Problem 53 - Introductory Chemistry Atoms First

Question

If you have 1 mole of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) : (a) How many moles of carbon atoms do you have? (b) How many moles of hydrogen atoms do you have? (c) How many oxygen atoms do you have? (Note that we are not asking for moles here.)

Step-by-Step Solution

Answer

(a) In one mole of glucose, there are 6 moles of Carbon atoms. (b) In one mole of glucose, there are 12 moles of Hydrogen atoms. (c) In one mole of glucose, there are \(3.6132 × 10^{24}\) Oxygen atoms.

Step 1: (a) Calculate the number of moles of Carbon atoms in 1 mole of glucose

In one mole of glucose, the empirical formula indicates that there are 6 carbon atoms. Therefore, the number of moles of carbon atoms in one mole of glucose would be the same as the number of moles of glucose. Since there is 1 mole of glucose, there are \(1 \times 6 = 6\) moles of Carbon atoms.

Step 2: (b) Calculate the number of moles of Hydrogen atoms in 1 mole of glucose

In one mole of glucose, the empirical formula indicates that there are 12 hydrogen atoms. Therefore, the number of moles of hydrogen atoms in one mole of glucose would be the same as the number of moles of glucose multiplied by the number of hydrogen atoms in the glucose empirical formula. Since there is 1 mole of glucose, there are \(1 \times 12 = 12\) moles of Hydrogen atoms.

Step 3: (c) Calculate the number of Oxygen atoms in 1 mole of glucose

In one mole of glucose, the empirical formula indicates that there are 6 oxygen atoms. To find the number of oxygen atoms, we need to remember that 1 mole of a substance contains Avogadro's number (\(6.022 \times 10^{23}\)) of particles. Therefore, we will multiply the number of moles of oxygen atoms in one mole of glucose by Avogadro's number to find the number of oxygen atoms. Since there is 1 mole of glucose, there are \(1 \times 6 = 6\) moles of Oxygen atoms. Now we multiply by Avogadro's number: Number of Oxygen atoms = Moles of Oxygen atoms × Avogadro’s number Number of Oxygen atoms = \(6 \times (6.022 \times 10^{23}) = 3.6132 × 10^{24}\) Oxygen atoms

Key Concepts

Avogadro's Number

Avogadro's number is a fundamental concept in chemistry that bridges the gap between the microscopic world of atoms and the macroscopic world of grams and liters. It is defined as exactly 6.02214076 x 10^23 particles (atoms, molecules, ions, etc.) and is named in honor of the Italian scientist Amedeo Avogadro.

When we say '1 mole' of a substance, we mean that it contains Avogadro's number of particles. This constant allows chemists to count atoms by weighing and to calculate the number of particles in a given mass of a substance using stoichiometry. For example, if you're asked to find the number of oxygen atoms in a mole of glucose, as in the textbook exercise, you would multiply the number of moles of oxygen (6 moles as there are 6 oxygen atoms in glucose) by Avogadro's number to get the total number of atoms.

Understanding Avogadro's number is crucial to converting between moles and the number of particles—a fundamental skill in chemical calculations.

Empirical Formula

The empirical formula of a compound is a representation of the simplest whole-number ratio of elements present in the compound. In contrast to the molecular formula, which denotes the actual number of atoms of each element in a molecule, the empirical formula provides a simplified version that can be the same for multiple molecules that share a common ratio.

For instance, the empirical formula for glucose is CH2O, which shows the ratio of carbon to hydrogen to oxygen is 1:2:1. However, the actual molecular formula for glucose is C6H12O6, indicating that these elements are present in a multiple of the empirical formula. When solving stoichiometric problems, as seen in the textbook exercise, the empirical formula plays a pivotal role because it directly pertains to the stoichiometry of the atoms within a single molecule and thereby influences calculations of moles and mass.

Knowing how to interpret an empirical formula is essential in stoichiometry as it underpins the relationship between moles of different atoms within a single molecule of a compound.

Mole Concept

The concept of the mole is one of the pillars of stoichiometry and provides a bridge between the world of atoms and the laboratory scale. A mole is a unit that represents a specific number of chemical units (atoms, molecules, ions, etc.), similar to how a dozen represents 12 items.

The mole concept enables chemists to measure substances in terms of quantity rather than mass, which is particularly useful since atoms and molecules are extremely small and cannot be counted directly. It is analogous to counting eggs by the dozen rather than by their total mass. Through the use of the mole concept, we relate the mass of a substance to the number of particles it contains, thanks to the molar mass and Avogadro's number.

In applying the mole concept to the textbook exercise, we understand that 1 mole of glucose contains Avogadro's number of glucose molecules and by extension, 6 moles of carbon atoms, 12 moles of hydrogen atoms, and 6 moles of oxygen atoms. This reasoning is instrumental for conducting stoichiometric calculations in chemistry.