Aspartame is an artificial sweetener that is 160 times sweeter than sucrose (table sugar) when dissolved in water. It is marketed as NutraSweet. The molecular formula for aspartame is C14H18N2O5.
a) Calculate the molar mass of for 2 moles of aspartame.
b) How many moles of molecules are present in 35.0 g of aspartame?
c) Calculate the mass in grams of 4.56 mol of aspartame.
d) How many molecules are in 4.0 ng of aspartame?
e) How many atoms of oxygen are in 2.2 g of aspartame?
f) What is the mass in grams of 1.0 x 10^32 molecules of aspartame?
g) What is the mass in grams of three molecules of aspartame?
The correct answer and explanation is :
Let’s solve each part of this question step by step using the molecular formula of aspartame: C₁₄H₁₈N₂O₅
a) Molar Mass of 2 moles of aspartame
First, calculate the molar mass of aspartame:
- C: 14 × 12.01 g/mol = 168.14 g/mol
- H: 18 × 1.008 g/mol = 18.144 g/mol
- N: 2 × 14.01 g/mol = 28.02 g/mol
- O: 5 × 16.00 g/mol = 80.00 g/mol
Total molar mass = 168.14 + 18.144 + 28.02 + 80.00 = 294.30 g/mol
So, for 2 moles:
2 × 294.30 = 588.60 g
b) Moles in 35.0 g of aspartame
Moles = mass / molar mass = 35.0 g / 294.30 g/mol ≈ 0.119 mol
c) Mass of 4.56 mol of aspartame
Mass = moles × molar mass = 4.56 mol × 294.30 g/mol ≈ 1342.01 g
d) Molecules in 4.0 ng of aspartame
Convert 4.0 ng to grams: 4.0 × 10⁻⁹ g
Moles = (4.0 × 10⁻⁹ g) / 294.30 g/mol ≈ 1.359 × 10⁻¹¹ mol
Molecules = moles × Avogadro’s number
≈ 1.359 × 10⁻¹¹ × 6.022 × 10²³ ≈ 8.19 × 10¹² molecules
e) Oxygen atoms in 2.2 g of aspartame
Moles = 2.2 g / 294.30 g/mol ≈ 0.00747 mol
Molecules = 0.00747 × 6.022 × 10²³ ≈ 4.5 × 10²¹ molecules
O atoms = 4.5 × 10²¹ × 5 = 2.25 × 10²² atoms of O
f) Mass of 1.0 × 10³² molecules
Moles = (1.0 × 10³²) / (6.022 × 10²³) ≈ 1.661 × 10⁸ mol
Mass = 1.661 × 10⁸ mol × 294.30 g/mol ≈ 4.89 × 10¹⁰ g
g) Mass of 3 molecules of aspartame
Moles = 3 / (6.022 × 10²³) ≈ 4.984 × 10⁻²⁴ mol
Mass = 4.984 × 10⁻²⁴ mol × 294.30 g/mol ≈ 1.47 × 10⁻²¹ g
Explanation (Approx. 300 words):
Aspartame is a low-calorie artificial sweetener known for being much sweeter than table sugar (sucrose), requiring a much smaller quantity to achieve the same taste. Understanding its chemical makeup and related calculations involves applying concepts from stoichiometry and molecular chemistry. The molecular formula of aspartame is C₁₄H₁₈N₂O₅, which provides us with the number and type of atoms in a single molecule.
The molar mass is a critical value that tells us how much one mole (6.022 × 10²³ molecules) of a substance weighs. By adding the atomic masses of each atom in aspartame, we get approximately 294.30 g/mol. This value helps in converting between mass and number of molecules or moles, depending on the given problem.
To find out how many moles are in a certain mass (like 35.0 g), we divide by the molar mass. Conversely, if moles are given, we multiply to get the mass. The relationship between molecules and moles involves Avogadro’s number (6.022 × 10²³ molecules/mol), a fundamental constant in chemistry.
When we’re working with very small amounts like nanograms (ng), the math involves converting to grams, then using the same steps. Determining how many oxygen atoms are present involves multiplying the number of molecules by how many oxygen atoms are in each molecule—five in this case. Even from a few grams of aspartame, the number of individual atoms or molecules can reach into the trillions or more.
Such calculations showcase how chemistry allows us to understand matter at both the molecular and macroscopic levels, providing essential insights into everything from food science to pharmaceuticals.