Acids and Bases for the DAT
/Learn key DAT concepts about acids and bases, plus practice questions and answers
Learn key DAT concepts about acids and bases
Table of Contents
Part 1: Introduction to acids and bases
Part 2: Definitions
a) Lewis and Bronsted-Lowry acids and bases
b) Strength
c) Important acids and bases
d) Amphoteric species
e) Equilibrium constants
f) pH and pOH
Part 3: Buffer system
a) Buffer systems
b) Henderson-Hasselbalch equation
Part 4: Titrations
a) Titrating a strong acid and strong base
b) Titrating weak acids and bases
c) pKa of multiprotic acids
Part 5: High-yield terms
Part 6: Questions and answers
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Part 1: Introduction to Acids and Bases
In chemistry, acids and bases are fundamental concepts essential for understanding various chemical reactions and properties of substances. Acids are substances that can donate protons (H+) or accept electrons, while bases are substances that can accept protons or donate electrons. The strength of an acid or base is often characterized by its ability to donate or accept protons, measured by the pH scale. Acids typically have a pH less than 7, with lower values indicating stronger acidity, while bases have a pH greater than 7, with higher values indicating stronger basicity. The interplay between acids and bases is crucial in various chemical processes, including neutralization reactions, buffer systems, and the regulation of pH in biological systems. As you study this guide, pay attention to bolded, high-yield terms and use the questions at the end to test your DAT-readiness.
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Part 2: Definitions
a) Lewis and Bronsted-Lowry acids and bases
Many students commonly associate acids and bases with hydrogen and hydroxide ions. For instance, a solution with a high concentration of hydrogen ions (H+) is deemed acidic, while one with a high concentration of hydroxide ions (OH-) is recognized as basic. Although this perspective is valid, it is not the sole interpretation.
The Lewis and Bronsted-Lowry definitions provide alternative insights into the properties of acids and bases. Lewis acids and bases pertain to electron movement. A Lewis acid accepts an electron pair, while a Lewis base donates a pair of electrons.
Among the various definitions, the Lewis framework is the most inclusive and emphasizes electron behavior. In contrast, the Bronsted-Lowry definitions are somewhat less inclusive, centering on proton movement. A Bronsted-Lowry acid donates a proton (H+), and a Bronsted-Lowry base accepts a proton. It's noteworthy that every Bronsted-Lowry base is also a Lewis base, though the reverse isn't always true.
In the realm of acids and bases, all substances have conjugates formed through the gain or loss of a hydrogen ion. A conjugate acid is a Bronsted-Lowry base that has gained a proton, while a conjugate base is a Bronsted-Lowry acid that has lost a proton. Strong acids typically have weak conjugate bases, and strong bases have weak conjugate acids. This stems from the fact that a strong acid avoids forming a species that readily accepts a proton, maintaining its strength.
b) Strength
Understanding the strengths of acids and bases is crucial in the context of the DAT. The strength of an acid or base is often quantified by its ability to dissociate in water. Strong acids are substances that fully dissociate in water. These acids exhibit high reactivity and release a large number of protons, resulting in a low pH. On the other hand, weak acids only partially dissociate in water, releasing fewer protons and exhibiting a relatively higher pH. Similarly, strong bases also fully dissociate in water. This dissociation yields hydroxide ions (OH-) and contributes to a higher pH. Conversely, weak bases only partially dissociate, leading to a lesser increase in hydroxide ion concentration and a slightly lower pH compared to strong bases.
c) Important acids and bases
For the DAT, it's crucial to commit to memory various common strong acids and bases. Strong bases are formed when soluble hydroxides of group 1 and group 2 elements of the periodic table react with the hydroxide ion. Be(OH)2 is the lone exception to this trend. The following list compiles several frequently encountered strong bases, with any base not mentioned here assumed to be weak:
- Potassium hydride: KH
- Lithium hydride: LiH
- Lithium hydroxide: LiOH
- Sodium hydroxide: NaOH
- Potassium hydroxide: KOH
- Rubidium hydroxide: RbOH
- Caesium hydroxide: CsOH
- Magnesium hydroxide: Mg(OH)2
- Calcium hydroxide: Ca(OH)2
- Strontium hydroxide: Sr(OH)2
- Barium hydroxide: Ba(OH)2
Elements from Group 17, the halogens, are known to typically produce strong acids. These acids generate highly stable conjugate bases upon dissociation, thanks to the large atomic radius of the resulting ion. For instance, hydrobromic acid (HBr) dissociates into a hydrogen ion and bromide ion. The larger size of the bromide ion provides ample space for the negative charge to disperse, ensuring ion stability.
The exception to this pattern is hydrofluoric acid (HF), whose weakness arises from the instability of the dissociated products. The fluoride anion's negative charge is particularly unstable due to the small atomic radius of the ion, making the dissociation of HF less favorable. The list below outlines several commonly encountered strong acids, and any acid not included can be assumed to be weak:
- Hydroiodic acid: HI
- Hydrobromic acid: HBr
- Hydrochloric acid: HCl
- Perchloric acid: HClO4
- Sulfuric acid: H2SO4
- Nitric acid: HNO3
d) Amphoteric species
Amphoteric species exhibit the versatile ability to function as either Bronsted-Lowry acids or bases. In an acidic environment, these species assume the role of a base, while in a basic environment, they function as an acid.
An illustration of amphoteric species can be found in amino acids, which are categorized as zwitterions—molecules with simultaneous positive and negative charges. Amino acids demonstrate their amphoteric nature by acting as acids through the amino group (or N-terminus) donating protons, and as bases through their carboxylate group (or C-terminus) accepting protons.
