Spinel is a mineral that contains 37.9% Al, 17.1% Mg, and45.0% O by mass and has

Question

Spinel is a mineral that contains 37.9% Al, 17.1% Mg, and45.0% O by mass and has a density of 3.28 g/cm3. If the crystal structure is cubic with an edge length of 809 pm,how many total atoms are there in a unit cell? (I know I need to find the empirical formula first which comesout to Al2MgO4. They gave me a densityas well as an edge length. I know by taking the cube of theedge length will give me the unit cell's volume, (8.09 x10-10 cm)3= 5.295 x10-28cm3. My molar mass is 142.268g/mol. I figure that in order to find the number ofatoms/unit cell, I need to have something like this:

Explanation / Answer

mass of 1 unit cell = volume*density mass '' = (809 pm)^3 * 3.28 g/cm3   *(100 cm/1e12 pm)^3 =1.73667842e-21 grams => convert to atomic mass units with Avogadro's constant 1.73667842e-21 grams *6.022e23 = 1045.82774 amu formula mass of 142 (given by you). 37.9/27 = 1.4037037 17.1/24.3 = 0.703703704 45/16 = 2.8125 => Al2MgO4 1045.8 amu * 1 formula unit / 142.3 amu *( 7 atom/ formulaunit) = 51.5 ~ 52

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