Difficulty: Intermediate | Prerequisites: General equilibrium concepts, logarithms, molarity

This material sits at the heart of acid-base chemistry in CHEM 202. You need a solid grasp of equilibrium expressions and how to set up simple algebra before any of this will click. The concepts here, ranking acid strength from pKa values and calculating Ka from experimental pH data, appear on virtually every general chemistry exam. If you can work an ICE table cleanly and convert between Ka and pKa without hesitation, you are in good shape for the quantitative portion of Exam 2.

TL;DR

Every acid has a Ka (how much it dissociates in water) and a pKa (the negative log of Ka). Smaller pKa means stronger acid, larger Ka. To find Ka from experimental pH data, set up an ICE table, convert pH to [H3O+], and solve the equilibrium expression. These two skills, ranking acids by pKa and calculating Ka from pH, are the quantitative backbone of acid-base questions on Exam 2.

Key Terms

Ka (acid dissociation constant)

The equilibrium constant for the dissociation of an acid in water. A larger Ka means the acid gives up its proton more readily.

In simple terms, Ka tells you what fraction of the acid actually falls apart in solution. Big number = strong tendency to dissociate.

pKa

The negative base-10 logarithm of Ka: pKa = -log(Ka). A smaller pKa corresponds to a stronger acid.

Think of it as a more convenient scale for comparing acid strength. Lower pKa = stronger acid, always.

ICE table (Initial, Change, Equilibrium)

A bookkeeping method for tracking concentrations through an equilibrium reaction. You list the initial concentration, the change (usually ±x), and the resulting equilibrium concentrations.

In simple terms, it is a simple grid that keeps your algebra organised when solving for unknowns in equilibrium problems.

Weak acid

An acid that only partially dissociates in water. Its Ka is much less than 1.

Think of it as an acid that holds on to most of its protons. Vinegar (acetic acid) is a classic example.

Strong acid

An acid that dissociates completely in water. You do not write an equilibrium expression for it because the reaction goes to completion.

Conjugate base

The species that remains after an acid donates a proton. For HA, the conjugate base is A⁻.

Hydronium ion (H3O+)

The species formed when a proton is accepted by water. Its concentration determines the pH of the solution: pH = -log[H3O+].

Core Content

pKa vs Ka: the Inverse Relationship

• pKa = -log(Ka), so as Ka gets larger, pKa gets smaller

• Smallest pKa = strongest acid (most dissociated)

• Largest pKa = weakest acid (least dissociated)

• You do not need to convert pKa to Ka to rank acid strength. pKa values alone are enough: just compare them directly

• The acid with the lowest pKa will also produce the solution with the lowest pH (most acidic), assuming equal concentrations

• The acid with the highest pKa will produce the solution with the highest pH (least acidic), again assuming equal concentrations

Ranking Acid Strength from pKa Values

Given four acids all at 0.1 M:

The key insight: you can answer every part of this question using pKa alone. No need to compute Ka.

Calculating Ka from pH Using an ICE Table

When you know the initial concentration of a weak acid and the pH of the solution, you can work backwards to find Ka.

Step 1: Convert pH to [H3O+]

• [H3O+] = 10^(-pH)

• Example: pH = 2.71 gives [H3O+] = 10^(-2.71) = 1.95 x 10^(-3) M

Step 2: Set up the ICE table

For the generic weak acid dissociation HA + H2O ⇌ A⁻ + H3O+:

• Initial: [HA] = 0.25, [A⁻] = 0, [H3O+] = 0

• Change: [HA] = -x, [A⁻] = +x, [H3O+] = +x

• Equilibrium: [HA] = 0.25 - x, [A⁻] = x, [H3O+] = x

Step 3: Identify x

Since x = [H3O+] and we already calculated that from pH, x = 1.95 x 10^(-3)

Step 4: Solve for Ka

Ka = (x)(x) / (0.25 - x) = (1.95 x 10^(-3))^2 / (0.25 - 1.95 x 10^(-3)) = 1.53 x 10^(-5)

Note: if you ignore x in the denominator (the 5% approximation), you get Ka = 1.52 x 10^(-5). Both are acceptable unless the question specifies otherwise.

