a more alkaline or basic solution.
Because the scale is logarithmic, a change of 1 on the pH scale means a tenfold change in the concentration. Additionally, the lower the number on the pH scale the higher the concentration in solution. For example, a solution with a pH of 3 has ten times more protons in solution than a solution with a pH of 4.
The pH of a solution can be measured using various methods, with pH meters and pH indicator papers (for example litmus paper) being common tools in laboratories. pH meters rely on a glass electrode sensitive to hydrogen ions, while indicator papers change color based on the pH of the solution, providing a quick visual assessment.
Acid/Base Equilibrium Constants
Remember that the expression for a reaction at equilibrium is the concentrations of the products divided by the concentrations of the reactants all raised to the power of their molar coefficients. K is the value associated with this ratio. Weak acids and bases do not react completely and instead reach equilibrium. Moving forward, we will be discussing Kw, Ka, and Kb in the context of acid base reactions. Don’t worry! Each of these are calculated in exactly the same way as K. The subscripts w, a, and b just indicate the specific type of equilibrium reaction involved. For example, Ka is the equilibrium constant for the reaction of a weak acid that reaches equilibrium.
Kw and The Autoionization of Water
Water molecules have the unique ability to act as both acids and bases in a self-ionization reaction. When this happens, two water molecules participate in a proton transfer where one water acts as an acid and gives a proton, and a second water acts as a base and takes a proton. The conjugate formed from the acidic water is a hydroxide ion (OH⁻), and the conjugate formed from the basic water is a hydronium ion (H₃O⁺). The equilibrium constant for this reaction is Kw, and the concentration of each ion in pure water is approximately 1.0×10^−7 M. Since the concentration of hydronium ions is equal to the concentration of hydroxide ions in pure water at equilibrium, the Kw value at 25 degrees Celsius is 1.0×10−14 which is the product of 1.0×10^−7 and 1.0×10^−7).
Ka and pKa
Remember that not all acids give up their protons easily, and there is a range of dissociations among acids. Ka, or the acid dissociation constant, is a quantitative measure that describes the extent to which an acid ionizes or donates a proton (H+) in a solution. In other words, Ka is defined for acids which only partially dissociate in water. It is a reflection of the equilibrium constant for the dissociation reaction of an acid, represented as:
HA(aq) + H2O(l) ⇌ H3O+(aq) + A−(aq)
In this equation, HA represents the weak acid, H3O+ is the hydrogen ion formed when the acid gives up it’s proton, and A- is the conjugate base of the original acid. The expression for Ka is given by the ratio of the concentrations of the dissociated ions (H3O+ and A-) to the undissociated acid (HA) at equilibrium:
A higher value of Ka indicates a stronger tendency for the acid to ionize and donate protons, leading to a higher concentration of H+ ions in solution, and a lower pH. Conversely, a lower Ka value corresponds to a weaker acid that ionizes to a lesser extent, and a higher pH.
pKa is the negative logarithm (base 10) of the Ka value, and provides a more manageable scale for comparing acid strengths. Lower pKa values correspond to stronger acids.
Kb and pKb
Kb is the base dissociation constant, and measures the extent to which a base ionizes or accepts a proton (H+) in a solution. Similar to Ka for weak acids, Kb is specifically defined for bases, which only partially ionize in water. It quantifies the equilibrium constant for the dissociation reaction of a base, represented as:
B(aq) + H2O(l) ⇌ BH+(aq) + OH−(aq)
Here, B represents the weak base, BH+ is the conjugate acid, and OH- is the hydroxide ion. The expression for Kb is given by the ratio of the concentrations of the dissociated ions (BH+ and OH-) to the undissociated base (B) at equilibrium:
A higher value of Kb indicates a stronger tendency for the base to ionize and accept protons, resulting in a higher concentration of OH- ions in solution. Conversely, a lower Kb value corresponds to a weaker base that ionizes to a lesser extent.
Similar to the acid dissociation constant, the pKb is obtained by taking the negative logarithm (base 10) of the Kb value. The pKb provides a convenient scale for comparing base strengths, where lower pKb values correspond to stronger bases.
Using ICE Tables With Acid/Base Equilibria
ICE tables, which stand for Initial, Change, and Equilibrium, are a useful tool in determining concentrations present at equilibrium. These tables are particularly handy when dealing with weak acids or bases, as they only partially ionize in solution. Once the equilibrium concentrations of H+ or OH_ are found using and ICE table, the pH and/or pOH can be determined. One thing to note is that only concentrations are used in ICE tables and equilibrium expressions.
The equilibrium concentrations of acid base reactions are the "E" column in the ICE table. If a K value is known for the reaction at a particular temperature, solving for x in the expression gives you the [H+] or [OH-]. These values can then be used to determine the pH or pOH of a solution (and more!) using the equations listed by topic in the above study guide.
Acid-base buffers are solutions that resist changes in pH when an acid or base is added to them. They play a crucial role in maintaining the stability of pH in various chemical and biological systems. Buffers are typically composed of a weak acid and its conjugate base, or a weak base and its conjugate acid. Usually, the concentrations of conjugates are zero when a reaction begins. The acid or base has not started dissociating yet. As the reaction progresses, dissociation will continue until the system reaches equilibrium. If some amount of conjugate is present in the system initially (a buffer) this conjugate will consume dissociated ions as they form, preventing a significant change in pH.
Common examples of acid-base buffer systems include acetic acid (CH₃COOH) and its conjugate base acetate (CH₃COO-), or the bicarbonate (HCO₃-) ion and its conjugate acid carbonic acid (H₂CO₃). Biological systems, such as blood in the human body, also utilize buffers to maintain a stable pH, crucial for the proper functioning of enzymes and other biochemical processes.
The effectiveness of a buffer is quantified by it’s capacity, which refers to how well a solution resists changes in pH when an acid or base is added to it. It is a measure of how effectively the buffer system can neutralize added hydrogen ions (H+) or hydroxide ions (OH-). The greater the buffer capacity of a solution, the more it can neutralize these ions without causing a significant change in pH.
Buffer capacity is influenced by the concentration of the conjugate relative to the amount of acid or base present in the initial mixture. Specifically, a higher concentration of buffer components generally leads to a higher buffer capacity. The pH of a buffer system can be found by either using an ICE table remembering that the initial concentration of the conjugate is not zero. It can also be found using the Henderson-Hasselbach equation. Both methods are explained in the above study guide.
Buffers are most effective at resisting changes in pH when the acids and bases involved are of moderate strength. Think about it. Species that are very likely to dissociate do so because their conjugates are relatively unreactive. This means that if strong acids or bases are used, their stable conjugates are unlikely to react and consume H+ or OH-. The whole point of a buffer is to consume these ions, so acids or bases of moderate strength must be used because they have conjugates that are equipped to reverse the direction of the reaction.
Acid/base titrations are analytical techniques used to determine the concentration of an unknown acid or a base in a solution by reacting it with a standardized solution of known concentration. The process involves slowly adding the titrant, the solution of known concentration, to the analyte, the solution of unknown concentration, until the reaction between the two is complete. The point at which this occurs is known as the equivalence point. The theoretical basis of acid/base titrations lies in the stoichiometry of the chemical reaction between the acid and base and the equivalence point is when the moles of acid are equal to the moles of base (or vice versa). The key to the success of titrations is the use of indicators or pH meters to signal when the equivalence point is reached. Common indicators change color when the pH of the solution shifts within a certain range, providing a visual cue to the operator. The most common indication used in laboratory settings is phenolphthalein which is clear in acidic solutions and pink in basic solutions.