Problem 129 - Chemistry

Question

Avogadro's number has sometimes been described as a conversion factor between atomic mass units and grams. Use the fluorine atom ( 19.00 amu) as an example to show the relation between the atomic mass unit and the gram.

Step-by-Step Solution

Answer

The atomic mass of a fluorine atom is 19.00 amu, which is equivalent to 19.00 g/mol using Avogadro's number as a conversion factor.

Step 1: Understanding Avogadro's Number

Avogadro's number, denoted \(6.02214179 × 10^{23}\) represents the number of atoms in one mole of any substance. It's named after the scientist Amedeo Avogadro, who established that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules irrespective of the nature of the gas.

Step 2: Working out the Atomic Mass of Fluorine

The atomic mass of a fluorine atom is given as 19.00 amu (atomic mass units).

Step 3: Conversion to Grams using Avogadro's number

Avogadro's number can be used as a conversion factor to convert atomic mass unit to grams. We know that 1 mole of substance = atomic mass of the substance in grams. And 1 mole of any substance contains Avogadro's number of atoms or molecules. Therefore, the atomic mass of fluorine in grams is given by: \( 19.00 \ \text{amu} \times 1 g/mol = 19.00 g/mol \)

Key Concepts

Atomic Mass Unit

The atomic mass unit (amu) is a standard unit of mass that quantifies mass on an atomic or molecular scale. It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 at rest and in its ground state. When we say that the atomic mass of fluorine is 19.00 amu, we mean that each fluorine atom is 19.00 times heavier than one twelfth of a carbon-12 atom.

The significance of expressing atomic mass in amu is two-fold: it accounts for the minuscule mass of individual atoms and molecules, making the numbers manageable, and it creates a consistent scale for comparing the relative masses of different atoms. By using amu, chemists and physicists can easily relate the mass of atoms to each other and perform calculations in a standard format.

Molar Mass Conversion

Molar mass conversion is the process of converting the mass of a substance from atomic mass units (amu) to grams per mole (g/mol). This conversion is possible due to Avogadro's number, which provides a bridge between the atomic scale and the macroscopic world. Since Avogadro's number is defined as the number of atoms or molecules in one mole of substance, the molar mass of an element in grams per mole is numerically equal to its atomic mass in amu.

For example, fluorine has an atomic mass of 19.00 amu, which means that one mole of fluorine atoms will have a mass of 19.00 g. This conversion allows scientists to measure out amounts of a substance in grams that contain a specific number of atoms or molecules. In laboratory and practical applications, molar mass conversion is crucial for preparing solutions and performing stoichiometric calculations.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the relationship between the amounts of reactants and products in a chemical reaction. It involves calculations that use balanced chemical equations to determine the ratios of molecules and atoms involved in the reaction. A fundamental concept in stoichiometry is the mole, which allows chemists to count atoms and molecules in bulk by weighing them.

The use of the mole is made possible through conversions based on Avogadro's number and molar mass. By knowing the molar mass of substances, one can calculate how many moles of a reactant are needed to react completely with another reactant or to produce a given amount of product. Without stoichiometry, it would be incredibly difficult to predict the outcomes of chemical reactions or to scale reactions up from the laboratory to industrial production. The principles of stoichiometry are widely applied in fields like pharmaceuticals, manufacturing, and environmental science, where precise measurements and reactions are crucial.