Formulas

K_a = \frac{[\text{A}^-][\text{H}_3\text{O}^+]}{[\text{HA}]}

\text{pK}_a = -\log(K_a)

K_a = 10^{-\text{pK}_a}

[\text{H}_3\text{O}^+] = 10^{-\text{pH}}

ICE table layout (for HA + H2O ⇌ A⁻ + H3O+):

Real-World Applications

Butyric acid (Ka ≈ 1.5 x 10^(-5)) is responsible for the sharp, unpleasant smell of rancid butter. Knowing its Ka helps food scientists understand how readily it dissociates in solution and therefore how strongly it contributes to off-flavours at different pH levels.

Ranking acid strength by pKa is routine in pharmaceutical chemistry: drug designers select acids and bases with specific pKa values to control how a molecule behaves at physiological pH (around 7.4), which affects absorption and bioavailability.

Common Misconceptions

• Students often think a larger pKa means a stronger acid. It does not. Larger pKa = weaker acid. The scale runs opposite to what you might expect.

• Students sometimes confuse pH and pKa. pH describes the acidity of a particular solution. pKa is a property of the acid itself, regardless of concentration.

• When using an ICE table, students frequently forget to subtract x from the initial concentration in the denominator. Skipping this step (the "5% approximation") is only valid when x is very small relative to the initial concentration, typically less than 5%.

• Some students try to convert pKa to Ka before ranking acid strength. This is unnecessary and wastes time. pKa values can be compared directly.

Why It Matters / Exam Flags

⚠️ Expect a question asking you to rank acids by strength given pKa values, and to identify which solution has the highest or lowest pH. This is a quick-marks question if you know the rule: lowest pKa = strongest acid = lowest pH.

⚠️ ICE table calculations with Ka are a near-certainty on Exam 2. Be comfortable going in both directions: given Ka, find pH; given pH, find Ka.

⚠️ Know when the 5% approximation is valid and when you need to use the quadratic. If x is more than 5% of the initial concentration, keep x in the denominator.

⚠️ The exam may give you Ka and ask for pKa, or vice versa. Be fluent with the conversion: pKa = -log(Ka) and Ka = 10^(-pKa).

Quick Self-Test

1. True or False: An acid with pKa = 3.2 is stronger than one with pKa = 5.8.

1. Fill in the blank: To convert pH to hydronium ion concentration, use the formula [H3O+] = ______.

1. True or False: In an ICE table for a weak acid, the initial concentration of H3O+ is set to zero.

1. Fill in the blank: Ka = 10^(-______) when you know the pKa.

1. True or False: If two acids are at the same concentration, the one with the larger Ka will have a higher pH.

Practice Q&A

Q: Given three acids at 0.1 M, with pKa values of 1.5, 6.3, and 9.7, which produces the solution with the lowest pH?

A: The acid with pKa = 1.5. The lowest pKa means the strongest acid, which dissociates the most and produces the most H3O+, giving the lowest pH.

Q: A 0.10 M solution of a weak acid has a pH of 3.00. What is the Ka of this acid?

A: [H3O+] = 10^(-3.00) = 1.0 x 10^(-3) M. Using the ICE table: Ka = (1.0 x 10^(-3))^2 / (0.10 - 1.0 x 10^(-3)) = 1.0 x 10^(-6) / 0.099 = 1.01 x 10^(-5).

Q: An acid has Ka = 6.3 x 10^(-8). What is its pKa?

A: pKa = -log(6.3 x 10^(-8)) = 7.20.

Q: Two acids are both at 0.1 M. Acid X has pKa = 4.74 and Acid Y has pKa = 9.25. Which solution has the higher pH? Why?

A: Acid Y. A higher pKa means it is a weaker acid, so it dissociates less, produces fewer H3O+ ions, and therefore has a higher (less acidic) pH.

Q: A student calculates Ka for a weak acid and gets a value of 250. Is this reasonable for a weak acid? Why or why not?

A: No. A weak acid has Ka much less than 1, typically in the range of 10^(-2) to 10^(-14). A Ka of 250 would indicate a strong acid. The student likely made an arithmetic error.

Connections to Other Topics

This material connects directly to buffer chemistry: a buffer works best when the solution pH is close to the pKa of the weak acid component. Understanding Ka and pKa is a prerequisite for the Henderson-Hasselbalch equation, which you will use extensively in buffer and titration problems.

ICE tables reappear in solubility equilibria (Ksp) and in weak base problems (Kb), so the technique you learn here transfers to several later topics in the course.

Related Terms / Search Tags

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