Question

What is the molecular formula of each of the following compounds? $$ \begin{array}{l}{\text { (a) empirical formula } \mathrm{HCO}_{2} \text { , molar mass }=90.0 \mathrm{g} / \mathrm{mol}} \\ {\text { (b) empirical formula } \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}, \text { molar mass }=88.0 \mathrm{g} / \mathrm{mol}}\end{array} $$

Short answer

The molecular formulas for the given compounds are: (a) H2C2O4 (b) C4H8O2

Step-by-step solution

Calculate the molar mass of the empirical formula

First, we need to figure out the molar mass of the given empirical formulas. This can be done by adding the molar masses of the constituent elements. For (a): empirical formula = HCO2. Therefore, molar mass = (1*1.01)+(1*12.01)+(2*16.00) \(=\) 1.01 + 12.01 + 32.00 \(=\) 45.02 g/mol. For (b): empirical formula = C2H4O. Therefore, molar mass = (2*12.01)+(4*1.01)+(1*16.00) \(=\) 24.02 + 4.04 + 16.00 \(=\) 44.06 g/mol.

Determine the value of n

With the molar mass of empirical formulas, we can now calculate the value of n by dividing the molar mass of the molecular compound by the molar mass of the empirical formula. For (a): \(n = \frac{90.0 \mathrm{g/mol}}{45.02 \mathrm{g/mol}} = 2\) For (b): \(n = \frac{88.0 \mathrm{g/mol}}{44.06 \mathrm{g/mol}} = 2\)

Calculate the molecular formula

Now that we have the value of n, we can calculate the molecular formulas by multiplying the empirical formulas by n. For (a): molecular formula = (empirical formula) * n = (HCO2) * 2 = H2C2O4 For (b): molecular formula = (empirical formula) * n = (C2H4O) * 2 = C4H8O2

Provide the molecular formulas

The molecular formulas for the given compounds are as follows: (a) H2C2O4 (b) C4H8O2

Key concepts

Empirical Formula

Imagine the empirical formula as the simplified blueprint of a compound's composition. It represents the lowest whole number ratio of the elements within a molecule. For instance, the empirical formula for glucose is CH₂O, which reflects that for every carbon atom, there are two hydrogen atoms and one oxygen atom. This does not necessarily reflect the total number of atoms in the molecule, but rather the simple ratio that defines the proportion of elements.

To determine an empirical formula, one usually starts with the percent composition of each element, which can often be found from laboratory analyses. From there, the percent values are converted into moles, and the mole ratio of the elements is reduced to the simplest whole-number terms. This fundamental step is crucial as it lays the groundwork for determining the actual molecular formula of the compound.

Molar Mass Calculation

Calculating molar mass is like getting the total weight of all atoms within a compound. It requires adding the mass of each individual atom, as indicated in the periodic table, multiplied by the number of times that atom appears in the formula. This sum gives you the mass of one mole of the compound, which is measured in grams per mole (g/mol).

For educational clarity, let's say we have an empirical formula of C₃H₆O₃. The molar masses for carbon, hydrogen, and oxygen are approximately 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol, respectively. Therefore, the molar mass of C₃H₆O₃ would be calculated as follows:

• (3 * 12.01 g/mol) for Carbon
• (6 * 1.01 g/mol) for Hydrogen
• (3 * 16.00 g/mol) for Oxygen
• Summing these gives the molar mass of the compound.

The precision of this step is critical, as it affects subsequent calculations in finding the molecular formula.

Molecular Compound

A molecular compound is comprised of molecules formed by atoms of two or more different elements. The molecular formula provides a full account of the specific number of each type of atom in a molecule, representing the actual structure rather than just a ratio like the empirical formula. For example, the molecular formula for acetic acid is C₂H₄O₂, indicating two carbon atoms, four hydrogen atoms, and two oxygen atoms per molecule.

To deduce the molecular formula when given the empirical formula and molar mass, we use a factor (\(n\)) which is determined by dividing the molar mass of the molecular compound by the molar mass of the empirical formula. Multiplying the empirical formula by this factor gives us the true molecular formula, revealing the actual number of atoms present in a single molecule of the compound. This distinction is not just a nuance; it affects the physical and chemical properties and the behavior of the substance in various reactions.