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Iron crystallizes in a body–centered cubic structure. The volume of one Fe atom is 9.38 x 10–24 cm3, and the density of Fe is 7.874 g/cm3. Find an approximate value for Avogadro’s number.

  • Chemistry -

    mass of Fe atom = 56 grams/mol

    how many cm^3/mol ?

    56 g / 7.874 g/cm^3 = 7.11 cm^3/mol

    how many atoms is that?

    7.11 cm^3/mol / (9.38*10^-24 cm^3/atom)
    = .76*10^24 atoms/mol

    = 7.6 *10^23
    well, not too bad :)

  • Chemistry -

    Damon's method looks MUCH simpler than what I would do but here is mine.
    volume Fe atom = 9.38E-24 cc.
    V = (4/3)*pi*r^3 and solve for r = radius
    r = about 1.31E-8 cm
    For a body centered cubic, a = edge length. 4r = a(3)^1/2 and solve for a.
    a = about 3.03E-8 cm

    volume of unit cell = a^3 = about 2.77E-23 cc.

    mass unit cell = volume x density = 2.77E-23 x 7.874 = 2.18E-22

    u.c. = unit cell
    mass u.c. = 2.18E-22 atoms/unit cell x 55.85/N and solve for N.
    That's about 5.1E23 compared to the accepted value of 6.02E23.

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