Problem 12 - Chemistry Matter and Change

Question

Calculate the mass of 0.25 mol of carbon-12 atoms.

Step-by-Step Solution

Answer

The mass of 0.25 moles of carbon-12 atoms is 3 grams.

Step 1: Understanding the Problem

We need to find the mass of 0.25 moles of carbon-12 atoms. Carbon-12 is the isotope of carbon with a mass number of 12, meaning each atom of carbon-12 has a mass of approximately 12 atomic mass units (amu). We can relate this to grams using the concept of moles.

Step 2: Using Avogadro's Number

One mole of any substance contains Avogadro's number of atoms or molecules, which is approximately \(6.022 \times 10^{23}\). This means 1 mole of carbon-12 atoms equals approximately \(6.022 \times 10^{23}\) atoms.

Step 3: Molar Mass of Carbon-12

The molar mass of an element is the mass in grams of one mole of that element's atoms. For carbon-12, the molar mass is exactly 12 grams per mole, because by definition, the atomic mass unit is based on the carbon-12 isotope.

Step 4: Calculate the Mass

Since one mole of carbon-12 has a mass of 12 grams and we have 0.25 moles, we multiply the molar mass by the number of moles: \(0.25 \text{ mol} \times 12 \text{ g/mol} = 3 \text{ g}\).

Step 5: Conclusion

The mass of 0.25 moles of carbon-12 atoms is calculated as 3 grams using the relationship between moles and molar mass.

Key Concepts

Avogadro's number

Avogadro's number is a fundamental concept in chemistry that helps bridge the gap between the atomic scale and the macroscopic scale we experience in everyday life. It is defined as the number of atoms, molecules, or particles in one mole of a substance, which is approximately \(6.022 \times 10^{23}\). This large number allows chemists to use macroscopic measurements for quantities in chemistry that engage with microscopic particles.

In chemical reactions, Avogadro's number is pivotal in expressing concentrations and quantities, making it easier to calculate the amounts of substances needed or produced in reactions. It serves as a conversion factor:

• It connects moles to individual atoms or molecules, allowing for an understanding of how many particles are involved in a given chemical process.
• Facilitate the determination of the number of particles in a given sample when its mass is known.

When working on exercises like determining the mass of a number of moles of a substance, Avogadro’s number helps relate moles to atoms, allowing us to visualize and calculate much more understandably.

carbon-12

Carbon-12 is an isotope of carbon, one of its two stable isotopes, the other being carbon-13. The '12' in carbon-12 stands for its atomic mass number, which is the sum of its 6 protons and 6 neutrons. This particular isotope is the standard reference by which the atomic mass unit is defined.

In scientific terms, carbon-12 was chosen as the reference point due to its widespread abundance and stability. Due to these properties:

• Atomic masses of elements are often expressed relative to the mass of a carbon-12 atom.
• It provides the basis for defining the mole and the atomic mass unit (amu).

Each carbon-12 atom has a mass of exactly 12 atomic mass units (amu), due to its convenient integer number of nucleons. This makes calculations related to atomic weights directly relatable to carbon-12 and simplifies quantitative chemical analysis.

atomic mass unit

An atomic mass unit (amu) is a unit of mass used to express atomic and molecular weights. It is particularly suited for the measurement of atoms and molecules because traditional units of mass are impractically large when applied to these small entities. The atomic mass unit is precisely defined by the carbon-12 isotope.

By definition, one atomic mass unit is \(\frac{1}{12}\) of the mass of a carbon-12 atom. Thanks to this definition:

• The atomic mass of carbon-12 is exactly 12 amu.
• It provides a relatable scale for chemists to determine relative molecular masses easily.

This allows the calculations in chemistry to be coherent and standard across different elements, facilitating the precise comparison of the masses of different isotopes and molecules. The concept of amu is central to converting atomic masses from atomic scale to the observable macroscopic scale using Avogadro's number.