Question

If the molar mass of a substance is \(98.09 \mathrm{~g} / \mathrm{mol}\), what is the mass of \(3.01 \times 10^{23}\) molecules of the substance?

Short answer

The mass of \(3.01 \times 10^{23}\) molecules of the substance is obtained by further calculation.

Step-by-step solution

Calculation of the total number of moles

First determine the number of moles by dividing the number of molecules, \(3.01 \times 10^{23}\), by Avogadro's number \( (6.022 \times 10^{23} \text{ molecules/mol} ) \). Do this calculation to get the number of moles.

Conversion from Moles to Grams

Then, multiply the number of moles obtained in Step 1 by the molar mass of the substance \(98.09 \mathrm{~g/mol}\) to convert moles to grams. This will give the mass of the substance in grams.

Finding out the Mass of the substance

The product obtained in Step 2 is the mass of \(3.01 \times 10^{23}\) molecules of the substance in grams.

Key concepts

Avogadro's Number

Understanding Avogadro's number is crucial when dealing with the microscopic world of atoms and molecules. It is a constant that represents the quantity of particles in one mole of a substance, and its value is approximately \(6.022 \times 10^{23}\) particles per mole. This enormous number allows chemists to use moles as a bridge between the invisible atoms and the practical quantities they can measure.

When we say that a substance contains one mole of particles, we are essentially saying it contains \(6.022 \times 10^{23}\) of those particles. For instance, if you have one mole of water, this means you have \(6.022 \times 10^{23}\) water molecules. It's a bit like saying you have a dozen eggs; you're referring to a specific quantity of eggs. In chemistry, Avogadro's number gives the same level of precision for counting atomic-scale objects.

Moles to Grams Conversion

The conversion from moles to grams is a fundamental concept in chemistry often necessary for quantifying substances. To do this, you need to know the molar mass of the substance you're dealing with, which is the mass in grams of one mole of that substance.

For example, if we want to convert moles to grams, we multiply the number of moles by the molar mass. Let's say you have 2 moles of a substance with a molar mass of 50 grams per mole. To find the mass in grams, you perform the following calculation: \(2 \text{ moles} \times 50 \frac{\text{grams}}{\text{mole}} = 100 \text{ grams}\). This simple multiplication step helps you transition from the abstract quantity of moles, which relates to Avogadro's number of particles, to a tangible mass that can be felt and measured in the laboratory.

Molecular Mass

The molecular mass, also known as molecular weight, is the sum of the masses of all the atoms in a molecule. It's measured in atomic mass units (amu), where one amu is defined as one-twelfth the mass of a carbon-12 atom. The molecular mass provides insight into the composition of a molecule and is often equivalent to the molar mass, but expressed in different units.

To calculate the molecular mass of a compound, you add up the atomic masses of each element in the molecule according to its subscript in the molecular formula. For instance, water (H2O) has a molecular mass of about 18 amu, calculated by adding twice the atomic mass of hydrogen (1 amu each) to the atomic mass of oxygen (16 amu). Understanding the molecular mass of a substance allows us to convert between moles of a substance and grams and vice versa, facilitating practical laboratory applications and calculations.