Problem 87 - 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 \(\mathrm{O}\) percentage in the \(3: 4\). The compound is (a) \((\mathrm{COOH})_{2}\) (b) \(\mathrm{CH}_{3} \mathrm{OH}\) (c) \(\mathrm{HCHO}\) (d) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\)

Step-by-Step Solution

Answer

None of the given options satisfy both the required ratios.

Step 1: Understanding Ratios

The problem states two ratios: the ratio of carbon (C) to hydrogen (H) is 6:1, and the ratio of carbon (C) to oxygen (O) is 3:4. This means that any compound fitting these criteria must have a fixed proportionality between these elements.

Step 2: Defining Carbon Multiplier

Let's assume the number of carbon atoms in the compound is "x." Then, according to the first ratio (C:H = 6:1), the number of hydrogen atoms will be "x/6" if we are considering equal mass rather than individual atom count.

Step 3: Considering Carbon to Oxygen Ratio

From the C:O ratio of 3:4, the number of oxygen atoms will be "4x/3." We need to check all molecules by assuming each given option must satisfy both these ratios consistently.

Step 4: Verifying Each Option: Option (a)

For (a) \((\mathrm{COOH})_{2}\): This is \(\mathrm{C}_2\mathrm{O}_4\mathrm{H}_2\).- C: 2, H: 2, O: 4- C:H = 2:2 = 1:1- C:O = 2:4 = 1:2- This does not satisfy C:H = 6:1 or C:O = 3:4.

Step 5: Verifying Each Option: Option (b)

For (b) \(\mathrm{CH}_3\mathrm{OH}\): This is \(\mathrm{C}_1\mathrm{H}_4\mathrm{O}_1\).- C: 1, H: 4, O: 1- C:H = 1:4- C:O = 1:1- This does not satisfy C:H = 6:1 or C:O = 3:4.

Step 6: Verifying Each Option: Option (c)

For (c) \(\mathrm{HCHO}\): This is \(\mathrm{C}_1\mathrm{H}_2\mathrm{O}_1\).- C: 1, H: 2, O: 1- C:H = 1:2- C:O = 1:1- This does not satisfy C:H = 6:1 or C:O = 3:4.

Step 7: Verifying Each Option: Option (d)

For (d) \(\mathrm{CH}_3\mathrm{CH}_2\mathrm{OH}\): This is \(\mathrm{C}_2\mathrm{H}_6\mathrm{O}_1\).- C: 2, H: 6, O: 1- C:H = 2:6 = 1:3- C:O = 2:1- This also does not satisfy C:H = 6:1 or C:O = 3:4.

Step 8: Identifying Correct Answer

None of the provided options satisfy both the C:H = 6:1 ratio and C:O = 3:4 ratio simultaneously. Check if there's a possible oversight in interpretation or selection of options.

Key Concepts

Chemical Ratios

Chemical ratios are essential in understanding the composition of compounds. They provide a proportionate relationship between different elements in a molecule. In the problem given, we have two key ratios to work with: the ratio of carbon to hydrogen (C:H) as 6:1, and the ratio of carbon to oxygen (C:O) as 3:4. These ratios indicate how many parts of one element are related proportionally to another. For example, a C:H ratio of 6:1 suggests that for every 6 parts of carbon, there's 1 part of hydrogen. Ratios are a vital tool in determining empirical formulas as well as predicting the possible molecular structures of compounds.

Organic Compound Identification

Identifying organic compounds involves figuring out which molecules satisfy certain elemental ratios. Organic compounds primarily consist of carbon combined with hydrogen, oxygen, nitrogen, or other elements. In this exercise, the task is to find a compound that corresponds exactly to certain C:H and C:O ratios. This requires examining known organic compounds and determining if their elemental composition matches a given ratio. Normally, this involves checking all given options using their chemical formulas and breaking them down into individual atoms to see if they meet the desired ratios for carbon, hydrogen, and oxygen.

Empirical Formula

The empirical formula gives the simplest whole-number ratio of elements within a compound. Unlike the molecular formula, it doesn't necessarily show the actual number of atoms, but rather their reduced proportional relationship. In cases where chemical ratios are provided, as with C:H and C:O in this problem, the empirical formula helps us determine how elements are fundamentally related in any particular compound. After determining that none of the options provided matched the stated ratios, it's clear that an empirical formula approach might provide insights towards the correct compound or reveal inconsistencies in problem assumptions or available choices.

Molecular Formula

A molecular formula reveals the actual number of each type of atom in a molecule. This information goes beyond what the empirical formula can provide, showing precisely how a compound is structured. While an empirical formula reduces the elements to their simplest ratio, the molecular formula presents the full count. In the applied task, each option's molecular formula was broken down and verified against the given elemental ratios, confirming their actual fit. Understanding how molecular formulas relate to chemical ratios is crucial in selecting the correct molecular structure of organic compounds as we attempted to do with this exercise.

Stoichiometry

Stoichiometry is the study of quantitative relationships in chemical reactions. It involves calculations that derive from ratios and proportions of elements in compounds. In the context of the exercise, stoichiometry aids in confirming or refuting the presence of specific compounds by ensuring that their computed ratios correspond to the actual given ratios. It's like a balancing act that requires the proper amount of atoms to align with known chemical laws. By using stoichiometry, chemists and students can determine the exact amount of reactants needed to form a compound and verify their understanding of molecular structures based on given chemical equations.