Problem 108 - A Complete Resource Book in Chemistry for JEE Main

Question

The Ka value of formic acid and acetic acid are respectively \(1.77 \times 10^{-4}\) and \(1.75 \times 10^{-5}\). the ratio of the acid strength of \(0.1 \mathrm{~N}\) acids is (a) \(0.1\) (b) \(0.3\) (c) \(3.178\) (d) 100

Step-by-Step Solution

Answer

The ratio of acid strength is closest to 100.

Step 1: Understand Acid Strength

The strength of an acid can be understood in terms of its acid dissociation constant, or \( K_a \). The larger the \( K_a \) value, the stronger the acid because it dissociates more in solution, releasing more hydrogen ions.

Step 2: Calculate Ratio of Acid Strengths

To find the ratio of acid strengths, we can use the ratio of the \( K_a \) values of the acids. The given \( K_a \) values are: Formic Acid: \( 1.77 \times 10^{-4} \) Acetic Acid: \( 1.75 \times 10^{-5} \)The ratio is calculated as: \[ \text{Ratio} = \frac{K_{a(\text{formic})}}{K_{a(\text{acetic})}} = \frac{1.77 \times 10^{-4}}{1.75 \times 10^{-5}} \] Perform the division to get the ratio.

Step 3: Perform the Calculation

Execute the division: \[ \frac{1.77 \times 10^{-4}}{1.75 \times 10^{-5}} = \frac{1.77}{1.75} \times 10^{1} \] This simplifies to approximately: \[ 1.0114 \times 10^{1} = 10.114 \]

Step 4: Round the Result

Based on the simplified calculation: \[ 10.114 \] is approximately equal to 10 when considering significant figures in a practical sense. This result implies the ratio is closer to options given in the problem.

Key Concepts

Acid Dissociation Constant

The acid dissociation constant, represented as \( K_a \), is a measure of the strength of an acid in its ability to donate protons (\( H^+ \) ions). A higher \( K_a \) value indicates a stronger acid as it dissociates more completely in solution, providing more hydrogen ions.
Understanding \( K_a \) values is crucial when comparing acids. It showcases how easily an acid can ionize and thus display its strength. For instance, a \( K_a \) of \( 1.77 \times 10^{-4} \) indicates that formic acid is more willing to release hydrogen ions than acetic acid with a \( K_a \) of \( 1.75 \times 10^{-5} \).

• \( K_a \) is determined through equilibrium expressions involving concentration terms for the ionized and unionized form of the acid.
• Larger \( K_a \) implies stronger acid; conversely, a smaller \( K_a \) suggests a weaker acid.

Understanding the \( K_a \) value helps us calculate the ratio of acid strengths and decide which acid solution has a higher hydrogen ion concentration.

Formic Acid

Formic acid, also known as methanoic acid, is the simplest carboxylic acid with a \( K_a \) value of \( 1.77 \times 10^{-4} \).
Its structure consists of a carboxyl group \( (COOH) \) attached to a hydrogen atom, making it one of the smallest organic acids. The nature of this structure contributes to its ability to donate hydrogen ions, thereby showing its strength as an acid.

• Formic acid is not only stronger than acetic acid but is also widely found in various natural sources such as ant venom and stinging nettles.
• Its \( K_a \) suggests it dissociates well in aqueous solutions, releasing \( H^+ \) ions.

In comparing formic acid with others, its higher dissociation constant is key to identifying it as stronger, especially in the context of this exercise.

Acetic Acid

Acetic acid, scientifically known as ethanoic acid, has a \( K_a \) of \( 1.75 \times 10^{-5} \). It is a weaker acid compared to formic acid as seen through its lower \( K_a \).
Acetic acid is present in vinegar, providing its distinct sour taste. It consists of a carboxyl group \( (COOH) \) linked to a methyl group \( (CH_3) \), which affects its ionization capability.

• The methyl group in its structure slightly reduces the release of \( H^+ \) ions compared to formic acid.
• The lower dissociation constant implies acetic acid is less strong, making formic acid more effective in donating protons under identical conditions.

Understanding its chemical behavior is essential in contexts like food sciences and chemistry where acid strength plays a significant role.