Question

What is the mass (in amu) of \(100^{12} \mathrm{C}\) atoms? Of \(100{ }^{13} \mathrm{C}\) atoms?

Short answer

The mass of \(100^{12}\mathrm{C}\) atoms is 1200 amu while the mass of \(100^{13}\mathrm{C}\) atoms is 1300 amu.

Step-by-step solution

Determine the mass of \(100^{12}\mathrm{C}\) atoms

Given that each Carbon-12 atom has a mass of 12 amu, the mass of 100 atoms of Carbon-12 is: \(100 \times 12 = 1200\) amu.

Determine the mass of \(100^{13}\mathrm{C}\) atoms

On the other hand, each Carbon-13 atom has a mass of 13 amu (as it contains an additional neutron compared to Carbon-12). Hence, the mass of 100 atoms of Carbon-13 is: \(100 \times 13 = 1300\) amu

Key concepts

Isotopes

Atoms of the same element with different numbers of neutrons are known as isotopes. These isotopic variations cause differences in their atomic masses, but they typically behave identically in terms of their chemical reactions. For instance, the element carbon has several isotopes, with Carbon-12 (¹²C) and Carbon-13 (¹³C) being the most common in nature.

Let's consider the isotopes of carbon in the exercise. Carbon-12, the most abundant, has six protons and six neutrons, making its atomic mass 12 atomic mass units (amu), as it was used in step 1 of the solution. On the other hand, Carbon-13 contains one additional neutron, thus it has an atomic mass of 13 amu, highlighted in step 2. However, despite the differing masses, the chemical properties of ¹²C and ¹³C remain largely unaffected by these differences.

Chemistry Education

In chemistry education, understanding isotopes is fundamental because it helps students grasp more advanced concepts like atomic structures, chemical reactions, and radioactive decay. Examples like the given exercise enable students to link conceptual understanding with practical application, making the abstract concept of isotopes more tangible.

To improve comprehension, educators might consider using visual aids, such as diagrams of atomic structures, or interactive models that allow students to observe the effect of changing neutron numbers. Discussions on real-world applications of isotopes, such as in carbon dating or medical diagnostics, can also provide a deeper and more engaging learning experience.

Molar Mass

The molar mass of an element is another crucial concept and is the mass of one mole of its atoms, typically expressed in grams per mole (g/mol). It numerically equals the element's average atomic mass when expressed in amu. Therefore, knowing how to calculate atomic mass is a stepping stone to understanding molar mass.

In the context of the exercise, if one expands the calculation to Avogadro's number of atoms (\(6.022 \times 10^{23}\) atoms), one would calculate the molar mass in grams. For instance, the molar mass of Carbon-12 would be approximately 12 g/mol, which reflects both the simplicity and the practicality of using atomic mass units for smaller quantities of atoms.