Question

The compound adrenaline contains \(56.79 \%\) C, \(6.56 \%\) H, \(28.37 \%\) O, and \(8.28 \%\) N by mass. What is the empirical formula for adrenaline?

Short answer

The empirical formula for adrenaline is \(C_8H_{11}O_3N\).

Step-by-step solution

1. Convert mass percentages to moles

For each element (C, H, O, and N), we'll divide the given mass percentage by the element's molar mass to obtain the number of moles. Let us consider a 100g sample of adrenaline so that the mass percentages directly translate to mass in grams. Here are the molar masses of the elements: C = 12.01 g/mol, H = 1.01 g/mol, O = 16.00 g/mol, and N = 14.01 g/mol. For Carbon (C): Moles of C = (56.79 g) / (12.01 g/mol) = 4.732 moles For Hydrogen (H): Moles of H = (6.56 g) / (1.01 g/mol) = 6.495 moles For Oxygen (O): Moles of O = (28.37 g) / (16.00 g/mol) = 1.773 moles For Nitrogen (N): Moles of N = (8.28 g) / (14.01 g/mol) = 0.591 moles

2. Find the simplest whole-number ratio

To find the simplest whole-number ratio between the moles of each element, we will divide each mole value by the smallest value: For Carbon (C): 4.732 / 0.591 = 8.000 For Hydrogen (H): 6.495 / 0.591 = 10.997 ≈ 11 For Oxygen (O): 1.773 / 0.591 = 2.998 ≈ 3 For Nitrogen (N): 0.591 / 0.591 = 1 Now the simplest whole-number ratio is 8:11:3:1

3. Write the empirical formula

Based on the simplest whole-number ratio we found, the empirical formula for adrenaline is: \(C_8H_{11}O_3N_1\), or simply \(C_8H_{11}O_3N\).

Key concepts

Molar Mass

Understanding molar mass is the first step to determining the empirical formula of a compound like adrenaline. In essence, molar mass is the weight of one mole (6.02 x 10²³ particles) of a given substance and is expressed in grams per mole (g/mol). It's like the currency exchange between atoms and grams — a way to translate between the microscopic world of atoms and the macroscopic world that we can measure.[br][br]For instance, the molar mass of carbon (C) is 12.01 g/mol. This means if you have one mole of carbon atoms, it would weigh 12.01 grams. Similarly, hydrogen (H), oxygen (O), and nitrogen (N) have molar masses of 1.01 g/mol, 16.00 g/mol, and 14.01 g/mol, respectively. Using these values, we convert the mass percentage of each element into moles, which is the starting point for finding the empirical formula.

Mass Percentage

Essentially, the mass percentage tells us how much of an element is present in a compound relative to the total mass. Think of it as a recipe; mass percentage gives you the proportions of each ingredient necessary to make the perfect dish.[br][br]For adrenaline, we were given its composition in these percentages right off the bat: 56.79% carbon, 6.56% hydrogen, 28.37% oxygen, and 8.28% nitrogen. If we consider a 100g sample, it means translating those percentages into grams is direct: 56.79g C, 6.56g H, 28.37g O, and 8.28g N. This direct conversion simplifies the process, allowing us to then compare the amount of each element present by converting these masses to moles using their respective molar masses.

Mole-to-Mole Ratio

The mole-to-mole ratio is the bridge that connects different elements within a compound. Once we have the number of moles of each element, we need to express their relationship through the simplest whole-number ratios to reach the empirical formula.[br][br]We do this by dividing the number of moles of each element by the smallest number of moles present among them, which in the case of adrenaline is nitrogen, with 0.591 moles. The results give us the relative numbers of atoms of each element that combine to form the simplest unit of the compound. These ratios are the essence of the compound's formula, reflecting the fundamental proportions in which the elements combine.

Chemical Composition

A compound's chemical composition is its identity card; it shows the specific elements and the number of each atom type that makes up the compound. The empirical formula derived from the mole ratio gives us the simplest, most reduced representation of this composition, revealing the basic building blocks of the molecular structure.[br][br]In adrenaline, for example, the mole-to-mole ratio resulted in an empirical formula of C₈H₁₁O₃N. This formula indicates that in the most basic form of adrenaline, eight carbon atoms are combined with eleven hydrogen atoms, three oxygen atoms, and one nitrogen atom. This quintessential information allows chemists to understand, predict, and manipulate the compound's properties and reactions.