Problem 53 - Introductory Chemistry Atoms First

Question

Naturally occurring hydrogen on Earth has an atomic mass of \(1.0079\) amu. Suppose you were on another planet and found the atomic mass of hydrogen to be \(1.2000\) amu. How would you explain this? (The atomic mass of \({ }_{1}^{1} \mathrm{H}\) is \(1.0078252\) amu; the atomic mass of \({ }_{1}^{2} \mathrm{H}\) is \(2.1041022\) amu.)

Step-by-Step Solution

Answer

The difference in the atomic mass of hydrogen on the other planet can be explained by a higher relative abundance of the heavier isotope, \({ }_{1}^{2}\mathrm{H}\), compared to its abundance of lighter isotope, \({ }_{1}^{1}\mathrm{H}\). This results in a higher weighted average atomic mass value of \(1.2000\) amu compared to hydrogen found on Earth.

Step 1: Understand the isotopes of hydrogen and their atomic masses on Earth

On Earth, hydrogen has two naturally occurring isotopes: \({ }_{1}^{1}\mathrm{H}\) with atomic mass \(1.0078252\) amu and \({ }_{1}^{2}\mathrm{H}\) with atomic mass \(2.1041022\) amu. The given average atomic mass of hydrogen on Earth is \(1.0079\) amu, which is a weighted average of the isotopes' atomic masses based on their relative abundances.

Step 2: Compare the average atomic mass of hydrogen on the other planet

We are given that the average atomic mass of hydrogen on the other planet is \(1.2000\) amu, which is greater than the average atomic mass on Earth. This suggests that the relative abundance of the isotopes on the other planet is different than on Earth.

Step 3: Explain the difference in atomic mass

The difference in the average atomic mass of hydrogen between Earth and the other planet can be explained by a greater abundance of the heavier isotope, \({ }_{1}^{2}\mathrm{H}\), on the other planet. This would shift the weighted average of the atomic masses towards the value of \(2.1041022\) amu, resulting in the observed average atomic mass of \(1.2000\) amu. In conclusion, the difference in the atomic mass of hydrogen on the other planet can be explained by a higher relative abundance of the heavier isotope, \({ }_{1}^{2}\mathrm{H}\), compared to its abundance of lighter isotope, \({ }_{1}^{1}\mathrm{H}\). This results in a higher weighted average atomic mass value of \(1.2000\) amu compared to hydrogen found on Earth.

Key Concepts

Isotopes of Hydrogen

Hydrogen, the simplest and most abundant element in the universe, possesses multiple forms called isotopes. These isotopes of hydrogen are atoms with the same number of protons but different numbers of neutrons.

The most common isotope, known as protium, has one proton and no neutrons, hence its atomic mass is approximately 1 amu. The second isotope, deuterium, contains one neutron in addition to the proton, giving it an atomic mass close to 2 amu. Lastly, there is tritium, with two neutrons and one proton, which has an atomic mass of about 3 amu but is radioactive and less commonly found.

These isotopic variations are integral to understanding variations in hydrogen's atomic mass across different environments, such as Earth versus another planet.

Average Atomic Mass

The average atomic mass of an element is the weighted average of the masses of its isotopes, considering their relative abundance in a given sample or environment. For hydrogen on Earth, this value is around 1.0079 amu, a figure that closely resembles the mass of the most abundant isotope, protium.

To calculate this value, one multiplies the mass of each isotope by its relative abundance (expressed as a decimal fraction) and then sums the results. If the relative abundance changes, so does the average atomic mass, which explains differences you might find on other planets or when comparing any two samples of the element.

Relative Abundance of Isotopes

The term relative abundance refers to the proportion of each isotope present in a mixture of isotopes. For example, on Earth, protium is far more abundant compared to deuterium. The variation in relative abundance can significantly impact the average atomic mass of an element.

Should you encounter a higher atomic mass of hydrogen, such as the 1.2000 amu on another planet, this would indicate a significantly greater proportion of the heavier deuterium isotope in that particular environment. This concept is essential for scientists in fields such as geochemistry and astrophysics, where isotopic compositions can reveal important clues about the origins and histories of substances.

Atomic Mass Unit (amu)

The atomic mass unit (amu) is a standard unit of mass used to express atomic and molecular weights. Precisely defined, one amu is one twelfth the mass of a carbon-12 atom. Since the masses of electrons are negligible compared to those of neutrons and protons, and both have masses close to 1 amu, the atomic mass of an isotope is approximately the sum of its protons and neutrons.

Understanding the concept of amu is critical when discussing isotopes and their average atomic mass, as it provides a common scale for comparison. For hydrogen, the difference of small fractions of an amu can have a significant impact on its physical and chemical properties, just as the atomic mass difference has on the hypothetical planet.