Ice crystallizes in a hexagonal lattice. At the low temperature at which the structure was determined, the lattice constants were `a = 4.53 Å` and `c = 7.41 Å` (as shown in fig.) How many `H_(2)O` molecules are contained in a unit cell ? (Density of ice `= 0.92 gm//c c`)

Options

A. 1
B. 2
C. 3
D. 4

Explanation

The volume V of the unit cell in Figures:
V=Area of rhombus base xx Height (c)
`=(a^(2)sin60^(@))xxc=(4.53overset(@)A)^(2)(0.866)(7.41overset(@)A)`
`=132overst(@)A^(3)=132xx10^(-24)cm^(3)`
Mass of unit cell=V xx Density
`=(132xx10^(-24)cm^(3))(0.92gcm^(-3))(6.02xx10^(23))`
=73g
Number of moles of `H_(2)O=(73)/(18)=4`.