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A confiscated white substance, suspected of being cocaine, was purified by a forensic chemist and subjected to elemental analysis. Combustion of a 50.86-mg sample yielded 150.0 mg CO2 and 46.05 mg H2O. Analysis for nitrogen showed that the compound contained 9.39% N by mass. The formula of cocaine is C17H21NO4. Can the forensic chemist conclude that the suspected compound is cocaine?

  • stoichiometry -

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  • stoichiometry -

    In the cocaine formula for every N (14 g/mole) atom here are 17 C (12g) atoms and 2 H (1g) atoms
    Therefore thee ratios of masses of those three elements must be:
    N -- 14
    C --17*12 = 204
    H --2*1 =2

    Now how many moles of C in 150 g CO2?
    (I am going to use grams instead of milligrams for everything because we are only interested in ratios in the end)
    mole of CO2 = 12 +32 = 44 g/mole
    so we have 150/44 = 3.41 moles CO2
    and therefore 3.41 moles of C
    which is 3.41 * 12 = 40.9 grams of C

    Now how many moles of H in 46.05 g of H2O?
    mole of H2O = 2+16 = 18 g/mole
    so we have 46.05/8 = 2.56 moles H2O
    and thus 2*2.56 = 5.12 moles of H

    Now check ratios of either moles or grams
    moles C/moles H = 3.41/5.12 = .666
    but we know that we need 17 moles C to every 2 moles H if it is cocaine!
    check my arithmetic and do more similar analysis for Nitrogen as well

  • typo -

    46/18 not 46/8
    The calculation is right above but I typed 8 instead of 18

  • stoichiometry -

    It says 21 moles of Hydrogen , not 2 !

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