Easy pKa and pKb Practice Questions

Concept Explanation

pKa and pKb are logarithmic scales used to represent the strength of acids and bases, respectively, with lower values indicating stronger substances. These values are derived from the acid dissociation constant (Ka) and the base dissociation constant (Kb). Because Ka and Kb values often involve very small numbers (like 1.8 × 10⁻⁵), the negative logarithm is used to convert them into a more manageable scale, similar to how pH calculations simplify hydrogen ion concentrations.

Understanding these values is fundamental in acid-base chemistry. The mathematical relationship is defined by the following formulas:

• pKa = -log[Ka]

• pKb = -log[Kb]

• Ka = 10^(-pKa)

• Kb = 10^(-pKb)

A crucial relationship exists for conjugate acid-base pairs in water at 25°C: the sum of pKa and pKb always equals 14.00 (pKw). This means if you know the strength of an acid, you can immediately determine the strength of its conjugate base. In practical chemistry, this relationship is vital for understanding buffer solutions and titration curves. Generally, a pKa less than 0 indicates a strong acid, while a pKa between 0 and 14 indicates a weak acid. The same logic applies to pKb for bases.

Solved Examples

1. Calculating pKa from Ka: An unknown acid has a Ka of 4.5 × 10⁻⁴. Calculate its pKa.

   1. Identify the formula: pKa = -log(Ka).

   2. Substitute the value: pKa = -log(4.5 × 10⁻⁴).

   3. Calculate the logarithm: log(4.5) ≈ 0.65; log(10⁻⁴) = -4.

   4. Combine: - (0.65 - 4) = 3.35.

   5. The pKa is 3.35.

2. Calculating Kb from pKb: Ammonia has a pKb of 4.75. What is its Kb value?

   1. Identify the formula: Kb = 10^(-pKb).

   2. Substitute the value: Kb = 10^(-4.75).

   3. Calculate the exponent: 10^(-4.75) ≈ 1.78 × 10⁻⁵.

   4. The Kb of ammonia is 1.78 × 10⁻⁵.

3. Finding the Conjugate Pair: If Hydrocyanic acid (HCN) has a pKa of 9.21, what is the pKb of its conjugate base, the cyanide ion (CN⁻)?

   1. Use the relationship: pKa + pKb = 14.00.

   2. Rearrange for pKb: pKb = 14.00 - pKa.

   3. Substitute the value: pKb = 14.00 - 9.21.

   4. The pKb of CN⁻ is 4.79.

Practice Questions

Test your knowledge with these easy to moderate pKa and pKb practice questions.

1. Calculate the pKa of Acetic acid if its Ka is 1.8 × 10⁻⁵.

2. A weak base has a Kb of 1.2 × 10⁻⁶. What is its pKb?

3. If an acid has a pKa of 3.20, what is the pKb of its conjugate base?

4. Convert a pKa of 10.5 into its corresponding Ka value.

5. A solution of Methylamine has a pKb of 3.36. Calculate its Kb.

6. Which is a stronger acid: Acid A with pKa = 2.5 or Acid B with pKa = 4.8?

7. Calculate the pKb of the conjugate base of Nitrous acid (HNO₂), which has a Ka of 4.0 × 10⁻⁴.

8. If the pKb of a base is 9.0, what is its Kb?

9. Determine the pKa of the conjugate acid of a base that has a pKb of 5.25.

10. Given Ka = 6.3 × 10⁻⁸, find the pKa.

Answers & Explanations

1. pKa = 4.74. Calculation: -log(1.8 × 10⁻⁵) = 4.74. This is a classic value for acetic acid commonly seen in chemistry labs.

2. pKb = 5.92. Calculation: -log(1.2 × 10⁻⁶) = 5.92.

3. pKb = 10.80. Calculation: 14.00 - 3.20 = 10.80. This uses the constant relationship between conjugate pairs.

4. Ka = 3.16 × 10⁻¹¹. Calculation: 10^(-10.5) = 3.16 × 10⁻¹¹.

5. Kb = 4.37 × 10⁻⁴. Calculation: 10^(-3.36) = 4.37 × 10⁻⁴.

6. Acid A. Lower pKa values correspond to higher Ka values, meaning Acid A (2.5) is stronger than Acid B (4.8).

7. pKb = 10.60. First, find pKa: -log(4.0 × 10⁻⁴) = 3.40. Then, pKb = 14.00 - 3.40 = 10.60.

8. Kb = 1.0 × 10⁻⁹. Calculation: 10^(-9.0) = 1.0 × 10⁻⁹.

9. pKa = 8.75. Calculation: 14.00 - 5.25 = 8.75.

10. pKa = 7.20. Calculation: -log(6.3 × 10⁻⁸) = 7.20.

Quick Quiz

Frequently Asked Questions

What is the difference between Ka and pKa?

Ka is the acid dissociation constant that measures the actual equilibrium concentration ratio, while pKa is the negative logarithm of that value. The pKa scale is used to make it easier to compare acid strengths without using scientific notation.

Can pKa values be negative?

Yes, very strong acids like Hydrochloric acid (HCl) have pKa values less than zero. A negative pKa indicates that the acid almost completely dissociates in water, according to Khan Academy's chemistry resources.

How does temperature affect pKa and pKb?

Since dissociation is an equilibrium process, pKa and pKb values are temperature-dependent. Most standard tables provide these values at 25°C, but they will shift if the temperature of the solution changes.

Why is the sum of pKa and pKb always 14?

This sum is derived from the autoionization constant of water (Kw), which is 1.0 × 10⁻¹⁴ at 25°C. Taking the negative log of Kw gives pKw, which equals 14, establishing the link between Ka and Kb calculations.

Is a high pKb value good for a base?

No, a high pKb value indicates a weak base. Strength in bases is indicated by a high Kb value or a low pKb value, just as strong acids have low pKa values.

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