Problem 41 - A Complete Resource Book in Chemistry for JEE Main

Question

An organic dibasic acid is used in volumetric analysis. The percentage of elements are \(\mathrm{C}=26.7 \%\), \(\mathrm{H}=2.2 \%\) and \(\mathrm{O}=71.1 \%\). Find the empirical formula of the acid. (a) \(\mathrm{CH}_{2} \mathrm{O}\) (b) \(\mathrm{CHO}_{2}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{O}_{2}\) (d) \(\mathrm{CH}_{4} \mathrm{O}\)

Step-by-Step Solution

Answer

The empirical formula of the acid is \( \mathrm{CHO}_{2} \).

Step 1: Converting percentages to masses

Assume you have 100 grams of the dibasic acid. This makes it straightforward to convert the percentages to grams: - Carbon: 26.7 grams - Hydrogen: 2.2 grams - Oxygen: 71.1 grams.

Step 2: Converting masses to moles

Convert the masses of each element to moles using the molar mass of each element: - Moles of Carbon: \( \frac{26.7}{12} = 2.225 \)- Moles of Hydrogen: \( \frac{2.2}{1} = 2.2 \)- Moles of Oxygen: \( \frac{71.1}{16} = 4.44375 \)

Step 3: Finding the smallest mole ratio

Divide each mole quantity by the smallest number of moles calculated: - Ratio for Carbon: \( \frac{2.225}{2.2} = 1.011 \)- Ratio for Hydrogen: \( \frac{2.2}{2.2} = 1 \)- Ratio for Oxygen: \( \frac{4.44375}{2.2} = 2.019 \)

Step 4: Simplifying to whole numbers

Round each ratio to the nearest whole number to find the subscripts for each element in the empirical formula: - Carbon: Rounded from 1.011 to 1 - Hydrogen: Already 1- Oxygen: Rounded from 2.019 to 2Thus, the empirical formula is \( \mathrm{CHO}_{2} \).

Key Concepts

Dibasic Acid

A dibasic acid is a type of acid that can donate two protons or hydrogen ions per molecule in a chemical reaction. This characteristic is what defines its term "dibasic."
The ability of an acid to donate protons is a fundamental concept in acid-base chemistry, and it plays a crucial role in various chemical processes.
When analyzing a dibasic acid, it's essential to understand that its reactions and stoichiometry are often more complex compared to monobasic acids.
For instance, in a complete neutralization with a base like sodium hydroxide, a dibasic acid would require two moles of the base to neutralize one mole of the acid.
Here are some key properties:

• They often show two distinct endpoints in a titration curve.
• Common examples include sulfuric acid (\(H_2SO_4\)) and oxalic acid (\(H_2C_2O_4\)).
• The presence of two acidic hydrogens impacts their behavior in many chemical reactions.

Understanding these basics can aid in comprehending why a dibasic acid is utilized in certain types of chemical analyses, like volumetric analysis.

Volumetric Analysis

Volumetric analysis is a technique in chemical analysis that involves measuring the volume of a solution as a way to determine the concentration of a solute.
This method is commonly used in titrations, where a solution of known concentration, called a titrant, is added to a solution with an unknown concentration to determine its content.
Titrations play a significant role in various fields, from industrial to academic research, due to their accuracy and ease of execution.
Here are key steps in a typical titration:

• Preparation of solutions: Ensure that the solutions of the titrant and the sample are correctly prepared.
• Execution: Slowly add the titrant to the analyte until the reaction reaches completion at the endpoint, usually indicated by a color change.
• Calculation: Finally, calculate the concentration of the unknown using the volume of titrant used and its concentration.

The accurate measurement of volume in these reactions makes volumetric analysis a reliable technique for determining concentrations of solutions in chemistry labs.

Elemental Composition Analysis

Elemental composition analysis involves determining the percentage or proportion of elements within a compound. This is a crucial step when working with empirical formulas, as it allows chemists to understand the basic makeup of a compound.
The empirical formula represents the simplest whole-number ratio of the elements within a compound. Calculating it involves:

• Converting percentage composition to grams, based on a 100-gram sample for simplicity.
• Converting grams to moles using the atomic masses of the elements.
• Finding the simplest whole-number ratio among the moles of elements.

In the exercise related to a dibasic acid, the elemental composition helps identify that the simplest ratio of Carbon, Hydrogen, and Oxygen is 1:1:2.
This is how you derive the empirical formula \(CHO_2\), enabling chemists to predict and understand the chemical reactions and properties of the compound.
This step forms the foundation for analyzing and synthesizing new chemical compounds in the lab.