Question

Why do we need to count atoms by weighing them?

Short answer

We need to count atoms by weighing them because atoms are extremely small and numerous, making it impossible to count them individually. By using the mole concept, we can relate the mass of a substance to the number of atoms or molecules it contains. This approach simplifies the process and makes it more practical, as it allows us to estimate the quantity of atoms in a sample by weighing it and calculating its molar mass.

Step-by-step solution

Understanding the size of atoms

Atoms are extremely small, with diameters of about 0.1 to 0.5 nanometers. They are so small that even the most advanced microscopes cannot detect them individually. Hence, counting atoms one by one is nearly impossible given their extremely small size and the vast number of atoms present in a sample.

Introducing the mole concept

To overcome the difficulties in counting atoms individually, scientists have adopted a unit called "mole" to count a large number of atoms or molecules. A mole is defined as the amount of substance that contains as many entities as there are in 12 grams of pure carbon-12, which is equal to Avogadro's number, approximately \(6.022 \times 10^{23}\) entities.

Relating mass and number of atoms

Atomic mass unit (amu) is used to determine the mass of an individual atom. It is defined as one-twelfth the mass of one carbon-12 atom. The molar mass (mass of one mole of substance) can then be determined using the molecular/atomic weight of the substance, which is the sum of the atomic masses of all atoms in a single molecule or substance, expressed in grams per mole. Weighing a sample of a substance and calculating the molar mass allows us to estimate the number of atoms or molecules present in that substance without counting them individually. This approach is both simpler and more practical, given the limitations of counting atoms due to their size and number.

Example: Counting carbon atoms in a pencil lead

Let's assume the pencil lead has a mass of 2 grams and is made entirely of graphite, which consists of carbon atoms. The atomic mass of carbon is 12 amu, and its molar mass is 12 g/mol. 1. First, determine the number of moles in the 2-gram pencil lead: \[n = \frac{mass}{molar\ mass} = \frac{2\ grams}{12\ g/mol} = 0.167\ moles\] 2. Next, multiply the number of moles by Avogadro's number to find the number of carbon atoms: \[Number\ of\ atoms = n \times Avogadro's\ number = 0.167\ moles \times (6.022 \times 10^{23}\ atoms/mol) \approx 1.004 \times 10^{23}\ atoms\] By weighing the pencil lead and using the mole concept, we can easily determine the number of carbon atoms present in the lead without having to count them individually.

Key concepts

Atomic Mass Unit (amu)

The concept of the atomic mass unit (amu) is essential for understanding the mass of atoms and molecules. Since atoms are incredibly tiny, their mass is minuscule and challenging to express in the units we typically use, like grams. To solve this, scientists created the atomic mass unit.

• An atomic mass unit is defined as one-twelfth of the mass of a carbon-12 atom.
• This provides a standard for measuring atomic masses relative to each other.

By using amu, we can represent the mass of individual atoms in a way that is practical and meaningful. For instance, the atomic mass of carbon is approximately 12 amu, which tells us it is twelve times heavier than an atom specified as a reference, in this case, carbon-12. This comparative method makes it feasible to discuss and calculate the masses of different atoms and molecules efficiently.

Avogadro's Number

Avogadro's number is a critical concept used in chemistry to deal with the impracticality of counting atoms or molecules individually due to their incredibly small size and large quantity in any given sample. Avogadro's number is defined as:

• Approximately \(6.022 \times 10^{23}\).
• Represents the number of atoms or molecules in one mole of a substance.

This number bridges the atomic scale to the macroscopic scale, allowing us to use a measurable amount of a substance to infer the number of atoms or molecules it contains. For example, when saying a mole of carbon atoms contains \(6.022 \times 10^{23}\) atoms, it allows scientists to work with quantities that are tangible, like grams or liters, rather than unmanageable numbers of individual atoms.

Molar Mass

Molar mass serves as a bridge between a substance's atomic makeup and its mass in grams. It refers to the mass of a mole of a substance and is expressed in grams per mole (g/mol). This concept illustrates how amount scales up from individual atoms and molecules:

• To calculate molar mass, sum up the atomic masses of all atoms within a molecule.
• Molar mass lets scientists convert between the mass of a substance and the number of moles.

For instance, carbon's molar mass is 12 g/mol, meaning one mole of carbon weighs 12 grams. By weighing a sample in grams and knowing the molar mass, you can readily determine how many moles of the substance are present, which in turn tells you how many atoms or molecules are in that sample. This method is invaluable for both theoretical calculations and practical laboratory work, forming the backbone of much of chemical analysis.