Problem 48 - Chemistry

Question

The empirical formula of a compound is CH. If the molar mass of this compound is about \(78 \mathrm{~g},\) what is its molecular formula?

Step-by-Step Solution

Answer

The compound's molecular formula is \(C_6H_6\).

Step 1: Determine the molar mass of the empirical formula

You calculate the molar mass of the empirical formula \(CH\). Carbon (C) has an atomic mass of approximately \(12 \mathrm{~g/mol}\) and Hydrogen (H) has an atomic mass of approximately \(1 \mathrm{~g/mol}\). Add these together to find the molar mass of the empirical formula, which equates to \(13 \mathrm{~g/mol}\).

Step 2: Determine the ratio of the actual molar mass to the empirical formula mass

You divide the given molar mass of the compound \(78 \mathrm{~g/mol}\) by the molar mass of the empirical formula \(13 \mathrm{~g/mol}\). The result is 6. Therefore, the molecular formula contains 6 times the atoms as the empirical formula.

Step 3: Write out the Molecular Formula

Since we found out that the molecular formula contains six times the atoms as the empirical formula, we can write out the molecular formula of the compound as \(C_6H_6\).

Key Concepts

Empirical Formula

An empirical formula represents the simplest whole-number ratio of the atoms in a compound. It shows which elements are present and in what ratio. For instance, in the compound with an empirical formula of CH, the ratio of carbon to hydrogen is 1:1.

• Provides basic information about the composition of the compound.
• Helps chemists to understand the basic structure of unknown compounds.

However, the empirical formula does not tell us how many atoms are actually present in the molecule. It must sometimes be used as a stepping stone to discover the molecular formula. Understanding the empirical formula is crucial to unraveling the full dimensions of a compound's composition.

Molar Mass Calculation

Calculating molar mass is essential in converting between moles and grams, allowing us to measure the substance's quantity. To find the molar mass of a compound given its empirical formula, you add together the atomic masses of each element according to the formula. Using our example, the empirical formula CH consists of:

• Carbon (C) with an atomic mass of approximately 12 g/mol
• Hydrogen (H) with an atomic mass of approximately 1 g/mol

Adding these together results in a molar mass of 13 g/mol for the empirical formula.
It's important to double-check the atomic masses from a reliable periodic table. Molar mass calculation is a pivotal step in determining the molecular formula, especially when given an actual molar mass of the compound, as it helps establish the "multiplying factor" needed to derive the molecular formula.

Atomic Mass

Atomic mass is the mass of an atom, typically expressed in atomic mass units (amu). It is approximately equivalent to the number of protons and neutrons in the atom. For chemical calculations, it's expressed in grams per mole (g/mol), which aids in conversions in chemical equations and formulas. For example, the atomic mass of:

• Carbon (C) is about 12 g/mol.
• Hydrogen (H) is about 1 g/mol.

This knowledge allows chemists to calculate the molar mass of compounds and understand their composition on a much deeper level. Having a handle on atomic mass is vital to apply this understanding practically in balancing equations and stoichiometric calculations.

Chemical Composition

Chemical composition refers to the identity and proportion of the elements within a compound. It's a detailed fingerprint of a compound that highlights how each element contributes to the overall structure and function. To find a compound's full chemical composition:

• Start with its empirical formula.
• Use the empirical formula to compute the molar mass.
• Determine the molecular formula using the provided molar mass.

In our example exercise, starting with the empirical formula (CH), and given the molar mass of roughly 78 g/mol, we can decode the compound's specific make-up as benzene, with the molecular formula C₆H₆. Understanding chemical composition is not just about memorizing formulas. It's about unlocking insights into how compounds interact, behave, and react under different conditions. This knowledge is indispensable for innovating and solving complex chemical problems.