The density of mercury is 13.6 g / mL. Calculate approximately the diameter of an atom of mercu

step 1 Hello everyone so the N .A is 6 .023 into 10 the power 23 Atomic weight of HG that is equal to 2

The density of mercury is 13.6 g / mL. Calculate...

The density of mercury is $13.6 \mathrm{~g} / \mathrm{mL}$. Calculate approximately the diameter of an atom of mercury assuming that each atom is occupying a cube of edge length equal to the diameter of the mercury atom.

Key Concepts

Volume per Atom Calculation

To determine the space an individual atom occupies, one first calculates the volume of one mole of the substance using its density and molar mass, and then divides this volume by Avogadro's number. This provides the average volume assigned to a single atom in the material.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, represents the number of atoms or molecules in one mole of a substance. This constant is essential for calculating the volume occupied by a single atom by dividing the molar volume by Avogadro's number.

Cube Geometry

Assuming that each atom occupies a cubic volume allows us to relate the atomic volume to a measurable length. The volume of a cube is calculated as the cube of its edge length, so by taking the cube root of the volume per atom, one obtains an approximate diameter of the atom when the edge length is equated to the atomic diameter.

Density

Density is defined as the mass per unit volume of a substance. In problems involving atoms and molecules, knowing the density allows one to relate the total mass of a sample to the volume it occupies, thereby providing a means to calculate the space attributed to a single atom when combined with molar quantities.

Molar Mass

Molar mass is the mass of one mole of a substance and is a key factor in connecting macroscopic measurements (like grams and milliliters) to the number of atoms or molecules present. It is used along with density to determine the volume occupied by one mole of a substance.

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