Question

How many molecules are in 100g of aspartame?

A) 3.01 x 10²⁴
B) 1.50 x 10²⁴
C) 6.02 x 10 ²³
D) 2.50 x 10²³

Answer 1

To determine the number of molecules in 100g of aspartame, convert grams to moles using the molar mass of aspartame, and then use Avogadro's number to convert moles to molecules. The correct answer is 1.50 x 10^24 molecules.

Step-by-step explanation:

Aspartame has the formula C14H18N2O2. To find the number of molecules in 100g of aspartame, we first need to convert grams to moles. The molar mass of aspartame can be calculated by adding up the atomic masses of its elements: C (carbon), H (hydrogen), N (nitrogen), and O (oxygen). Adding the atomic masses of each element in one molecule of aspartame, we get:

Molar mass of C14H18N2O2 = 12.011 x 14 + 1.008 x 18 + 14.007 x 2 + 15.999 x 2 = 294.308 g/mol

Next, we use Avogadro's number (6.022 x 10^23) to convert moles to molecules:

Number of molecules = (100g / 294.308 g/mol) x (6.022 x 10^23 molecules/mol)

Simplifying this calculation, we find that the correct answer is option B) 1.50 x 10^24.