Question

How many molecules are in 5 mg of aspartame?

Answer 1

`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..