Problem 51 - Chemistry The Central Science

Question

What is the molecular formula of each of the following compounds? $$ \begin{array}{l}{\text { (a) empirical formula } \mathrm{CH}_{2}, \text { molar mass }=84.0 \mathrm{g} / \mathrm{mol}} \\ {\text { (b) empirical formula } \mathrm{NH}_{2} \mathrm{Cl} \text { , molar mass }=51.5 \mathrm{g} / \mathrm{mol}}\end{array} $$

Step-by-Step Solution

Answer

The molecular formulas for the given compounds are: (a) C_6H_{12} (b) NH_2Cl

Step 1: Calculate the molar mass of the empirical formula

Using the periodic table, find the molar mass of the elements present in the empirical formula CH_2. C: 12.01 g/mol H: 1.008 g/mol Total molar mass of CH2 = 12.01 + (2 x 1.008) = 14.026 g/mol

Step 2: Determine the ratio between the given molar mass and the empirical formula's molar mass

The given molar mass of compound (a) is 84.0 g/mol. Divide the given molar mass by the empirical formula's molar mass: Ratio = \(\frac{84.0}{14.026}\) ≈ 6

Step 3: Multiply the empirical formula by the ratio determined in step 2 to get the molecular formula

Since the ratio is 6, the molecular formula will be six times the empirical formula: Molecular formula = (CH_2) x 6 = C_6H_{12} The molecular formula of compound (a) is C_6H_{12}. For Compound (b):

Step 1: Calculate the molar mass of the empirical formula

Using the periodic table, find the molar mass of the elements present in the empirical formula NH_2Cl. N: 14.01 g/mol H: 1.008 g/mol Cl: 35.45 g/mol Total molar mass of NH_2Cl = 14.01 + (2 x 1.008) + 35.45 = 51.476 g/mol

Step 2: Determine the ratio between the given molar mass and the empirical formula's molar mass

The given molar mass of compound (b) is 51.5 g/mol. Divide the given molar mass by the empirical formula's molar mass: Ratio = \(\frac{51.5}{51.476}\) ≈ 1

Step 3: Multiply the empirical formula by the ratio determined in step 2 to get the molecular formula

Since the ratio is 1, the molecular formula will be the same as the empirical formula: Molecular formula = NH_2Cl The molecular formula of compound (b) is NH_2Cl.

Key Concepts

Empirical Formula

The empirical formula of a chemical compound is the simplest way to represent the relative number of atoms of each element in the compound. It displays the smallest whole-number ratio between the elements.
For example, in the empirical formula \( \mathrm{CH}_2 \), carbon and hydrogen atoms are present in a 1:2 ratio. It doesn't depict how many atoms are present in a molecule, only the relative number of each atom.
This can often be different from the molecular formula, where we consider the actual number of atoms in a molecule. Calculating the empirical formula involves analyzing the percentage composition of a compound and deducing the simplest ratio of elements.
Here are easy steps to find the empirical formula:

• Convert the percentage of each element to grams.
• Convert grams to moles by dividing by the element's atomic mass.
• Find the mole ratio of the elements by dividing each mole value by the smallest number obtained in the previous step.
• If necessary, multiply these numbers to obtain whole numbers, providing the simplest integer ratio.

Keeping all this in mind, the empirical formula is crucial for understanding and deducing the composition of chemical compounds.

Molar Mass

Molar mass is a fundamental concept in chemistry that links the micro-world of atoms and molecules to the macro-world of grams and kilograms. It is defined as the mass of one mole of a substance, often expressed in grams per mole (g/mol).
To calculate the molar mass of a compound, you sum the atomic masses of all the atoms in its chemical formula.
In the exercise, the molar mass is crucial for deriving the molecular formula from the empirical formula. By using the ratio of the given molar mass to the empirical formula's molar mass, it's possible to determine how many times the empirical unit repeats in the molecular formula.
Here’s how you determine molar mass for an empirical formula:

• Identify each element in the formula and its number of atoms.
• Use the periodic table to find the atomic mass of each element.
• Multiply the atomic mass by the number of atoms of that element in the formula.
• Add all these values together to get the total molar mass of the compound.

The clarity of this calculation is necessary for accurately determining the molecular formula, thus highlighting the importance of understanding molar mass.

Chemical Compounds

Chemical compounds are substances formed by the chemical combination of two or more elements. These compounds have properties distinctly different from the individual elements that comprise them.
A chemical compound is typically represented by a chemical formula, such as \( \mathrm{H}_2\mathrm{O} \) for water. The formula gives information about the elements present and the ratio of these elements in the compound.
Chemical compounds can have various types of bonds and structures, including covalent, ionic, and metallic bonds. Though this is not directly detailed in the exercise, it is essential to understand that empirical and molecular formulas are different aspects of nomenclature used in chemistry to describe the composition of these compounds.
Here's what you need to know:

• The empirical formula represents the simplest ratio of elements.
• The molecular formula conveys the actual number of atoms of each element in a molecule.
• Understanding the distinction is important when analyzing chemical reactions and synthesizing new compounds.

In the context of our exercise, focusing on compounds, empirical formulas, and molar mass helps reveal the molecular formula, enhancing understanding of chemical composition.