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
Solution :
Relationship between molar moss, density of the substance and unit cell edge length, is deduced in the following steps
i. If edge length of cubie unit cell is a, the volume of unit cell is sigma ^ r
ii. Suppose that mass of one particle is m and that there are particles per unit cell.
Mass of unit cell-mn (1.1)
iii. The density of unit cell (p), which is same as density of the substance is given by mass of unit cell P volume of unit cell = 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_{4} is Avogadro number) (1.3) msN Therefore, m = M / N_{4}
v. Combining Eq. (1.1) and (1.3), gives \mathcal{D} = (nM)/(sigma ^ j * N_{d}) (1.4) By knowing any four parameters of Eq. (1.4), the fifth can be calculated
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