In 1817, which law of periodicity showed that the atomic weight of phosphorus is the mean of those of nitrogen and arsenic?

Dobereiner’s Law of Triads

The correct answer is option 3. Dobereiner’s Law of Triads.

Dobereiner’s Law of Triads, proposed by the German chemist Johann Wolfgang Döbereiner in 1817, was one of the early attempts to identify patterns among the chemical elements. This law suggested that certain groups of three elements, called triads, exhibited similar chemical properties, and the atomic weight of the middle element in the triad was approximately the arithmetic mean of the atomic weights of the other two elements.

In the case of phosphorus, nitrogen, and arsenic, these three elements were observed to form a triad based on their similar chemical properties. Phosphorus has an atomic weight of approximately \(31\), nitrogen around 14, and arsenic around \(75\). In this triad, the atomic weight of phosphorus \((31)\) is indeed very close to the mean of the atomic weights of nitrogen and arsenic, which is \(\frac{14 + 75}{2} = 44.5\).

One of the key observations supporting Dobereiner’s Law of Triads was that the elements within a triad tended to have similar chemical properties. For example, nitrogen, phosphorus, and arsenic are all nonmetals and exhibit some similar chemical behaviors, such as forming compounds with hydrogen and oxygen.

While Dobereiner's law worked for some triads, it was not universally applicable to all groups of three elements. Moreover, the concept of triads became less useful as more elements were discovered, and it was eventually replaced by more comprehensive periodic laws, such as Mendeleev’s Periodic Law and the modern periodic table.

Despite its limitations, Dobereiner’s Law of Triads represented an early step toward organizing the chemical elements and identifying patterns among them. It provided inspiration for later chemists, including Dmitri Mendeleev, who developed more systematic approaches to categorizing the elements, leading to the development of the periodic table.

In summary, Dobereiner’s Law of Triads was an early attempt to identify patterns among the chemical elements based on their similar properties and atomic weights. While it had limitations and was eventually superseded by more comprehensive periodic laws, it played a significant role in the development of our understanding of the periodicity of elements.