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The well know mineral flourite is chemic...

The well know mineral flourite is chemically calcium fluoride. It is a well known fact that in one unit cell of this mineral, there are four `Ca^(2+)` ions and eight `F^(-)` ions and `Ca^(2+)` ions are arranged in f.c.c. lattice. The `F^(-)` ions fill all the tetrahedral holes in the face centred cubic lattice of `Ca^(2+)` ions. The edge length of the unit cell is `5.46xx10^(-8)` cm. The density of the solid is `3.18"g cm"^(-3)`. Use this information to calculate Avogadro's number (Molar mass of `CaF_(2)=78.0"g mol"^(-1)`)

Text Solution

Verified by Experts

Density = `(Z xx M)/(a^3 xx N_A)`
`3.18 g cm^(-3) = (4 xx 78.08 g mol^(-1))/((5.46 xx 10^(-8) cm)^(3) xx N_A)`
`:. N_A = 6.02 xx 10^(23)`.
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The well known mineral fluorite is chemically calcuim fluride. It is well known that in one unit of this mineral, there are 4 Ca^(2+) ions and 8 F^(-) ions, and that Ca^(2+) ions are arranged in a fcc lattice. The F^(-) ions fill all the tetrahedral holes in the face - centred cubic lattice of Ca^(2+) ions. The edge of the unit cell is 5.46 xx 10^(-8) cm in length . The density of the solid is 3.18 " g cm"^(-3) . Use this information to calculate Avogadro's number ( Molar mass of CaF_(2) = 78.08 " g mol" ^(-1) )

The well known mineral fluorite is chemically calcium fluoride. It is well known that is one unit of this mineral, there are 4 Ca^(2+) ions and 8 F^- ions, and that Ca^(2+) ions are arranged in a fcc lattice. The F^- ions fill all the tetrahedral holes in the face-centred cubic lattice of Ca^(2+) ions. The edge of the unit cell is 5.46xx10^(-8) cm in length . The density of the solid is 3.18 "g cm"^(-3) . Use this information to calculate Avogadro's number (Molar mass of CaF_2=78.08 "g mol"^(-1) )

Knowledge Check

  • Lithium iodide crystal has a face centred cubic unit cell . If the edge length of the unit cell is 550 pm , determine the ionic radius of I^(-) ion

    A
    `144.4` pm
    B
    `294.4 p m`
    C
    `194.4 p m`
    D
    `164.4 p m`

  • The edge length of sodium chloride unit cell is 564 pm. If the size of Cl^- ion is 181 pm. The size of Na^+ ion will be

    A
    101 pm
    B
    181 pm
    C
    410 pm
    D
    202 pm

  • The Ca^(2+) and F^(-) ions are located in CaF_(2) crystal, respectively at face centred cubic lattice points and in

    A
    Tetrahedral void
    B
    half of tetrahedral points
    C
    octahedral points
    D
    half of octahedral voids.

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    Explore conceptually related problems

    The well-known mineral fluorite is chemically calcium fluoride. It is known that in one unit cell of this mineral there are 4Ca^(2+) ions and 8F^(-) ions and that Ca^(2+) ions are arranged in a fce lattice. The F^(-) ions fill all the tetrahedral holes in the face-centred cubic lattice of Ca^(2+) ions. The edge of the unit cell is 5.46 xx 10^(-8) cm in length. The density of the solid is 3.18 g cm^(-3) . Use this information to calculate Avogadro's number. [Molar mass of CaF_(2) = 78.08 g mol^(-1) ]

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