Question

What is the total number of \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{O}\) atoms in 0.260 moles of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} ?\)

Short answer

In 0.260 moles of glucose, there are \(9.38 \times 10^{24}\) C atoms, \(1.88 \times 10^{25}\) H atoms, and \(9.38 \times 10^{24}\) O atoms.

Step-by-step solution

- Determine the number of atoms per molecule

Look at the molecular formula of glucose, which is \(\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6}\). This indicates that one molecule of glucose contains 6 carbon (C) atoms, 12 hydrogen (H) atoms, and 6 oxygen (O) atoms.

- Calculate the number of each type of atom in the given moles

Use Avogadro's number, which is \(6.022 \times 10^{23}\) atoms/mole, to convert moles of glucose to the number of atoms. Multiply the number of moles by Avogadro's number for each element: \(0.260 \text{ moles of glucose} \times 6.022 \times 10^{23} \text{ molecules/mole}\times 6 \text{ C atoms/molecule} = 9.38 \times 10^{24} \text{ C atoms}\), and similarly for H and O.

- Perform the calculations

Calculate the total number of carbon atoms: \(0.260 \text{ moles} \times 6 \text{ atoms/molecule} \times 6.022 \times 10^{23} \text{ atoms/mole} = 9.38 \times 10^{24} \text{ C atoms}\). Calculate the total number of hydrogen atoms: \(0.260 \text{ moles} \times 12 \text{ atoms/molecule} \times 6.022 \times 10^{23} \text{ atoms/mole} = 1.88 \times 10^{25} \text{ H atoms}\). Calculate the total number of oxygen atoms: \(0.260 \text{ moles} \times 6 \text{ atoms/molecule} \times 6.022 \times 10^{23} \text{ atoms/mole} = 9.38 \times 10^{24} \text{ O atoms}\).

Key concepts

Avogadro's Number

In chemistry, Avogadro's number is a fundamental constant that provides a direct link between the microscopic scale of atoms and the macroscopic scale that we can measure in the laboratory. It is defined as the number of constituent particles, usually atoms or molecules, contained in one mole of a substance. Avogadro's number is approximately \(6.022 \times 10^{23}\) particles per mole.

When working on problems like the total number of atoms in a given amount of a substance, Avogadro's number becomes incredibly significant. To convert moles of a substance to the number of molecules or atoms, as in our example with glucose, you multiply the number of moles by Avogadro's number. This conversion factor is crucial in understanding the quantities involved in chemical reactions and stoichiometry.

Molecular Formula

The molecular formula of a compound provides crucial information about the composition of the substance. It tells us the exact number of each type of atom present in a single molecule of the compound.

For instance, glucose has the molecular formula \(\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6}\). This formula indicates that each molecule of glucose contains 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms. Understanding the molecular formula is vital because it allows chemists to calculate the amounts of reactants needed for a reaction and the quantities of products that can be formed, which are foundational principles of stoichiometry.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the relationships between reactants and products in a chemical reaction. It is based on the conservation of mass where the total mass of reactants equals the total mass of products, which implies that matter cannot be created or destroyed in an isolated system.

Through stoichiometry, chemists can predict the quantities of substances consumed and produced in a given reaction, ensuring that they are able to calculate the precise amounts needed for reactions to occur completely. It involves calculations based on the mole concept and principles like the Avogadro's number to bridge the gap between the molecular scale and real-world measurements.

Atom Counting in Compounds

Atom counting in compounds is a fundamental skill that involves determining the number of each type of atom present in a certain quantity of a substance. It is an application of both the molecular formula and Avogadro's number. By understanding the molecular formula, you can identify the number of each type of atom in a single molecule. Then, by using Avogadro's number, you can scale up this information to find the number of atoms in any given number of moles of the substance.

In our glucose example, atom counting is used to find the total number of carbon, hydrogen, and oxygen atoms in 0.260 moles of glucose. This is done by taking the number of each type of atom from the molecular formula and multiplying by Avogadro's number for the given moles. The result is a clear understanding of the quantity of each atom present in the sample, which is essential for studies of chemical composition and reactions.