Question

A certain compound with a molar mass of 120.0 g/mol crystallizes with the sodium chloride (rock salt) structure. The length of an edge of the unit cell is 461 pm. What is the density of this compound

Answer 1

The density of the compound is 4.64 g/
`cm^(3)`.

Step-by-step explanation:

Sodium chloride crystallize as FCC face centered cubic structure. It consist of four atoms of NaCl. So the unknown compound which crytallizes like NaCl wil have volume as:

radius in fcc is calculated as

`√(2a)` = 4r

putting the value where a is length of the edge.

`√(2X461)`

= 651.9 = 4r so r= 162.98 pm

volume is calculated by the formula:

`(4)/(3)` π
`r^(3)`

putting the values,

`(4)/(3)` x 3.14 x (
`1.62 X 10^(-8)`)^3

= 4.25X 10 ^-24

1.7 X
`10^(-23)`
`cm^(3)` = volume of the fcc cell.

mass of the substance = 4 x 120 x 1.6605 x 10^(-24) g/u) (as it contains four atoms)

= 7.9x
`10^(-23)`

density =
`(mass)/(volume)`

putting the values

density =
`( 7.9x10^-23 )/(1.7 x 10^(-23) )`

density = 4.64 g/
`cm^(3)`