An element crystallizes in a f.c.c. lattice with cell edge of 250 pm. Calculate the density if 300 g of this element contain 2 × 10²⁴ atoms.

Solution

We space have space given colon straight a equals space 250 space pm space equals space 250 space straight x space 10 to the power of negative 12 end exponent straight m straight z equals space 4 straight m equals 300 straight g straight m equals space straight M over straight N subscript straight A space left parenthesis where space straight M space is space molar space mass right parenthesis straight M space equals space fraction numerator 300 space straight x space 6.02 space straight x space 10 to the power of 23 over denominator 2 space straight x space 10 to the power of 24 end fraction space equals space 90.3 space straight g divided by mol Density comma space straight d equals fraction numerator space zM over denominator straight a cubed straight N subscript straight A end fraction straight d space equals space fraction numerator 4 space straight x space 90.3 over denominator left parenthesis 250 right parenthesis cubed space straight x space 10 to the power of negative 36 end exponent space straight x space 6.02 space straight x space 10 to the power of 23 space end fraction space equals space 38.4 space straight g divided by space cm cubed density space equals space 38.4 space straight g divided by cm cubed

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