When gold crystallizes, it forms face-centred cubic cells. The unit cell edge length is 408 pm. Calculate the density of gold. Molar mass of gold is 197 g/mol.- Chemistry

12th class chemistry 

1.solid stata

Problem 1.1: 

When gold crystallizes, it forms face-centred cubic cells. The unit cell edge length is 408 pm. Calculate the density of gold. Molar mass of gold is 197 g/mol.

Solution:

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 1.5.2 Relationship between molar mass, density of the substance and unit cell edge length, is deduced in the following steps

i. If edge length of cubic unit cell is a, the volume of unit cell is a³.

ii. Suppose that mass of one particle is m and that there are n particles per unit cell.

Mass of unit cell = mx n (1.1)

iii. The density of unit cell (p), which is same

as density of the substance is given by mass of unit cell Pvolume of unit cell mxn a = density of substance (1.2)

iv. Molar mass (M) of the substance is given by M = mass of one particle number of particles per mole (N, is Avogadro number) (1.3) = mxN Therefore, m= M/N

v. Combining Eq. (1.1) and (1.3), gives

nM PN (1.4) By knowing any four parameters of Eq. (1.4), the fifth can be calculated