Question

A compound with the empirical formula \(\mathrm{CH}_{2}\) was found to have a molar mass of approximately \(84 \mathrm{~g}\). What is the molecular formula of the compound?

Short answer

The molecular formula of the compound can be determined by first calculating the molar mass of the empirical formula CH₂, which is 14 g/mol. Then, divide the given molar mass of the compound (84 g/mol) by the molar mass of the empirical formula to find the number of empirical units, which is 6. Finally, multiply the empirical formula by the number of empirical units to obtain the molecular formula, C₆H₁₂.

Step-by-step solution

Find the molar mass of the empirical formula

First, calculate the molar mass of the empirical formula CH₂. From the periodic table, the atomic mass of Carbon (C) is 12 g/mol and Hydrogen (H) is 1 g/mol. Since there are two Hydrogen atoms, the molar mass of CH₂ is: Molar mass of CH₂ = (1 × 12) + (2 × 1) = 12 + 2 = 14 g/mol

Calculate the number of empirical formula units in the molecular formula

Now, we can find out how many empirical formula units make up the molecular formula by dividing the molar mass of the compound by the molar mass of the empirical formula: Number of empirical units = (Molar mass of the compound) / (Molar mass of empirical formula) Number of empirical units = 84 g/mol / 14 g/mol = 6

Find the molecular formula

Finally, we can find the molecular formula by multiplying the empirical formula by the number of empirical units. Since the empirical formula is CH₂ and we have 6 units, the molecular formula will be: Molecular formula = (CH₂) × 6 = C₆H₁₂ Therefore, the molecular formula of the compound is C₆H₁₂.

Key concepts

Empirical Formula

The empirical formula of a compound represents the simplest whole-number ratio of the elements within that compound. It does not display the actual number of atoms, but rather the simplest ratio in which the atoms are present. For instance, the empirical formula for glucose (C₆H₁₂O₆) is CH₂O, indicating a reduced ratio of 1 carbon atom to 2 hydrogen atoms to 1 oxygen atom, while glucose actually has 6 times that number of atoms.

To determine the empirical formula, one may start by using the percent composition of each element present or, if available, the mass of each element in a sample. These values allow the calculation of the mole ratio of the elements, which is then simplified to the smallest whole numbers to yield the empirical formula. In the case where molecular formulas are given, they can be simplified to obtain the empirical formula if needed.

Molar Mass

Molar mass is defined as the mass of one mole of a substance. It is typically expressed in units of grams per mole (g/mol). This property is fundamental as it bridges the gap between the atomic scale and the real-world scale, enabling chemists to count atoms by weighing. Molar mass can be determined by summing the atomic masses of all the atoms in a compound's molecular (or empirical) formula.

For example, in the given compound with an empirical formula of CH₂, the molar mass is calculated by adding the atomic mass of one carbon atom (12 g/mol) and two hydrogen atoms (1 g/mol each), totaling 14 g/mol. It's crucial to ensure that the molar mass is measured accurately because it forms the foundation for further calculations involving substance amounts, like determining the number of moles in a given mass of compound.

Chemical Composition

Chemical composition refers to the identity and ratio of the elements that make up a compound. This composition can provide insights into the properties, reactivity, and behavior of the substance. Knowing the chemical composition is useful in fields such as pharmacology, materials science, and chemistry, for creating and studying compounds, as well as in various applications like manufacturing and drug design.

The chemical composition is typically represented using a chemical formula which could be either molecular or empirical. The former identifies the actual number of atoms of each element in a molecule, while the latter is a simplified version that represents the smallest whole number ratio of the constituent atoms. In the study of chemical reactions, understanding the composition allows chemists to predict the products and reactants involved, to balance chemical equations, and ensure that the law of conservation of mass is observed.