Question

Succinic acid occurs in fungi and lichens. Its empirical formula is \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) and its molar mass is \(118.1 \mathrm{g} / \mathrm{mol}\). What is its molecular formula?

Short answer

The molecular formula is \(\mathrm{C}_4\mathrm{H}_6\mathrm{O}_4\).

Step-by-step solution

Determine the empirical formula mass

Calculate the molar mass of the empirical formula \(\mathrm{C}_2\mathrm{H}_3\mathrm{O}_2\). This requires multiplying the number of each type of atom by its atomic mass and summing the values:- Carbon (C): \(2 \times 12.01 \ \mathrm{g/mol} = 24.02 \ \mathrm{g/mol}\)- Hydrogen (H): \(3 \times 1.01 \ \mathrm{g/mol} = 3.03 \ \mathrm{g/mol}\)- Oxygen (O): \(2 \times 16.00 \ \mathrm{g/mol} = 32.00 \ \mathrm{g/mol}\)Sum: \(24.02 + 3.03 + 32.00 = 59.05 \ \mathrm{g/mol}\). Thus, the empirical formula mass is \(59.05 \ \mathrm{g/mol}\).

Calculate the ratio of molecular to empirical formula mass

Divide the given molar mass of the compound by the empirical formula mass to find the ratio:\[\text{Ratio} = \frac{118.1 \ \mathrm{g/mol}}{59.05 \ \mathrm{g/mol}} \approx 2\]This means that the molecular formula is twice the empirical formula.

Determine the molecular formula

Multiply the subscripts in the empirical formula \(\mathrm{C}_2\mathrm{H}_3\mathrm{O}_2\) by 2 to obtain the molecular formula:\[\mathrm{C}_{2 \times 2}\mathrm{H}_{3 \times 2}\mathrm{O}_{2 \times 2} = \mathrm{C}_4\mathrm{H}_6\mathrm{O}_4\]Thus, the molecular formula is \(\mathrm{C}_4\mathrm{H}_6\mathrm{O}_4\).

Key concepts

Understanding Empirical Formulas

An empirical formula is a chemical formula that shows the simplest whole-number ratio of atoms in a compound. It does not provide information on the actual number of atoms, but rather the relative proportions of different elements in a molecule. For example, let's consider the empirical formula for succinic acid, which is \( \mathrm{C}_2 \mathrm{H}_3 \mathrm{O}_2 \). This indicates that in the simplest form, the ratio of carbon to hydrogen to oxygen in succinic acid is 2:3:2.

To determine an empirical formula, chemists use experimental data to identify the relative number of atoms in a compound. This involves measuring the mass of each element in a sample and using atomic masses to calculate the simplest ratio. It's essential in chemistry because it allows for the identification of unknown compounds and helps infer properties about newly discovered substances.

So, while the empirical formula gives useful information about the composition of a compound, it doesn’t tell us how the atoms are arranged or the actual number of atoms. This is why knowing both the empirical and molecular formulas can be critical in chemistry.

Calculating Molar Mass

Molar mass is an essential concept in chemistry, representing the mass of one mole of a substance. It's expressed in grams per mole (\( \text{g/mol} \)). To calculate the molar mass of a compound from its empirical formula, you need to sum the mass of each element in the compound.

In the example of succinic acid with the empirical formula \( \mathrm{C}_2 \mathrm{H}_3 \mathrm{O}_2 \), the molar mass is calculated by adding:

• 2 carbon atoms: \(2 \times 12.01 \ \text{g/mol} = 24.02 \ \text{g/mol}\)
• 3 hydrogen atoms: \(3 \times 1.01 \ \text{g/mol} = 3.03 \ \text{g/mol}\)
• 2 oxygen atoms: \(2 \times 16.00 \ \text{g/mol} = 32.00 \ \text{g/mol}\)

Adding these values gives \( 59.05 \ \text{g/mol} \) as the empirical formula mass.

Accurate calculation of molar mass is critical when using the empirical formula to find the molecular formula, as it allows chemists to scale the empirical formula to reflect the actual molecule's size. Essentially, having a precise molar mass helps in determining how many "empirical unit" groups are in the actual molecular structure.

Exploring Chemical Compounds

Chemical compounds consist of two or more different elements that are chemically bonded together. These compounds are categorized by the way atoms are combined in proportions that are definite and do not change. Understanding chemical compounds involves knowing their formations, behaviors, and the types of bonds that hold them together.

For instance, with succinic acid, the empirical formula \( \mathrm{C}_2 \mathrm{H}_3 \mathrm{O}_2 \) tells us about its simplest form of atom ratios. However, when looking into its molecular formula \( \mathrm{C}_4 \mathrm{H}_6 \mathrm{O}_4 \), it gives clarity on the actual number of atoms within a molecule of succinic acid, illustrating how chemical compounds aren't merely a single set but multiples of the empirical unit.

Understanding topics such as covalent and ionic bonds also play a vital role in chemical compounds. In covalent compounds such as succinic acid, atoms share electrons resulting in a stable electronic configuration. On the other hand, ionic compounds involve the transfer of electrons from one atom to another, creating ions.

By exploring chemical compounds, one appreciates the diversity of elements and how they combine to form the myriad of substances we see around us every day, each with unique properties and uses.