(a) In what unique way did Mendeleev order the elements to make his discovery? (b) What was his discovery? (c) How does his ordering differ from the modern ordering?

Mendeleev arranged the known elements in a tabular format according to their atomic weights, while also considering their chemical properties and similar reactivity patterns. The periodicity of the elements in terms of chemical properties was the base of this arrangement.

Through his unique ordering, Mendeleev was able to discover the periodic law which states that the properties of elements are a periodic function of their atomic weights. This led to the formation of the first version of the periodic table - a systematic arrangement of elements based on their atomic weights and similarities in chemical properties. Mendeleev also predicted the existence of several elements that had not yet been discovered and left gaps in his table for them. This prediction later came true and validated his approach.

Mendeleev's ordering of the elements is quite similar to the modern periodic table but with a few key differences. The most significant difference is that the modern periodic table is based on the atomic number (number of protons in the nucleus) of the elements, rather than their atomic weights, as in Mendeleev's original table. Additionally, Mendeleev's periodic table did not include any of the noble gases (Group 18) since they were not discovered at that time. The modern periodic table also arranges the elements into more distinct groups and periods, better displaying the trends in properties, such as reactivity, electronegativity, and atomic radius. There are other minor differences as well, but the primary distinction between Mendeleev's ordering and the modern ordering is the use of atomic number rather than atomic weight in the modern periodic table.