Problem 83 - Chemistry and Chemical Reactivity

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?

Step-by-Step Solution

Answer

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

Step 1: Calculate Empirical Formula Mass

The empirical formula of succinic acid is \( \mathrm{C}_2 \mathrm{H}_3 \mathrm{O}_2 \). Calculate the mass of this empirical formula: Carbon (C): 2 atoms \( \times \ 12.01 \ \mathrm{g/mol} = 24.02 \ \mathrm{g/mol} \), Hydrogen (H): 3 atoms \( \times \ 1.008 \ \mathrm{g/mol} = 3.024 \ \mathrm{g/mol} \), Oxygen (O): 2 atoms \( \times \ 16.00 \ \mathrm{g/mol} = 32.00 \ \mathrm{g/mol} \). Therefore, the empirical formula mass is: \( 24.02 + 3.024 + 32.00 = 59.044 \ \mathrm{g/mol} \).

Step 2: Find the Multiple of the Empirical Formula

Divide the molar mass of the compound by the empirical formula mass to find the multiple: \( \frac{118.1 \ \mathrm{g/mol}}{59.044 \ \mathrm{g/mol}} \approx 2 \). This indicates that the molecular formula is twice that of the empirical formula.

Step 3: Determine the Molecular Formula

Multiply each element's subscript in the empirical formula by the multiple found in Step 2. Thus, the molecular formula is \( \mathrm{C}_{2\times2} \mathrm{H}_{3\times2} \mathrm{O}_{2\times2} = \mathrm{C}_4 \mathrm{H}_6 \mathrm{O}_4 \).

Key Concepts

Empirical Formula

The empirical formula represents the simplest whole-number ratio of elements within a compound. It gives the relative number of atoms of each element in the compound, without determining any specific number of atoms like the molecular formula does. For instance, with succinic acid, the empirical formula is \(\mathrm{C}_2 \mathrm{H}_3 \mathrm{O}_2\). This tells us that for every two carbon atoms, there are three hydrogen and two oxygen atoms.
Understanding empirical formulas is crucial because they lay the groundwork for deriving a molecular formula, which is what chemists primarily use to represent compounds in practical applications. The key takeaway is that the empirical formula does not necessarily reflect the actual amounts of atoms in a compound, just their smallest ratio.

Molar Mass

Molar mass is a fundamental concept that refers to the mass of a given substance (chemical element or compound) divided by the amount of substance. The molar mass is expressed in units of grams per mole (g/mol), which essentially provides a bridge between the microscopic world of atoms and the macroscopic world we can measure.
For succinic acid, the molar mass is given as \(118.1 \mathrm{g/mol}\). It is found by summing up the atomic masses of all the atoms in a compound's molecular formula. However, before we can do this for a molecular formula, we need to first calculate it from the empirical formula, using the molar mass as a guide.

Chemical Calculations

Chemical calculations involve using mathematical techniques to determine quantities, compositions, and transformations of chemical substances. The ability to perform these calculations is integral to understanding chemical formulas and reactions. One of the most common calculations is finding the molecular formula from an empirical formula, using known information such as the molar mass.
In this exercise with succinic acid, to find the molecular formula, we start by calculating the empirical formula's mass, which is a key part of unlocking the true makeup of the compound. These calculations help us understand not just what elements are in a compound, but in what exact proportions they exist, leading to a deeper understanding of the compound itself.

Stoichiometry

Stoichiometry is a branch of chemistry that focuses on the quantitative relationships, or ratios, between elements and compounds in chemical reactions. It is based on the balanced chemical equation and enables chemists to predict how much of each substance is consumed or produced in a given reaction.
While stoichiometry often deals with reactions, understanding it from a compositional standpoint, like in determining the molecular formula of succinic acid, is insightful. We use stoichiometry to ascertain the proportions of elements in compounds, and from there, determine how those ratios describe entire molecules. Ensuring you have the stoichiometry correct means accurately predicting these relationships down to their molecular formulas, crucial for practical chemistry applications.