Problem 68 - General Chemistry: Principles and Modern Applications

Question

William Prout (1815) proposed that all other atoms are built up of hydrogen atoms, suggesting that all elements should have integral atomic masses based on an atomic mass of one for hydrogen. This hypothesis appeared discredited by the discovery of atomic masses, such as 24.3 u for magnesium and 35.5 u for chlorine. In terms of modern knowledge, explain why Prout's hypothesis is actually quite reasonable.

Step-by-Step Solution

Answer

Prout's hypothesis is quite reasonable when considering the isotopic composition of elements. Each isotope of an element has an integral atomic mass, which aligns with the concept that they're built up of hydrogen atoms. The non-integral atomic masses presented in the periodic table are due to these masses being a weighted average of the masses of the various isotopes of that element.

Step 1: Understand Isotopes

Firstly, it needs to be understood that most elements in nature exist as a mixture of isotopes. Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons, meaning they have different atomic masses.

Step 2: Understand Calculation of Atomic Mass

The atomic mass of an element is not determined by the mass of one atom, but is an average value from all its isotopes taking in consideration their abundance in nature. Hence, the atomic mass is a weighted average, which may not be an integer.

Step 3: Discuss Examples

Taking the examples: Chlorine exists primarily as two isotopes, one having atomic mass 35 and the other 37. Considering their natural abundance, the average atomic mass comes as 35.5 u. Similarly, Magnesium's most common isotopes have masses of 24, 25, and 26. The weighted average atomic mass of these isotopes is 24.3 u.

Step 4: Final Explanation

Therefore, looking at isotopes and the calculation of atomic masses, Prout's hypothesis holds true. Every element can be concluded as being composed of multiple hydrogen atoms, as the atomic masses are integral for each individual isotope. The non-integral atomic masses from the periodic table are due to the weighted average of isotopic masses.

Key Concepts

Atomic Mass

The atomic mass of an element is a key characteristic that defines its identity and behavior. However, it is not as straightforward as just weighing a single atom. Instead, atomic mass is a reflection of the masses of all isotopes of that element.
Each isotope has a different mass because it contains a different number of neutrons. This variety in neutron number means each isotope has its own distinct mass, even though they all belong to the same element.
To obtain the atomic mass of an element, all isotopic masses are considered along with their natural abundances.
For instance:

• Hydrogen: The simplest element, yet it has isotopes such as protium, deuterium, and tritium, each contributing to hydrogen's atomic mass.
• Chlorine: With isotopes of atomic masses 35 and 37, it has an average atomic mass of approximately 35.5 units due to their relative proportions.

Thus, the atomic mass captures the collective contribution of all isotopes rather than a single value.

Weighted Average

The concept of a weighted average is essential in understanding how atomic masses of elements are calculated. Unlike a simple average, a weighted average takes into account the proportion or abundance of each constituent. In the case of atomic masses, this is the relative abundance of each isotope.
To compute the weighted average atomic mass:

• Multiply the mass of each isotope by its natural abundance (as a decimal).
• Sum the results for all isotopes of the element.

For example, imagine calculating the atomic mass for an element with two isotopes:
- Isotope A: mass of 10 u, abundance of 75% - Isotope B: mass of 12 u, abundance of 25%
The weighted average atomic mass is calculated as:
\[ (10 \, \text{u} \times 0.75) + (12 \, \text{u} \times 0.25) = 7.5 \, \text{u} + 3 \, \text{u} = 10.5 \, \text{u} \].
This process explains why atomic masses are often not integers, reflecting the distribution of isotopes for any given element.

Atomic Structure

To understand isotopes and atomic mass calculations, it is crucial to grasp the fundamentals of atomic structure. Atoms are composed of three basic particles:

• Protons: Positively charged particles found in the nucleus, defining the element's identity.
• Neutrons: Neutral particles also in the nucleus, contributing to the isotope variation.
• Electrons: Negatively charged particles orbiting the nucleus, involved in chemical reactions.

The number of protons in an atom remains fixed for a given element, but the neutron count can vary, giving rise to different isotopes. This variation in neutron number is at the heart of why the atomic mass is a weighted average: each isotope has a distinct mass contribution.
While electrons play a critical role in chemical bonding and reactions, it is the interplay of protons and neutrons in the nucleus that determines isotopic and atomic mass characteristics. Understanding atomic structure provides the foundation for unraveling why the atomic mass of an element appears as a non-integral value, resulting from the weight of its isotopes.