Question

Serotonin is a compound that conducts nerve impulses in the brain. It contains \(68.2 \% \mathrm{C}, 6.86 \% \mathrm{H}, 15.9 \% \mathrm{N},\) and 9.08\(\% \mathrm{O}\) . Its molar mass is 176 \(\mathrm{g} / \mathrm{mol} .\) Determine its molecular formula.

Short answer

The molecular formula of Serotonin is \( C_{10}H_{12}N_{2}O \).

Step-by-step solution

Converting percentages to grams

Since we are given the percentage composition of Serotonin, we can assume that we have 100 g of Serotonin and convert the percentage to grams for each element. Then, we have: - 68.2 g of Carbon (C) - 6.86 g of Hydrogen (H) - 15.9 g of Nitrogen (N) - 9.08 g of Oxygen (O)

Converting grams to moles

Now, we will convert the mass of each element to moles using their respective molar masses: - Carbon - C: \( \frac{68.2 g}{12.01 \frac{g}{mol}} = 5.68 \space mol \) - Hydrogen - H: \( \frac{6.86 g}{1.01 \frac{g}{mol}} = 6.79 \space mol \) - Nitrogen - N: \( \frac{15.9 g}{14.01 \frac{g}{mol}} = 1.14 \space mol \) - Oxygen - O: \( \frac{9.08 g}{16.00 \frac{g}{mol}} = 0.57 \space mol \)

Determining the empirical formula

Now, we will divide the moles of each element by the lowest moles among them, which is for Oxygen (0.57 moles). By doing so, we have: - Carbon - C: \( \frac{5.68}{0.57} \approx 10 \) - Hydrogen - H: \( \frac{6.79}{0.57} \approx 12 \) - Nitrogen - N: \( \frac{1.14}{0.57} \approx 2 \) - Oxygen - O: \( \frac{0.57}{0.57} \approx 1 \) So, the empirical formula of Serotonin is \( C_{10}H_{12}N_{2}O \).

Calculating the molar mass of the empirical formula

Now, let's calculate the molar mass of the empirical formula: \( C_{10}H_{12}N_{2}O: = 10(12.01) + 12(1.01) + 2(14.01) + 16.00 = 176.23 g/mol \)

Determining the molecular formula

Now, we will use the molar mass of Serotonin (176 g/mol) and the molar mass of the empirical formula (176.23 g/mol) to find the molecular formula. Since the molar mass of Serotonin (176 g/mol) is approximately equal to the molar mass of the empirical formula (176.23 g/mol), the molecular formula is the same as the empirical formula. Therefore, the molecular formula of Serotonin is \( C_{10}H_{12}N_{2}O \).

Key concepts

Empirical Formula Calculation

Understanding the empirical formula calculation is vital for students studying chemistry. It represents the simplest whole number ratio of atoms of each element in a compound. In our exercise involving Serotonin, calculating the empirical formula begins with converting the percentage composition into masses, assuming you have 100 g of the substance. This conversion is intuitive because percentage literally means 'per hundred'.

Once we have the mass of each element in grams, we need to determine how many moles of each element are present. This step utilizes the concept of molar mass, which is the mass of one mole of a substance. After finding the number of moles, we compare them by dividing each by the smallest number of moles present in the compound. The resulting ratios provide us with the simplest whole number ratio of atoms – our empirical formula, which in this case is the chemical blueprint for Serotonin, or more formally, C₁₀H₁₂N₂O.

Molar Mass

The molar mass is a physical property defined as the mass of a given substance (chemical element or chemical compound) divided by the amount of substance. Measured in grams per mole (g/mol), it's essentially the mass of one mole of a substance.

Understanding molar mass allows us to convert between the mass of a substance and the number of moles. This conversion is a foundation for stoichiometry and is often the stepping stone for solving complex chemical equations. In the Serotonin example, we use the molar mass of each element to convert the mass in grams we obtained from the percentage composition to moles, which helps us establish precise stoichiometric relationships between elements.

Percentage Composition

Percentage composition is the relative amount of each element within a compound, represented as a percentage of the total mass of the compound. This concept helps chemists understand the composition of substances and aids in calculating empirical and molecular formulas.

For instance, Serotonin's makeup was given in percentage by weight, so the calculation began by assuming you have a 100-gram sample, making it straightforward to convert the percentages directly to grams. This first step is critical because it allows you to determine the number of moles of each constituent element, which paves the way to finding the empirical formula. In practical situations, chemists use the percentage composition to deduce the purity of a compound or to identify its elemental constituents.

Stoichiometry

Stoichiometry can be likened to the recipe for a cake – it tells you how much of each ingredient you need. In chemistry, stoichiometry deals with the quantitative relationships, or ratios, that substances undergo in a chemical reaction. The mole concept is the cornerstone of stoichiometry, acting as a bridge to translate masses of substances to amounts of entities, such as atoms or molecules.

In determining the molecular formula of Serotonin, stoichiometry is used to compare the molar mass of Serotonin to that of the empirical formula. Since they match, it reveals that the empirical and molecular formulae are the same. Thus, stoichiometry isn't only about reactions—it also extends to understanding the relationship between empirical and molecular formulas, especially when dealing with unknown compounds or when synthesizing new ones.