Answer to Question #123113 in General Chemistry for Fırat

Question #123113
S - 1) The specific weight of the X2Y3 compound is 4.8 g / cm3. The atomic weights of X and Y are 30 and 15 g respectively, the atomic radii are 0.55 and 1.5 Angstroms. Avagadro number: 6.02x1023.

a) How many atoms are there in 1 cm X2Y3?

b) How many atoms are in 1 g of X2Y3.
1
Expert's answer
2020-06-22T09:17:43-0400

a)

we solve by the formula

"\\rho=\\frac{nA}{VcNa}"


p=4.8g / cm3

A=105 g/mol

Na=6.02x1023.  

Vc=a^3

"a=4r\\sqrt{2}"

0.55A=0.055 10^-7cm3

1.5A=0.15 10^-7cm3

"a=4\\times0.055\\times10^{-7}\\times\\sqrt{2}=0.31\\times10^{-7}"

"Vc=(0.31\\times10^{-7})^3=0.03\\times10^{-21}"

"a=4\\times0.15\\times10^{-7}\\times\\sqrt{2}=0.31\\times10^{-7}=0.84\\times10^{-7}"

"Vc=(0.84\\times10^{-7})^3=0.59\\times10^{-21}"

"Vc=0.59\\times10^{-21}+0.03\\times10^{-21}=0.62\\times10^{-21}"


"4.8=\\frac{n\\times105}{0.62\\times10^{-21}\\times6.02\\times10{23}}"


n=17



b)

find the mass

"\\gamma=\\frac{m}{V}"

"m=\\gamma\\times V=4.8\\times"0.62\times10^{-21}=2.976\times10^{-21}

"n=\\frac{m\\times M}{Na}=\\frac{2.976\\times10^{-21}\\times105}{6.02\\times10^{23}}=51.9\\times10^{-44}"


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