Problem 79 - Chemistry: The Central Science

Question

Consider the stable elements through lead \((Z=82)\). In how many instances are the atomic weights of the elements out of order relative to the atomic numbers of the elements?

Step-by-Step Solution

Answer

There are 7 instances where the atomic weights of the elements are out of order relative to their atomic numbers for stable elements through lead (Z=82). These instances are: 1. Argon \((Z=18)\) and potassium \((Z=19)\) 2. Cobalt \((Z=27)\) and nickel \((Z=28)\) 3. Tellurium \((Z=52)\) and iodine \((Z=53)\) 4. Cerium \((Z=58)\) and praseodymium \((Z=59)\) 5. Thulium \((Z=69)\) and ytterbium \((Z=70)\) 6. Gold \((Z=79)\) and mercury \((Z=80)\) 7. Thallium \((Z=81)\) and lead \((Z=82)\)

Step 1: List the stable elements

List the stable elements with their atomic numbers and atomic weights. To save time, you can use a periodic table or search online for a list of the stable elements and their atomic weights. For this problem, work with elements up to lead (Pb) with atomic number 82.

Step 2:Compare the order of atomic numbers and atomic weights

Compare the order of atomic numbers and atomic weights for each stable element. Start by checking if the element with the smallest atomic weight has the smallest atomic number. Then, continue this process for the rest of the elements. If you encounter an element with atomic weights in a different order than their atomic numbers, count that as an instance. For example: Compare the atomic weight of hydrogen (1.008) with the atomic weight of helium (4.0026). Hydrogen has a lower atomic weight and a lower atomic number, so these two elements are not an instance of out-of-order elements.

Step 3: Count the instances of out-of-order elements

Count the total number of instances where atomic weights are not in the same order as their atomic numbers. These are instances where the order of atomic weights does not match the order of atomic numbers for a pair of elements. After going through all stable elements up to lead (82), you will find that there are only 7 instances in which the atomic weights of the elements are not in the same order as their atomic numbers: 1. Argon \((Z=18)\) and potassium \((Z=19)\) 2. Cobalt \((Z=27)\) and nickel \((Z=28)\) 3. Tellurium \((Z=52)\) and iodine \((Z=53)\) 4. Cerium \((Z=58)\) and praseodymium \((Z=59)\) 5. Thulium \((Z=69)\) and ytterbium \((Z=70)\) 6. Gold \((Z=79)\) and mercury \((Z=80)\) 7. Thallium \((Z=81)\) and lead \((Z=82)\) From our analysis, there are 7 instances (out-of-order pairs) where the atomic weight order does not match with the atomic number order.

Key Concepts

Understanding the Periodic Table

The periodic table is a fundamental tool in chemistry that organizes all known chemical elements in an informative array. It is designed to highlight the recurring properties of elements, facilitating the understanding of chemical behavior and relationships among elements. The typical layout consists of rows called periods and columns known as groups or families.

Elements are arranged in order of increasing atomic number, which is the number of protons in an atom's nucleus. This number is unique to each element and is central to the element's identity. As you move from left to right in a period, the atomic weight generally increases. Atomic weight, measured in atomic mass units (amu), is the average mass of atoms of an element, accounting for the presence of isotopes and their relative abundance.

However, it's important to note that the atomic weight doesn't increase uniformly, as it's influenced by the number of neutrons and the natural abundance of an element's isotopes. This can sometimes lead to unexpected orderings, which might seem like a discrepancy if one expects strict atomic weight increase with atomic number. Students typically familiarize themselves with the table's arrangement throughout their study of chemistry, using it as a key reference for understanding elemental properties and predicting how different elements will react with one other.

Stable Elements on the Periodic Table

In the context of the periodic table, stable elements are those that do not undergo radioactive decay over observable timescales. In essence, they have a balance of protons and neutrons in their nucleus that confers stability. In our exercise, we consider elements up to and including lead (Pb), with atomic number 82, because all elements beyond lead are radioactive to some degree.

Stability in elements is also related to their atomic structure and the completion of electron shells, with noble gases being prime examples of naturally stable elements thanks to their full valence shells. Understanding stability is crucial not just for fundamental chemistry, but also for practical applications, such as materials science and nuclear chemistry. Knowing stable elements and their properties enables chemists to predict and explain various chemical reactions and why some elements readily combine while others do not.

Element Order Discrepancy Explained

The element order discrepancy is observed when the atomic weights of certain pairs of elements do not align with the increasing order of their atomic numbers. This can seem counterintuitive since one might expect these two values to correlate directly. However, this is where the nuanced nature of atomic structure plays a role.

Several factors contribute to this discrepancy, including variations in the number of neutrons and the distribution of naturally occurring isotopes. Isotopes are atoms of the same element that have different numbers of neutrons, causing them to have different atomic weights. Naturally occurring isotopes have different abundances, which affect the average atomic weight of an element. In some cases, an element with a higher atomic number might have a lower atomic weight than its predecessor due to these isotopic abundances.

For example, cobalt with an atomic number of 27 actually has a slightly larger atomic weight than nickel with an atomic number of 28 due to the relative isotopic abundances. When evaluating elements based on these criteria, students are encouraged to be attentive to the precise definition of atomic weight as an average that includes isotopic composition, which clarifies why these order discrepancies occur.