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 their acid strengths is approximately 10.114, closest option is (d) 100.

Step 1: Understand the Relationship of Ka and Acid Strength

The acid dissociation constant, referred to as \( K_a \), is a quantitative measure of the strength of an acid in solution. Generally, a larger \( K_a \) value indicates a stronger acid because it implies more dissociation into ions. We have formic acid with \( K_a = 1.77 \times 10^{-4} \) and acetic acid with \( K_a = 1.75 \times 10^{-5} \).

Step 2: Calculate the Ratio of Acid Strengths

The ratio of the strengths of the acids is given by the ratio of their \( K_a \) values. This can be calculated as:\[\text{Ratio} = \frac{K_{a,\text{formic}}}{K_{a,\text{acetic}}} = \frac{1.77 \times 10^{-4}}{1.75 \times 10^{-5}}\]

Step 3: Perform the Division

To determine the ratio, divide the numerical coefficients and handle the powers of ten separately:\[\text{Ratio} = \frac{1.77}{1.75} \times \frac{10^{-4}}{10^{-5}}\]Which simplifies to:\[\text{Ratio} = 1.0114 \times 10^1 = 10.114\]

Step 4: Choose the Closest Answer

After calculating, the closest answer from the provided options is (d) 100. Though our calculated ratio is approximately 10.114, the possible answers are discrete, hence (d) is the most reasonable approximation given the limited number of options.

Key Concepts

Understanding Acid Strength

When we talk about acid strength, we're discussing an acid's ability to donate protons (H⁺ ions) to a solution. A key measure of acid strength is the acid dissociation constant, known as \( K_a \). A higher \( K_a \) value indicates a stronger acid because it shows that a greater proportion of the acid molecules dissociate into ions.
To put it simply:

• The larger the \( K_a \), the stronger the acid.
• The smaller the \( K_a \), the weaker the acid.

This relationship is important when comparing acids because it provides a quantitative way to measure their strength.
For example, in our exercise, formic acid has a \( K_a \) of \(1.77 \times 10^{-4}\), while acetic acid has a \( K_a \) of \(1.75 \times 10^{-5}\), indicating that formic acid is stronger than acetic acid.

Exploring Formic Acid

Formic acid, with the chemical formula HCOOH, is the simplest carboxylic acid. It's naturally found in the venom of some ants and stinging insects and is used in various industrial applications.
Formic acid's \( K_a \) value is \(1.77 \times 10^{-4}\), which means it has a relatively high tendency to release protons in solution compared to weaker acids like acetic acid. This makes it a stronger acid in the context of our comparison.
With such strong acid characteristics:

• Formic acid readily donates protons in aqueous solutions.
• It plays a significant role in both biological and chemical processes.

When you encounter formic acid, remember it as a potent participant in acidity discussions due to its higher \( K_a \) value.

Characteristics of Acetic Acid

Acetic acid, with the chemical formula CH₃COOH, is a well-known carboxylic acid most commonly associated with vinegar. It has a lower \( K_a \) than formic acid, specifically \(1.75 \times 10^{-5}\), indicating that it's weaker in terms of proton donation capability.
Despite its weaker nature compared to formic acid:

• Acetic acid is very important in the food industry and as a chemical reagent.
• Its milder acidity makes it safer for dietary uses.

Understanding that acetic acid is less dissociative than formic acid helps in appreciating its utility and behavior in various applications, particularly in scenarios where less reactivity is desired.