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) \(\mathrm{C}_{2} \hat{\mathrm{H}}_{4} \mathrm{O}_{2}\) (d) \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{4}\)

Short answer

The simplest molecular formula is option (b): \(\mathrm{CH}_2\mathrm{O}_2\).

Step-by-step solution

Understand the Empirical Formula

The empirical formula of a compound shows the simplest whole-number ratio of atoms of each element present in the compound. Given is the empirical formula \( \text{CH}_2\text{O}_2 \), which means the simplest ratio of carbon, hydrogen, and oxygen in the compound is 1:2:2.

Identify Possible Molecular Formulas

The molecular formula of a compound is a whole-number multiple of the empirical formula. Therefore, possible molecular formulas for \( \text{CH}_2\text{O}_2 \) could be: \( (\text{CH}_2\text{O}_2) \times n \) where \( n \) is a whole number.

Check Each Option

Evaluate each answer option to see if it is a whole-number multiple of the empirical formula:(a) \( \text{CH}_2\text{O} \) - does not match since it lacks enough oxygen atoms.(b) \( \text{CH}_2\text{O}_2 \) - matches exactly, with \( n = 1 \).(c) \( \text{C}_2\text{H}_4\text{O}_2 \) - can be obtained by multiplying the empirical formula by \( n = 2 \).(d) \( \text{C}_3\text{H}_6\text{O}_4 \) - this is a multiple \( n = 3\) of the empirical formula.

Determine the Simplest Molecular Formula

Among the options, the simplest molecular formula is the one where \( n = 1 \) since this reflects the base ratio as-is without further multiplication.Thus, the simplest molecular formula is \( \text{CH}_2\text{O}_2 \), which corresponds to option (b).

Key concepts

Molecular Formula

In chemistry, the molecular formula of a compound reveals the exact number of each type of atom present in a molecule. This number is not always the simplest ratio, but it's a direct representation of the molecule's actual atomic composition. To derive a molecular formula, you often begin with the empirical formula, which provides the simplest whole-number ratio of elements.
However, knowing the empirical formula alone isn't enough to pinpoint the exact molecular formula. You need additional information, like the molar mass, to determine how many times the empirical formula is repeated in the actual molecule. For example, if your empirical formula is \( \text{XY}_2 \) and your molar mass is double that of the empirical formula, the molecular formula will likely be \( \text{X}_2\text{Y}_4 \).
This multiplication factor, known as \( n \), tells you how many times over the empirical formula's unit fits into the actual molecule. If \( n = 1 \), the empirical and molecular formulas are identical, indicating the simplest case possible.

Chemical Compounds

Chemical compounds are substances formed by two or more elements combined in fixed ratios. These compounds can exist as solids, liquids, or gases, and they can have vastly different properties than the individual elements that comprise them. Identifying a compound's formula is key to understanding its properties and potential chemical behavior.

• The empirical formula gives you the basic ratio of elements, which is the simplest way to represent a compound.
• Common compound types include acids, bases, salts, and more. Acids often contain hydrogen as a key component.
• The molecules themselves are held together by chemical bonds, which could be ionic, covalent, or metallic depending on the compound's nature.

Understanding the chemical compounding not only helps in deducing formulas but also in predicting reactions and synthesizing new materials.

Step-by-Step Solution

Solving chemistry problems, like finding the possible molecular formula from an empirical formula, requires a structured approach. Here's a simple step-by-step guide to tackle such problems:

• Understand the Given Information: Start by clearly understanding what the empirical formula represents. For example, \( \text{CH}_2\text{O}_2 \) tells us there's 1 carbon (C), 2 hydrogen (H), and 2 oxygen (O) atoms per formula unit.
• Consider the Multiplication Factor: The molecular formula is a multiple of the empirical formula. Calculate other potential formulas by considering different integer factors \( n \).
• Analyze the Options: Compare these potential formulas with the given options. Only formatted options that are exact multiples of the empirical formula and match the given molar properties should be considered.
• Select the Simple Solution: Among possible molecular formulas, the one where \( n = 1 \) is often the simplest and exact match unless additional data suggests otherwise.

This methodical approach helps avoid mistakes and leads to the correct answer efficiently.