Problem 50 - Chemistry The Central Science

Question

For each of the following groups which metal would you expect to have the highest melting point; (a) gold (Au), rhenium (Re), or cesium (Cs); (b) rubidium (Rb), molybdenum (Mo), or indium (In); (c) ruthenium (Ru), strontium (Sr), or cadmium (Cd)?

Step-by-Step Solution

Answer

In summary, the metals with the highest melting points for each group are: (a) Rhenium (Re), (b) Molybdenum (Mo), and (c) Ruthenium (Ru). This is due to their smaller atomic radii, higher effective nuclear charges, and stronger metallic bonding compared to the other metals in their respective groups.

Step 1: Understanding factors affecting melting points of metals

The melting point of a metal depends on the strength of the metallic bonds within its structure. This strength, in turn, depends on factors such as: 1. Number of valence electrons that are available for bonding. 2. The atomic radius (distance between the nucleus and the outermost electron shell). 3. The effective nuclear charge (the positive charge experienced by the valence electrons). A higher number of valence electrons, a smaller atomic radius, and a greater effective nuclear charge will generally result in stronger metallic bonds and therefore a higher melting point.

Step 2: Comparing the metals in Group A

(а) Gold (Au), Rhenium (Re), or Cesium (Cs): Gold (Au): Atomic Number - 79 Rhenium (Re): Atomic Number - 75 Cesium (Cs): Atomic Number - 55 Looking at the periodic table, we notice that cesium (Cs) is an alkali metal, which is far from rhenium and gold in the table. Alkali metals generally have a larger atomic radius, fewer valence electrons, and weaker metallic bonding compared to transition metals. As a result, Cs will likely have a lower melting point than gold and rhenium. Comparing gold (Au) and rhenium (Re), both are transition metals with similar properties, but rhenium (Re) has a smaller atomic radius and a higher effective nuclear charge, indicating stronger metallic bonding. Therefore, rhenium (Re) is expected to have the highest melting point in group A.

Step 3: Comparing the metals in Group B

(b) Rubidium (Rb), Molybdenum (Mo), or Indium (In): Rubidium (Rb): Atomic Number - 37 Molybdenum (Mo): Atomic Number - 42 Indium (In): Atomic Number - 49 We notice that Rubidium (Rb) is an alkali metal, while molybdenum (Mo) is a transition metal and indium (In) is a post-transition metal (metalloid). As in the previous group, alkali metals have weaker metallic bonding and lower melting points compared to transition metals, so Rubidium (Rb) is not expected to have the highest melting point. Comparing molybdenum (Mo) and indium (In), molybdenum (Mo) is a transition metal with a smaller atomic radius and higher effective nuclear charge than indium (In), resulting in stronger metallic bonding. Therefore, molybdenum (Mo) is expected to have the highest melting point in group B.

Step 4: Comparing the metals in Group C

(c) Ruthenium (Ru), Strontium (Sr), or Cadmium (Cd): Ruthenium (Ru): Atomic Number - 44 Strontium (Sr): Atomic Number - 38 Cadmium (Cd): Atomic Number - 48 Strontium (Sr) is an alkaline earth metal, which generally have weaker metallic bonds and lower melting points than transition metals like ruthenium (Ru) and post-transition metals like cadmium (Cd). Comparing ruthenium (Ru) and cadmium (Cd), ruthenium (Ru) has a smaller atomic radius and higher effective nuclear charge, which results in stronger metallic bonding. Therefore, ruthenium (Ru) is expected to have the highest melting point in group C. In summary, for each group, the metals with the highest melting points are: (a) Rhenium (Re) (b) Molybdenum (Mo) (c) Ruthenium (Ru)