Water is another prominent example of an amphoteric species. Its behavior varies when encountering a base or acid. Below are instances of water's reactions in the presence of a protonated acid (HA) and a protonated base (HB)
H2O + B- ⇋ OH- + HB
It's important to recognize that in an acidic environment, water accepts a proton to yield the hydronium ion (H3O+). Conversely, in a basic environment, water donates a proton to generate a hydroxide ion (OH-). Water also exhibits a unique form of reaction known as autoionization, wherein it engages in a reaction with itself, as depicted in the following reaction:
e) Equilibrium constants
The autoionization of water also exhibits an equilibrium constant. For more detailed insights into equilibrium constants, refer to our guide on chemical equilibrium and kinetics.
Kw, denoted as the water dissociation constant, is a value you should know. At 298 Kelvin (25°C), Kw equals the product of the concentrations of hydroxide and hydrogen ions, which is 10-14. Like all equilibrium constants, this value is solely dependent on temperature. Alterations in factors such as concentration or volume do not affect the water dissociation constant. It can be utilized to determine the acid dissociation constant or base dissociation constant of a solution:
Two additional constants are the acid dissociation constant (Ka) and the base dissociation constant (Kb). These represent the equilibrium constants for the dissociation of an acid (HA) and the dissociation of a base (BH). The formulas for both Ka and Kb are presented below.
B + H2O ⇋ BH+ + OH- Kb = [BH+][OH-]/[B]
As strong acids dissociate completely, they generally possess a larger Ka value. Weak acids have a Ka value less than 1.0. Similarly, a higher Kb value indicates a strong base, while weak bases exhibit a Kb value less than 1.0. The negative logarithms (base 10) of the acid dissociation constant and base dissociation constants yield several critical values.
pKb = -log(Kb)
The pKa represents the pH at which half of the species in a solution are protonated, while the other half are deprotonated. If the pH exceeds the pKa, the species will primarily exist in the deprotonated form. Strong acids typically possess low pKa values, whereas strong bases tend to have low pKb values. An example will further illustrate this concept.
Let's determine the concentration of hydronium in a 3.0 M aqueous solution of benzoic acid, a weak acid.
Ka = 6.46 x 10-5
First, write the balanced equation for the chemical reaction.
C6H5COOH + H2O ⇋ C6H5COO- + H3O+
Using this formula, the Ka expression can be written as:
Ka = [H3O+][C6H5COO-]/[C6H5COOH] = 6.46 x 10-5
How do we determine [H3O+]? Recognize that [C6H5COO-] must equal [H3O+] since their stoichiometric ratios are 1:1. We can employ the variable x to represent the amount of C6H5COO-and H3O+formed. Additionally, the quantity of products formed will equal the initial concentration of benzoic acid minus x. Thus, the Ka expression can be rewritten as:Ka = (x)(x)/(3.0 - x)
Solving this equation is quite challenging. To make it solvable, a simplifying assumption must be made. Since the value of x is extremely small, it is considered negligible. Hence, the expression can be simplified to:
K a = (x)(x)/(3.0)
Finally, substitute the given Ka value to solve for x:
6.46 x 10-5 = (x)(x) / (3.0)
0.0001938 = x2
x = 0.014
Consequently, the concentration of hydronium in the solution equals 0.014 M.
f) pH and pOH
The pH scale serves as a measure to characterize the acidity of a solution. Solutions with a pH below 7 are regarded as acidic, while those with a pH above 7 are considered basic. A pH of 7 represents neutrality and corresponds to the pH of pure water. Strong acids generally exhibit a pH ranging from 0 to 3, while weak acids fall within the pH range of 3 to 7. On the other hand, strong bases typically have a pH between 12 and 14, while weak bases typically fall within the pH range of 7 to 12. The pH of a solution can be determined using the following equation:
The pH is represented as the negative logarithm of the concentration of hydrogen ions in a solution. Conversely, the pOH scale offers insight into the basicity of a solution and operates as the counterpart to the pH scale. A pOH below 7 indicates basicity, above 7 is acidic, and at 7 it is neutral. The equation provided below can be employed to determine the pOH of a solution.
The pOH is determined by taking the negative logarithm of the hydroxide ion concentration in a solution. In a given solution, the sum of its pOH and pH is always 14. For instance, if the pH of a solution is found to be 4, the corresponding pOH would be 10. This relationship is expressed by the equation:
pH + pOH = 14
Determining the pH or pOH of a solution of a strong acid or strong base is fairly easy. Consider the following:
A 1L aqueous solution contains 0.001 M hydrochloric acid. Find its pH.
Since hydrochloric acid (HCl) is a strong acid, it dissociates completely in solution.
Thus, [H3O+] must also be equal to 0.001.
This value can be used in the definition of pH:
pH = -log[H+] pH = -log(0.001) pH = -(-3) = 3
However, this task becomes considerably more challenging for weak acids and bases. Because weak acids and bases do not undergo complete dissociation in an aqueous solution, an alternative approach is required to determine the eventual pH. If the pKa of a weak acid or base is known, the concentration of H+ can be ascertained using the method outlined in the preceding section. Subsequently, this value can be employed in the pH definition. For example, let's calculate the pH of a 3.0 M aqueous solution of the weak acid benzoic acid (C6H5COOH), with a Ka value of 6.46 x 10-5. As per our earlier computations, we have established that the concentration of hydronium in the solution equals 0.014 M.
pH = -log(0.014)
While this may be a difficult value to obtain without a calculator, the following is true:
-log(0.010) > pH > -log(0.1)
-(-2) > pH > -(-1)
2 > pH > 1
Thus, the pH of the solution is assumed to be between 1 and 2. (To be precise, the exact value of the pH is 1.85.)
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