My 1 $^{st}$ Chemistry Problem!

Chemistry Level 1

Consider an ionic solid $MX$ with $NaCl$ structure. Construct a new structure $(Z)$ whose unit cell is constructed from the unit cell of $MX$ following the sequential instructions given below. Neglect the charge balance.

$(i)$ Remove all the anions $(X)$ except the central one

$(ii)$ Replace all the face centered cations $(M)$ by anions $(X)$

$(iii)$ Remove all the corner cations $(M)$

$(iv)$ Replace the central anion $(X)$ with cation $(M)$

Find $\dfrac {N_{anions}}{N_{cations}}$ in $Z.$

where $N_{anions} , N_{cations}$ denote number of anions and cations respectively.

The answer is 3.00.

1 solution

A Former Brilliant Member
Dec 28, 2018

$MX$ has $NaCl$ type structure From instructions it is clear that in $MX$ ionic solid. Cation M - undergoes $CCP$ anion $X$ - occupies all octahedral voids

$(i)$ No. of anions left = 1

$(ii)$ No. of anions added = 3

.No. of cations left = 1

$(iii)$ No. of cations left = 0

$(iv)$ No. of cations added = 1

No. of anions left = 3

Final no. of cations in an unit cell = 1

Final no. of anions in an unit cell = 3  Ratio = $\dfrac {N_{anions}}{N_{cations}} = \dfrac 31 = \boxed{3.00}$

My 1 s t ^{st} s t Chemistry Problem!

The answer is 3.00.

1 solution

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My 1 $^{st}$ Chemistry Problem!