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Chemistry

10th Edition
Steven S. Zumdahl + 2 others
ISBN: 9781305957404

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BuyFindarrow_forward

Chemistry

10th Edition
Steven S. Zumdahl + 2 others
ISBN: 9781305957404
Textbook Problem

Argon has a cubic closest packed structure as a solid. Assuming that argon has a radius of 190. pm, calculate the density of solid argon.

Interpretation Introduction

Interpretation:

        The atomic radius of solid Argon in its cubic close packing structure is given and its density has to be determined.

Concept introduction:

        In a crystalline solid, the components are neatly stacked and closely packed in a regular pattern. The components are imagined as spheres. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing. Cubic close packing structure has face-centered cubic (FCC) unit cell.

       In face-centered cubic unit cell, each of the six corners is occupied by every single atom. Each face of the cube is occupied by one atom.

       Each atom in the corner is shared by eight unit cells and each atom in the face is shared by two unit cells. Thus the number of atoms per unit cell in FCC unit cell is,

                  8×18atomsincorners+6×12atomsinfaces=1+3=4atoms       The edge length of one unit cell is given bya=2R2where  a=edge length of unit cellR=radiusofatom

Explanation

Explanation

Calculate volume of FCC unit cell.

givendata:R=190pm=190×10-12m

volumeofunitcell=a3a=2R2a3=(2R2)3=(2×190×10-12m×1.414)3=1.55×10-22cm3

              Solid Argon has cubic close packing structure with face-centered cubic unit cells. The atomic radius of solid Argon is given. The formula for the edge length of the cubic unit cell is known as a=2R2 in which ‘a’ corresponds to edge length of the unit cell and ‘R’ corresponds to radius of the atom in the unit cell. The value is substituted and ‘a3’value is calculated. This value corresponds to the volume of the unit cell.

Calculate the mass of a unit cell of solid Argon.

Average mass of one Ar atom=atomicmassofArAvogadronumber=39

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