How many atoms of carbon are in #"0.0235 g"# of cocaine hydrochloride, #"C"_17"H"_22"ClNO"_4#?

2 Answers

Answer:

#7.08*10^20#

Explanation:

First find the moles of carbon:

#n(C)=("0.0235 g")/("339.8168 g/mol cocaine hydrochloride") xx "17 mols C"/"1 mol cocaine hydrochloride"#

#n(C)= 1.176 xx 10^(-3)# #"mol"#s

Then multiply the moles by avogadro's constant to tell you the number of carbon atoms in the sample.

#(1.176*10^-3)(6.02*10^23)#

#=7.08*10^20# atoms of Carbon

Answer:

There are #color(blue)(7.08xx10^(20)color(white)(.)"atoms C"# in #"0.0235 g C"_17"H"_22"ClNO"_4"#.

Explanation:

The molecular formula for cocaine hydrochloride, #"C"_17"H"_22"ClNO"_4"#, tells us that one mole of #"C"_17"H"_22"ClNO"_4"# contains #"17 mol C"#.

#"0.0235 g C"_17"H"_22"ClNO"_4"# represents a fraction of a mole.

In order to determine the mol #"C"_17"H"_22"ClNO"_34"# in #"0.0235 g C"_17"H"_22"ClNO"_4"#, divide its given mass by its molar mass by multiplying by its inverse.

The molar mass of #"C"_17"H"_22"ClNO"_4"# is #"339.816 g/mol"#.
https://www.ncbi.nlm.nih.gov/pccompound?term=%22COCAINE+HYDROCHLORIDE%22

#color(blue)("Moles of Cocaine Hydrochloride"#

Divide its given mass by its molar mass by multiplying by its inverse.

#0.0235color(red)cancel(color(black)("g C"_17"H"_22"ClNO"_4))xx(1"mol C"_17"H"_22"ClNO"_4)/(339.816color(red)cancel(color(black)("g C"_17"H"_22"ClNO"_4)))="0.00006916 mol C"_17"H"_22"ClNO"_4#

#color(blue)("Atoms of Carbon"#

Multiply mol #"C"_17"H"_22"ClNO"_4# by #"17 mols C"# divided by #"1 mol C"_17"H"_22"ClNO"_4"#, then multiply by #6.022xx10^23# #"atoms/mol"#.

#0.000069161color(red)cancel(color(black)("mol C"_17"H"_22"ClNO"_4))xx(17"mol C")/(1color(red)cancel(color(black)("mol C"_17"H"_22"ClNO"_4)))="0.00117572 mol C"#

#0.00117572color(red)cancel(color(black)("mol C"))xx(6.022xx10^23"atoms C")/(1color(red)cancel(color(black)("mol C")))#

#= 7.08xx10^20"atoms C"#, rounded to three significant figures