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A solid has a structure in which X atoms...

A solid has a structure in which `X` atoms are located at cubic corners of unit cell, `O` atom are at the edge centres and `Y` atoms at cube centre.
Then the formula of compound is `X_(a)Y_(b)O_(c)`
If two atoms of `O` missing from any of two edge centres per unit cell, then the molecular formula is `X_(a)Y_(b)O_(z)`. Then, find the value of `(x + y + z) - (a + b+ c)`.

Text Solution

Verified by Experts

The correct Answer is:
4
a. Number of `X` atoms `= 8 xx (1)/(8) = 1//"unit cell"`
Number of `Y` atoms `=1//"unit cell"`
number of `O` atoms `= 12 xx 1/4 = 3//"unit cell"`
Formula is: `XYO_(3) rArr X_(a)Y_(b)O_(c)`
b. Number of O atoms missing from two edge centres per unit cell `= 2 xx 1/4 = 1/2//"unit cell"`
Number of O atoms left `= 3 - 1/2 = 2.5//"unit cell"`
Formula is `XYO_(2.5) rArr X_(2)Y_(2)O_(5) rArr X_(x)Y_(y)O_(z)`
The value of `
`(x+y+z)-(a+b+c)=(2+2+5)-(1+1+3)`
`=4`
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