The molecular formula of aspartame, the artificial sweetener marketed as NutraSweet®, is C₁₄H₁₈N₂O₅. (c) How many molecules of aspartame are present in 1.00 mg of aspartame?

Verified step by step guidance

1. Convert the mass of aspartame from milligrams to grams by using the conversion factor: 1 mg = 0.001 g.
2. Calculate the molar mass of aspartame (C_{14}H_{18}N_{2}O_{5}) by adding the atomic masses of all the atoms in the formula: 14 carbon atoms, 18 hydrogen atoms, 2 nitrogen atoms, and 5 oxygen atoms.
3. Use the molar mass to convert the mass of aspartame in grams to moles by dividing the mass in grams by the molar mass.
4. Use Avogadro's number (6.022 \times 10^{23} molecules/mol) to convert the number of moles of aspartame to the number of molecules by multiplying the moles by Avogadro's number.
5. The result from the previous step gives the number of molecules of aspartame in 1.00 mg.

Key Concepts

Molecular Formula

A molecular formula represents the number and types of atoms in a molecule. For aspartame, C14H18N2O5 indicates it contains 14 carbon atoms, 18 hydrogen atoms, 2 nitrogen atoms, and 5 oxygen atoms. Understanding the molecular formula is essential for calculating the molar mass and determining the number of molecules in a given mass.

Molar Mass

The molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the molar mass of aspartame, one must sum the atomic masses of all atoms in its molecular formula. This value is crucial for converting between mass and the number of molecules using Avogadro's number.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of particles (atoms, molecules, etc.) in one mole of a substance. This constant allows for the conversion between the mass of a substance and the number of molecules. In the context of aspartame, it helps determine how many molecules are present in a specified mass, such as 1.00 mg.