Question

What is the molecular formula of each of the following compounds? (a) empirical formula \(\mathrm{CH}_{2}\), molar mass \(=84 \mathrm{~g} / \mathrm{mol}\) (b) empirical formula \(\mathrm{NH}_{2} \mathrm{Cl}\), molar mass \(=51.5 \mathrm{~g} / \mathrm{mol}\)

Short answer

The molecular formula of the compounds are: (a) \(\mathrm{C}_6\mathrm{H}_{12}\) and (b) \(\mathrm{NH}_2\mathrm{Cl}\).

Step-by-step solution

Determine the molar mass of the empirical formula

First, find the molar mass of the empirical formula, CH₂. The molar mass of carbon (C) is 12 g/mol, and the molar mass of hydrogen (H) is 1 g/mol. So, the total molar mass of CH₂ is: \[12 + 2(1) = 14 \mathrm{~g/mol}\]

Determine the whole-number multiple

Next, divide the given molar mass of the compound by the molar mass of the empirical formula: \[\frac{84 \mathrm{~g/mol}}{14 \mathrm{~g/mol}} = 6\] So, the molecular formula is 6 times larger than the empirical formula.

Calculate the molecular formula

Multiply each element in the empirical formula, CH₂, by the whole-number multiple, 6: \[6(CH_2) \Rightarrow C_6H_{12}\] So, the molecular formula of this compound is \(\mathrm{C}_6\mathrm{H}_{12}\). #Part (b):#

Determine the molar mass of the empirical formula

First, find the molar mass of the empirical formula, NH₂Cl. The molar mass of nitrogen (N) is 14 g/mol, the molar mass of hydrogen (H) is 1 g/mol, and the molar mass of chlorine (Cl) is 35.5 g/mol. So, the total molar mass of NH₂Cl is: \[14 + 2(1) + 35.5 = 51.5 \mathrm{~g/mol}\]

Determine the whole-number multiple

Next, divide the given molar mass of the compound by the molar mass of the empirical formula: \[\frac{51.5 \mathrm{~g/mol}}{51.5 \mathrm{~g/mol}} = 1\] So, the molecular formula is 1 time larger than the empirical formula (meaning they are the same).

Calculate the molecular formula

Multiply each element in the empirical formula, NH₂Cl, by the whole-number multiple, 1: \[1(NH_2Cl) \Rightarrow NH_2Cl\] So, the molecular formula of this compound is \(\mathrm{NH}_2\mathrm{Cl}\).

Key concepts

Empirical Formula

The empirical formula represents the simplest whole-number ratio of atoms in a compound. It doesn't provide information about the actual number of atoms, just the ratio between them. For instance, in the empirical formula \(CH_2\), there are always twice as many hydrogen atoms as carbon atoms. This doesn't mean there are only two hydrogen atoms; instead, it reflects the relative proportions.

To derive an empirical formula, you start by determining the number of moles of each element in a sample. Then, you divide each element's mole value by the smallest mole value among them. Often, this results in whole numbers, but if it doesn’t, you can multiply each number by the same factor to get whole numbers.

The empirical formula is crucial as it serves as a stepping stone toward finding the molecular formula, providing insight into the simplest composition of a molecule.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, expressed in grams per mole \((\mathrm{g/mol})\). It's calculated as the sum of the atomic masses of all atoms in a molecule. For example, for the compound \(CH_2\), the molar mass is calculated by adding the atomic masses of one carbon atom \((12 \mathrm{~g/mol})\) and two hydrogen atoms \((2 \times 1 \mathrm{~g/mol} = 2 \mathrm{~g/mol})\), resulting in a molar mass of \(14 \mathrm{~g/mol}\).

Calculating the molar mass is vital for several purposes:

• Quantifying the amount of a substance.
• Converting between grams and moles when working with chemical equations.
• Determining the molecular formula of a compound when combined with its empirical formula.

Knowing the molar mass allows chemists to scale up empirical formulas to the actual molecular formula using the compound's known molar mass.

Chemical Compounds

Chemical compounds are substances composed of two or more different types of atoms bonded together. These bonds can be ionic, covalent, or metallic, and they define the structure and properties of the compound.

To describe a chemical compound's composition, scientists use formulas. There are two main types: *empirical formulas* and *molecular formulas*. The empirical formula shows the simplest ratio of elements, while the molecular formula reveals the actual number of each type of atom in a molecule. For example, the molecular formula \(C_6H_{12}\) indicates that the molecule contains six carbon and twelve hydrogen atoms, which could be simplified to the empirical formula \(CH_2\).

Understanding these formulas is essential for studying chemical reactions and properties, predicting compound behavior, and designing new materials.