Problem 59 - A Complete Resource Book in Chemistry for JEE Main

Question

\(60 \mathrm{~g}\) of a compound on analysis produced \(24 \mathrm{~g}\) carbon, \(4 \mathrm{~g}\) hydrogen and \(32 \mathrm{~g}\) oxygen. The empirical formula of the compound is (a) \(\mathrm{CH}_{4} \mathrm{O}\) (b) \(\mathrm{CH}_{2} \mathrm{O}_{2}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}\) (d) \(\mathrm{CH}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

The empirical formula is \(\mathrm{CH}_2\mathrm{O}\).

Step 1: Identify Atomic Masses

First, identify the atomic masses of carbon, hydrogen, and oxygen. The atomic mass of carbon (C) is approximately \(12\), of hydrogen (H) is approximately \(1\), and of oxygen (O) is approximately \(16\).

Step 2: Calculate Moles of Each Element

Calculate the moles of each element using the mass given and the atomic masses.For carbon: \(\frac{24 \text{ g}}{12 \text{ g/mol}} = 2 \text{ moles}\).For hydrogen: \(\frac{4 \text{ g}}{1 \text{ g/mol}} = 4 \text{ moles}\).For oxygen: \(\frac{32 \text{ g}}{16 \text{ g/mol}} = 2 \text{ moles}\).

Step 3: Determine the Simplest Whole Number Ratio

Find the simplest whole number ratio of moles of each element.The ratios are: - Carbon: \(2\)- Hydrogen: \(4\)- Oxygen: \(2\)Divide all by the smallest number of moles, which is \(2\).- Carbon: \(\frac{2}{2} = 1\)- Hydrogen: \(\frac{4}{2} = 2\)- Oxygen: \(\frac{2}{2} = 1\)

Step 4: Write the Empirical Formula

Using the smallest whole number ratio, write the empirical formula. From the ratio \(1:2:1\), the empirical formula of the compound is \(\mathrm{CH}_2\mathrm{O}\).

Key Concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry centered around the quantitative relationships between reactants and products in a chemical reaction. When determining an empirical formula, stoichiometry helps us calculate how elements combine in fixed proportions by mole.
To perform stoichiometric calculations, we need to:

• Identify extbf{atomic masses}. This is crucial to know how many grams of an element are present per mole. For example, carbon has an atomic weight of approximately 12 g/mol.
• Calculate the extbf{moles} of each element in a compound. This is done using the formula: number of moles = mass (g)/atomic mass (g/mol).
• Compare the extbf{relative mole numbers} to determine the ratio in which the elements combine.

By using stoichiometry, we can simplify the process of determining the simplest whole number ratio of atoms in a compound, as seen in the original problem where carbon, hydrogen, and oxygen were used to find the empirical formula.

Molecular Analysis

Molecular Analysis involves breaking down compounds to understand their composition and the molecular structure.
This process uses various techniques to identify the elemental components and quantify their amounts.
When it comes to finding an empirical or molecular formula, molecular analysis provides the initial data needed for calculation. In our problem:

• We were given the breakdown:
  • 24g of carbon
  • 4g of hydrogen
  • 32g of oxygen
  This is the essential data that molecular analysis provides.
• An understanding of mass percentages helps determine the contribution of each element in forming the entire compound.

Thus, through molecular analysis, we gain insight into how much of each atom type contributes to the compound, essential for subsequent stoichiometric calculations.

Chemical Formula Determination

Chemical formula determination is a method to find out the composition and ratio of elements within a compound.
It can be subdivided into empirical and molecular formula determination.

• The extbf{empirical formula} gives the simplest whole number ratio of atoms in a compound. It does not necessarily reflect the actual number of atoms in the compound, but it provides a reduced formula where ratios are simplified.
  • In this scenario, the empirical formula calculated was \( \text{CH}_2\text{O} \), representing the simplest atom ratio.
• A extbf{molecular formula}, in contrast, may be a multiple of the empirical formula and gives the actual number of atoms in a molecule.
  • It is determined when the molar mass of the full compound is known, providing more detailed information about the arrangement of atoms in the compound.

Overall, understanding chemical formulas helps in predicting how substances will react and interact in chemical processes.