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A metal crystallizes in fcc structure with a unit cell side of 500 pm. If the density of the crystal is 1.33 g/cc, the molar mass of the metal is closed to:
- a)23
- b)24
- c)25
- d)26
Correct answer is option 'C'. Can you explain this answer?
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A metal crystallizes in fcc structure with a unit cell side of 500 pm....
Given data:
- FCC structure
- Unit cell side = 500 pm = 500 x 10^-12 m
- Density = 1.33 g/cc
To find: Molar mass of the metal
Formula for density:
Density = (Z x M) / (a^3 x N_A)
where,
Z = number of atoms per unit cell, for FCC structure Z = 4
M = molar mass of the metal
a = unit cell side
N_A = Avogadro's number = 6.022 x 10^23 atoms/mol
Rearranging the above formula to find M:
M = (Density x a^3 x N_A) / (Z)
Substituting the given values:
M = (1.33 g/cc x (500 x 10^-12 m)^3 x 6.022 x 10^23 atoms/mol) / 4
M = 25.03 g/mol
Therefore, the molar mass of the metal is approximately 25 g/mol, which is closest to option (c).
- FCC structure
- Unit cell side = 500 pm = 500 x 10^-12 m
- Density = 1.33 g/cc
To find: Molar mass of the metal
Formula for density:
Density = (Z x M) / (a^3 x N_A)
where,
Z = number of atoms per unit cell, for FCC structure Z = 4
M = molar mass of the metal
a = unit cell side
N_A = Avogadro's number = 6.022 x 10^23 atoms/mol
Rearranging the above formula to find M:
M = (Density x a^3 x N_A) / (Z)
Substituting the given values:
M = (1.33 g/cc x (500 x 10^-12 m)^3 x 6.022 x 10^23 atoms/mol) / 4
M = 25.03 g/mol
Therefore, the molar mass of the metal is approximately 25 g/mol, which is closest to option (c).
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Community Answer
A metal crystallizes in fcc structure with a unit cell side of 500 pm....
Just apply the formula
density = n ×m / Na. V
density = n ×m / Na. V
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