How many molecules are in 5 mg of aspartame?

1 Answer
Jul 2, 2017

Answer:

#1 xx 10^19# #"molecules C"_14"H"_18"N"_2"O"_5#

Explanation:

We're asked to find the number of molecules of a given mass of a substance. We can do this using the molar mass of the substance and Avogadro's constant, #6.022 xx 10^23#.

Aspartame has the chemical formula #"C"_14"H"_18"N"_2"O"_5#, and its molar mass is calculated to be #294.30# #"g/mol"#.

Let's convert the given mass (#5# #"mg"#) to moles of aspartame:

#5cancel("mg")((1cancel("g"))/(10^3cancel("mg")))((1color(white)(l)"mol")/(294.30cancel("g"))) = color(red)(1.70 xx 10^-5# #color(red)("mol aspartame"#

Using Avogadro's constant, we can convert this value to molecules as so:

#color(red)(1.70xx10^-5)cancel(color(red)("mol"))((6.022xx10^23color(white)(l)"molecules")/(1cancel("mol")))#

#= color(blue)(1 xx 10^19# #color(blue)("molecules aspartame"#

which I'll leave at one significant figure, as allowed by the problem..