Question

What is the molecular formula of the molecule that has an empirical formula of \({CH}_{2} {O}\) and a molar mass of 120.12 \({g} / {mol}\) ?

Short answer

The molecular formula is \(C_{4}H_{8}O_{4}\).

Step-by-step solution

- Calculate the Molar Mass of the Empirical Formula

First, determine the molar mass of the empirical formula \(CH_2O\). The molar masses of C, H, and O are approximately 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol respectively. So, the molar mass of \(CH_2O\) is calculated as follows: \[12.01 + 2(1.01) + 16.00 = 30.03 \text{ g/mol}\].

- Determine the Number of Empirical Units in the Molecular Formula

Divide the molar mass of the compound (120.12 g/mol) by the molar mass of the empirical formula (30.03 g/mol): \[ \frac{120.12}{30.03} = 4\]. This means there are 4 empirical units in the molecular formula.

- Calculate the Molecular Formula

Multiply the subscripts in the empirical formula by the number of empirical units: \(CH_2O\) becomes \(C_{4}H_{8}O_{4}\). Therefore, the molecular formula is \(C_{4}H_{8}O_{4}\).

Key concepts

Empirical Formula

The empirical formula gives the simplest whole-number ratio of elements in a compound. It helps to identify the basic composition without providing exact quantities. For example, in this exercise, the empirical formula is \({CH}_{2} {O}\). This tells us that for every carbon (C) atom, there are two hydrogen (H) atoms and one oxygen (O) atom in the compound.

To calculate the empirical formula from percentage composition:

• Convert the percentage of each element to grams (if not already in grams). Imagine the total sample is 100 grams, making the percentage values equal to gram values.
• Convert grams to moles by dividing by the atomic masses of the respective elements.
• Determine the simplest ratio by dividing all the mole values by the smallest number of moles calculated.

The foundation of determining molecular formulas lies in the empirical formula. This is why understanding it is crucial.

Molar Mass Calculation

The molar mass of a compound is the mass of one mole of its molecules. It's calculated by summing up the masses of all the atoms in its molecular formula. In our exercise, it's a crucial step.

For the empirical formula \({CH}_{2} {O}\), calculate its molar mass as follows:
\[12.01 \text{g/mol for C} + 2 \times 1.01 \text{g/mol for H} + 16.00 \text{g/mol for O} = 30.03 \text{ g/mol}.\]

This computation is necessary to compare the empirical formula mass with the given molar mass of the compound. These are the steps:

• Identify the atomic mass of each element, usually found on the periodic table.
• Multiply the atomic mass by the number of atoms of that element in the empirical formula.
• Add the results for all elements to find the total molar mass.

With this method, you can find the molar mass, ensuring you correctly interpret the empirical data.

Molecular Formula

The molecular formula shows the exact number of each type of atom in a molecule. It can be determined using the empirical formula and the molar mass of the compound.

In our given exercise, the molecular formula is derived from empirical formula \({CH}_{2} {O}\) and the compound’s molar mass of 120.12 g/mol. Follow these steps:

• Calculate the molar mass of the empirical formula (as shown in the molar mass calculation section).
• Divide the given molar mass by the empirical formula molar mass: \[ \frac{120.12}{30.03} = 4\].
• Multiply the subscripts in the empirical formula by this factor to get the molecular formula: \({CH}_{2} {O}\) becomes \({C}_{4} {H}_{8} {O}_{4}\).

Understanding this concept allows you to link a compound's simple composition to its specific molecular makeup.