Question

If \(2.01 \times 10^{23}\) molecules of a substance have a mass of \(12.0 \mathrm{~g}\), what is the molar mass of the substance?

Short answer

The molar mass of the substance is the result of the calculation in Step 3, given in g/mol.

Step-by-step solution

Identify Given Values and Required Units

The number of molecules is given as \(2.01 \times 10^{23}\), and the mass as 12.0 g. The molar mass is to be calculated in g/mol.

Calculate the number of moles

To calculate the number of moles of the substance, divide the given number of molecules by Avogadro's number. So, the number of moles = Number of molecules / Avogadro's number = \(2.01 \times 10^{23}\) / \(6.02 \times 10^{23}\) mol.

Calculate the Molar Mass

Now, use the formula for molar mass, which is mass of the substance(m) divided by the number of moles(n). After plugging in the values, this yields: Molar mass = 12.0 g / (The moles calculated in step 2) g/mol.

Key concepts

Avogadro's Number

In chemistry, Avogadro's Number is a fundamental constant used to relate the number of individual atoms or molecules to the amount of a substance measured in moles. It is an incredibly large figure given as \(6.022 \times 10^{23}\). This number represents the quantity of atoms or molecules in one mole of a substance. For example, if you have one mole of water, it contains approximately \(6.022 \times 10^{23}\) water molecules. This concept allows chemists to carry out calculations on a macroscopic scale by tapping into the atomic level.

Avogadro's Number is crucial for translating between atomic-scale measurements and bulk-quantity measurements. This conversion is what enables chemists to work with easily measurable quantities in the laboratory. By using Avogadro's Number, you can determine how many atoms or molecules there are in a given sample, which helps in calculating other properties, such as molar mass or volume, depending on the conditions.

Moles

The mole is a core concept in chemistry that serves as a bridge between the atomic and macroscopic worlds. It is a unit that represents a specific number of particles, such as atoms, ions, or molecules. Specifically, one mole contains exactly \(6.022 \times 10^{23}\) entities, which is Avogadro's Number.

Using moles is advantageous because it enables chemists to express amounts of a chemical substance more easily. For example, instead of speaking of billions and billions of molecules, a chemist can simply refer to a number of moles. Calculating the number of moles in a sample involves dividing the number of particles (atoms or molecules) by Avogadro's Number. In the given exercise, this calculated the number of moles by taking the number of molecules and dividing it by \(6.022 \times 10^{23}\).

Understanding the concept of moles is essential to carry out chemical calculations, such as determining reaction yields, calculating concentrations, or converting between grams and molecules, ultimately making it a cornerstone concept in stoichiometry.

Molecular Mass

Molecular mass, also known as the molecular weight, is the mass of a single molecule of a chemical compound expressed in atomic mass units (amu). It is calculated by summing the atomic masses of all atoms in a molecule. For example, for a water molecule \(H_2O\), the molecular mass is derived by adding the atomic masses of 2 hydrogen atoms and 1 oxygen atom.

Understanding molecular mass is important for determining the molar mass of a substance, as seen in this exercise. Molar mass, which is the mass of one mole of a substance, is usually expressed in grams per mole (g/mol). It involves converting the mass of individual molecules to a macroscopic scale. To calculate it, you take the total mass of the substance and divide it by the number of moles.

In the example provided in the exercise, after finding the number of moles from the given molecules using Avogadro's Number, the molar mass is calculated by dividing the mass of the substance by the number of moles. This value helps in numerous applications, including stoichiometric calculations and determining the proportions of elements in reactions.