아보가드로 수 계산. Ba bcc 502 pm 3.50 g/cm3 68%

아보가드로 수 계산. Ba bcc 502 pm 3.50 g/cm3 68%

 

 

Barium metal crystallizes in a body-centered cubic lattice (the Ba atoms are at the lattice points only). The unit cell edge length is 502 pm, and the density of the metal is 3.50 g/cm3. Using this information, calculate Avogadro's number.

[Hint: First calculate the volume (in cm3) occupied by 1 mole of Ba atoms in the unit cells. Next calculate the volume (in cm3) occupied by one Ba atom in the unit cell. Assume that 68% of the unit cell is occupied by Ba atoms.]

 

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Ba의 몰질량 = 137.33 g/mol

 

 

 

body-centered cubic = 2 atoms/unit cell = Z

( 참고 https://ywpop.tistory.com/12440 )

( 참고 https://ywpop.tistory.com/7276 )

 

 

 

(502 pm) (1 m / 10^12 pm) (100 cm / 1 m) = 5.02×10^(-8) cm

 

(5.02×10^(-8) cm)^3 = 1.265×10^(-22) cm^3 = V

 

 

 

d = [Z × M] / [V × N_A] 또는

d = (M × Z) / (N_A × a^3)

( 참고 https://ywpop.tistory.com/12439 )

 

N_A = [Z × M] / [V × d]

= [2 × 137.33 g/mol] / [(1.265×10^(-22) cm^3) × 3.50 g/cm^3]

= [2 × 137.33] / [(1.265×10^(-22)) × 3.50]

= 6.2035×10^23 /mol

 

 

 

답: 6.20×10^23 /mol

 

 

 

 

[키워드] 고체화학 기준문서, 체심 입방 격자 기준문서, bcc 기준문서