Problem 17 - A Complete Resource Book in Chemistry for JEE Main

Question

The empirical formula of an acid is \(\mathrm{CH}_{2} \mathrm{O}_{2}\), the probable molecular formula of the simplest acid may be (a) \(\mathrm{CH}_{2} \mathrm{O}\) (b) \(\mathrm{CH}_{2} \mathrm{O}_{2}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\) (d) \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{4}\)

Step-by-Step Solution

Answer

The probable molecular formula may be \(\mathrm{CH}_{2} \mathrm{O}_{2}\) or \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\).

Step 1: Understanding the Empirical Formula

The empirical formula of a compound represents the simplest whole number ratio of the atoms in the compound. In this problem, we are given that the empirical formula is \(\mathrm{CH}_{2}\mathrm{O}_{2}\), indicating that for every 1 carbon atom, there are 2 hydrogen atoms and 2 oxygen atoms.

Step 2: Identifying the Given Options

We need to identify which of the given molecular formulas could also represent the simplest acid with the empirical formula \(\mathrm{CH}_{2}\mathrm{O}_{2}\). The options provided are: (a) \(\mathrm{CH}_{2} \mathrm{O}\) (b) \(\mathrm{CH}_{2} \mathrm{O}_{2}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\) (d) \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{4}\)

Step 3: Comparing Molecular Formulas with the Empirical Formula

We compare each option's molecular formula to see if it fits the ratio given by the empirical formula. - Option (a), \(\mathrm{CH}_{2} \mathrm{O}\): Does not match because it lacks the correct number of oxygen atoms. - Option (b), \(\mathrm{CH}_{2} \mathrm{O}_{2}\): Matches exactly the empirical formula. - Option (c), \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\): Matches, as the ratio of atoms can be reduced to \(\mathrm{CH}_{2} \mathrm{O}_{2}\). - Option (d), \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{4}\): Does not match, as it cannot be reduced to the same ratio as \(\mathrm{CH}_{2} \mathrm{O}_{2}\).

Step 4: Selecting the Correct Answer

Based on the matching of molecular formulas to the empirical formula \(\mathrm{CH}_{2} \mathrm{O}_{2}\), the correct answers are option (b) and (c), where both formulas match or simplify to the empirical formula. Therefore, the probable molecular formula of the simplest acid may be \(\mathrm{CH}_{2} \mathrm{O}_{2}\) or \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\).

Key Concepts

Molecular Formula

A molecular formula tells us the actual number of each type of atom in a molecule. It gives the specific arrangement of elements that combines to form a substance. A molecular formula can sometimes be the same as the empirical formula, but it often is a multiple of the empirical formula.
If we look at the exercise above, the molecular formula could potentially be

• the same as the empirical formula, such as \(\text{CH}_2\text{O}_2\)
• a simple multiple of the empirical formula, such as \(\text{C}_2\text{H}_4\text{O}_2\)

The real identifying feature of a molecular formula is that it tells us precisely how many atoms of each element are present. Thus, if given the molar mass of a compound, identifying the molecular formula becomes straightforward. We can calculate the molar mass from the empirical formula and check which option matches that molar mass.

Chemical Compounds

Chemical compounds are made when two or more elements combine in such a ratio that they create a new substance with distinct properties. Such compounds can be represented using their chemical formulas, which could either be molecular or empirical.
The empirical formula is the simplest form, showing the smallest whole-number ratio of the atoms involved. On the contrary, a molecular formula gives you an accurate depiction of how many atoms of each element are bound together.

• For example, water (\(\text{H}_2\text{O}\)) is a chemical compound composed of two hydrogen atoms and one oxygen atom.
• The empirical formula for glucose (\(\text{C}_6\text{H}_{12}\text{O}_6\)) would be \(\text{CH}_2\text{O}\).

Understanding the distinction between different types of formulas is key to mastering the concept of chemical compounds.

Stoichiometry

Stoichiometry is the method used to figure out the relationships between reactants and products in chemical reactions. It's like a mathematical recipe that ensures everything in a reaction is balanced.
Starting with an empirical formula, stoichiometry can help you find the molecular formula. You simply need to understand the proportions of each element within a compound and how these react during chemical transformations.

• If the molar mass of a compound is known, you can determine how the empirical formula relates to the molecular formula.
• This can involve calculating moles of elements and comparing ratios, often using the empirical formula as a stepping stone to find the exact molecular composition.

Stoichiometry ensures that the system remains balanced, with no atoms lost or gained in transformation, and is crucial for solving problems in a chemical context.