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A mysterious white powder found at a crime scene is analyzed and found to contain 66.9 ± 0.5% carbon by mass. One of the investigators hypothesizes that the substance is cocaine, [tex]C_{17}H_{21}NO_{4}[/tex]. What is the percent carbon, by mass, in cocaine?

Answer :

Final answer:

The percent by mass of carbon in the compound cocaine, C17H21NO4, is calculated to be approximately 67.3%, which tends to confirm the investigator's hypothesis that the white substance found at the crime scene could be cocaine.

Explanation:

The subject of this problem can be classified as Chemistry, specifically dealing with the concept of percent composition of a compound. The percent by mass of an element in a compound can be computed through the formula (mass of element/molar mass of compound) x 100%. In the suspected cocaine (C17H21NO4), we first need to calculate the formula's molar mass: cocaine's molar mass = 17(12.01 g/mol C) + 21(1.01 g/mol H) + 1(14.01 g/mol N) + 4(16.00 g/mol O) = 303.35 g/mol. Then, compute for the mass of carbon: mass of C = 17(12.01 g/mol) = 204.17 g/mol. Now we can calculate the percent carbon in cocaine: (204.17 g/mol carbon / 303.35 g/mol cocaine) x 100% = 67.3%. This is close to the 66.9 /- 0.5% carbon found in the sample from the crime scene, so it is plausible that the white material could be cocaine.

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