A metal has an fcc latticed.The edge length of the unit cell is `404` pm .The density of the metal is `2.72 g//cm^(-3)` .The molar mass of the metal is
`(N_(A)` Avogadro's constant `= 6.2 xx 10^(23) mol^(-1))`

Options

A. `30 g "mol"^(-1)`
B. `27 g"mol"^(-1)`
C. `20 g"mol"^(-1)`
D. `40 g"mol"^(-1)`

Answer

B

Explanation

Density is given by
` d= (Z xx M)/(N_A a^3) ` , where Z = number of formula units present in unit cell , which is 4 for fcc
a = edge length of unit cell .M = molecular mass
`2.72 = (4 xx M)/(6.02 xx 10^23 xx (404 xx 10^(-10))^3)`
`(because 1"pm" = 10^(-10) cm)`
`M = (2.72 xx 6.02 xx (404)^3)/(4 xx 10^7) = 26.99`
` = 27 g"mol"^(-1)`