Problem 82 - A Complete Resource Book in Chemistry for JEE Main

Question

An organic compound has \(\mathrm{C}\) and \(\mathrm{H}\) percentage in the ratio \(6: 1\) and \(\mathrm{C} \%\) and \(\mathrm{O} \%\) in the ratio \(3: 4\). The compound is (a) \(\mathrm{HCHO}\) (b) \(\mathrm{CH}_{3} \mathrm{OH}\) (c) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) (d) \((\mathrm{COOH})_{2}\)

Step-by-Step Solution

Answer

The compound is (a) HCHO.

Step 1: Identify Element Ratios

First, let's identify the elemental ratios given for carbon (C), hydrogen (H), and oxygen (O). According to the problem, the ratio of the percentage of C to H is 6:1, meaning that for every 6 parts of C, there is 1 part of H. Similarly, the ratio of C to O is 3:4, meaning for every 3 parts of C, there are 4 parts of O.

Step 2: Determine Element Percentages

Let's assign a variable to define the total parts of each element: let the whole compound be 6 parts of C + 1 part of H = 7 parts, and since C to O ratio is 3:4, multiply these by a common factor (e.g., the C in both ratios) that satisfies both conditions.

Step 3: Calculate Common Factor

Since the C part repeats as 6 and 3 in ratios, find a common multiple. Use 6 (from the C:H ratio) that matches the C:O condition. This fact helps to know that for 12C, we have 16O (as 4/3 of carbon) and 2H (from the 6 parts of C: 1 part of H).

Step 4: Assess Compound Options

We'll compare the ratios and percentages with the molecular formulae given for the options: - **(a) HCHO:** This compound consists of 12 parts C, 2 parts H, and 16 parts O which match our derived ratios where C is a multiple of 6 and O and H fit the proportions. - **(b) CH3OH:** C is 12, H is 4, O is 16; does not fit the Hydrogen part (as it is more). - **(c) CH3CH2OH:** Has 12 parts C, 6 parts H, 16 O; significantly more H than required. - **(d) (COOH)2:** Two of (12C+2H+32O); doesn't fit as H exceeds our fixed 1:6.

Step 5: Select the Correct Compound

From the steps and calculations above, only (a) HCHO matches the proportions needed: 12 parts of C, 2 parts of H, corresponding to a 6:1 ratio and 16 parts of O as 4/3 ratio with respect to C, satisfying the condition for a 3:4 ratio.

Key Concepts

Elemental Ratios

Elemental ratios are critical in determining the composition of compounds. Here, they refer to the relationship between the amounts of different elements in a compound. When the problem states that the ratio of carbon (C) to hydrogen (H) is 6:1, it means for every 6 parts of C, there is 1 part of H. The ratio of C to oxygen (O) being 3:4 means that for every 3 parts of C, there are 4 parts of O. These ratios are helpful as they help establish a baseline for the elemental composition of the compound. Knowing these ratios assists in the further calculations needed to determine the molecular formula. Understanding elemental ratios is fundamental, as it provides a starting point for breaking down the problem into manageable components.

Organic Compounds

Organic compounds are primarily made of carbon atoms in combination with hydrogen, oxygen, and sometimes other elements. The term 'organic' originates because these compounds are associated with living organisms. In this exercise, we explore a few possible organic compounds, such as formaldehyde (a formula of HCHO), methanol (CH3OH), ethanol (CH3CH2OH), and oxalic acid ((COOH)2). These compounds represent different configurations of carbon, hydrogen, and oxygen atoms. Each compound has distinct properties based on the arrangement and number of atoms within its molecular structure. Being familiar with organic compounds aids in recognizing the distinct combinations of elements leading to specific molecular formulas.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It allows chemists to predict the quantities of substances consumed and produced in reactions. In the context of the given problem, stoichiometry helps ensure the ratios of C, H, and O remain consistent throughout calculations. By applying stoichiometry, it's possible to determine that the compound containing 12 parts of carbon, 2 parts of hydrogen, and 16 parts of oxygen has the correct elemental ratios. This precise calculation facilitates selecting the right compound that fits the defined ratios. Thus, stoichiometry is a powerful tool in the analysis and prediction of compound formulas.

Molecular Formula Calculation

Calculating the molecular formula involves using given ratios and percentages of elements to identify the compound's specific formula. In the solution, we determined a common factor for carbon, leading to 12 parts of C, 2 parts of H, and 16 parts of O. By expressing these parts as proportions, you can find a suitable molecular formula for the compound. The process involves finding the compound where these calculated proportions match the molecular structure. Therefore, HCHO, or formaldehyde, fits the criteria as it adheres to the determined ratios of the elements, validating the solution through molecular formula calculation. Understanding this concept ensures accurate identification of chemicals based on quantitative data.