# How many molecules are in 5 mg of aspartame?

Jul 2, 2017

$1 \times {10}^{19}$ ${\text{molecules C"_14"H"_18"N"_2"O}}_{5}$

#### 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, $6.022 \times {10}^{23}$.

Aspartame has the chemical formula ${\text{C"_14"H"_18"N"_2"O}}_{5}$, and its molar mass is calculated to be $294.30$ $\text{g/mol}$.

Let's convert the given mass ($5$ $\text{mg}$) 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..