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Chapter 2: Problem 49

Calculate \(K_{\mathrm{a}}\) value from the following \(\mathrm{pK}_{\mathrm{a}}\) 's: (a) Acetone, \(\mathrm{pK}_{\mathrm{a}}=19.3\) (b) Formic acid, \(\mathrm{p} K_{\mathrm{a}}=3.75\)

Short Answer

Expert verified
Acetone: \(K_a = 5.01 \times 10^{-20}\); Formic acid: \(K_a = 1.78 \times 10^{-4}\).

Step by step solution

01

Understanding pK_a

The \(\text{pK}_{\mathrm{a}}\) value indicates the acid dissociation constant on a logarithmic scale, where a lower \(\text{pK}_{\mathrm{a}}\) value represents a stronger acid.
02

Relating pK_a to K_a

The relationship between \(\text{pK}_{\mathrm{a}}\) and \(K_a\) is given by the equation: \[\text{pK}_{\mathrm{a}} = -\log_{10}(K_a) \] This means you can calculate \(K_a\) using the inverse logarithm.
03

Calculate K_a for Acetone

Given \(\text{pK}_{\mathrm{a}} = 19.3\) for acetone, apply \(K_a = 10^{-\text{pK}_{\mathrm{a}}}\). Thus, \[K_a = 10^{-19.3}\approx 5.01 \times 10^{-20}\]
04

Calculate K_a for Formic acid

Given \(\text{pK}_{\mathrm{a}} = 3.75\) for formic acid, apply the same formula: \[K_a = 10^{-3.75} \approx 1.78 \times 10^{-4}\]
05

Verify and Interpret Results

Check the calculations for any errors. A smaller \(\text{pK}_{\mathrm{a}}\), meaning a larger \(K_a\), confirms that formic acid is significantly stronger than acetone as an acid.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

pKa
The term \( \text{pK}_{\mathrm{a}} \) is essential when discussing acids and their strength. It stands for "acid dissociation constant," which is a measure of how easily an acid releases its hydrogen ions into a solution. Lower \( \text{pK}_{\mathrm{a}} \) values indicate stronger acids, as they are more eager to donate protons.

  • Understanding the Scale: The \( \text{pK}_{\mathrm{a}} \) is shown on a logarithmic scale, meaning each whole number change represents a tenfold change in acidity.
  • Comparing Acids: If comparing acids, the one with the lower \( \text{pK}_{\mathrm{a}} \) will be stronger. For example, a \( \text{pK}_{\mathrm{a}} \) of 3 is much stronger than a \( \text{pK}_{\mathrm{a}} \) of 5 as an acid.

This scale is vital for chemists to predict and understand the behavior of various acids in different environments.
Ka Calculation
The connection between \( \text{pK}_{\mathrm{a}} \) and \( K_a \) is central in acid strength calculations. The formula \( \text{pK}_{\mathrm{a}} = -\log_{10}(K_a) \) allows us to switch between these two expressions of acidity.

  • Calculating \( K_a \): Use the inverse logarithm, i.e., \( K_a = 10^{-\text{pK}_{\mathrm{a}}} \), to find the acid鈥檚 dissociation constant from its \( \text{pK}_{\mathrm{a}} \).
  • Importance of \( K_a \): This tells us how much of the acid will dissociate in a solution, contributing to its acidity.

It's a straightforward calculation once you鈥檙e comfortable with logarithms and exponents. Mastery of this conversion is key to understanding chemical equilibrium in acids.
Acetone
Acetone, known for its use in nail polish removers and as a solvent, is a fascinating compound with a \( \text{pK}_{\mathrm{a}} \) value of 19.3. This high \( \text{pK}_{\mathrm{a}} \) suggests acetone is extremely weak as an acid.

  • Chemical Structure: It has the chemical formula \( \text{C}_3\text{H}_6\text{O} \), featuring a carbonyl group which is central to its chemical behavior.
  • Applications: Often used as a solvent in laboratories because it dissolves a wide range of chemical compounds.
  • Role as an Acid: Due to its high \( \text{pK}_{\mathrm{a}} \), acetone dissociates minimally, contributing little to acididity in a solution.

Despite its low acidity, acetone is an important compound industrially and in laboratories.
Formic Acid
Formic acid, with a \( \text{pK}_{\mathrm{a}} \) of 3.75, is a much stronger acid compared to acetone. This compound is the simplest carboxylic acid and is known for its presence in ant venom and its use in preserving feed for livestock.

  • Chemical Makeup: Its chemical formula is \( \text{HCOOH} \) and it features a formyl group bound to a hydroxyl group.
  • Applications: Used in textile and leather processing and as a preservative.
  • Acid Strength: The relatively low \( \text{pK}_{\mathrm{a}} \) indicates it donates protons more readily than many other acids, confirming its role as a stronger acid.

Understanding formic acid through its \( \text{pK}_{\mathrm{a}} \) value aids in appreciating its reactivity and uses across various industries.

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Most popular questions from this chapter

Draw electron-dot structures for the following molecules, indicating any unshared electron pairs. Which of the compounds are likely to act as Lewis acids and which as Lewis bases? (a) \(\mathrm{AlBr}_{3}\) (b) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{2} \quad\) (c) \(\mathrm{BH}_{3}\) (d) HF (e) \(\mathrm{CH}_{3} \mathrm{SCH}_{3}\) (f) TiCl \(_{4}\)

Use the \(\delta+/ \delta\) - convention to indicate the direction of expected polarity for each of the bonds indicated. (a) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{Cl}\) (b) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{NH}_{2}\) (c) \(\mathrm{H}_{2} \mathrm{~N}-\mathrm{H}\) (d) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{SH}\) (e) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{MgBr}\) (f) \(\mathrm{H}_{3} \mathrm{C}-\mathrm{F}\)

What is the \(\mathrm{pH}\) of a \(0.050 \mathrm{M}\) solution of formic acid, \(\mathrm{p} K_{\mathrm{a}}=3.75 ?\)

1,3 -Cyclobutadiene is a rectangular molecule with two shorter double bonds and two longer single bonds. Why do the following structures not represent resonance forms?

Identify the most electronegative element in each of the following molecules: (a) \(\mathrm{CH}_{2} \mathrm{FCl}\) (b) \(\mathrm{FCH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Br}\) (c) \(\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\) (d) \(\mathrm{CH}_{3} \mathrm{OCH}_{2} \mathrm{Li}\)
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