2. Levetiracetam is marketed under the trade name Keppra it is a drug used for to prevent seizures. The chemical formula for this drug is C&H14N202.
a. What is the molar mass of this drug? 170.209 g/mol
b. How many moles are in 15mg of this drug (1000mg = 1 gram)?
c. How many molecules are in 15mg of this drug?
d. How many oxygen atoms are in 15mg of this drug?
e. How many aitrogen atoms are in 15mg of this drug?

a. C₈H₁₄N₂O₂ = 107.209 g/mol

b. Approximately 1.4 × 10⁻⁴ moles

c. 8.423 × 10¹⁹ molecules

d. 1.685 × 10²⁰ atoms of oxygen

e. 1.685 × 10²⁰ atoms of nitrogen

Explanation:

The chemical formula is found as follows;

X×12 + 14×1 + 14×2 + 16×2 = 170.209

Where:

X = Number of carbon atoms per mole of C&H₁₄N₂O₂

Therefore;

X × 12 = 170.209 - 74 = 96.209

X = 96.209/12 = 8.017 ≈ 8

The chemical formula is C₈H₁₄N₂O₂

b. The number of moles, n, is found as follows;

c. The number of molecules, N, is given by the following relation;

N = × n

Where:

= Avogadro's number = 6.02 × 10²³ molecules

∴ N = 6.02 × 10²³ × 1.4 × 10⁻⁴ = 8.423 × 10¹⁹ molecules

d. The number of oxygen atom per molecule of C₈H₁₄N₂O₂ = 2 oxygen atoms

The number molecules of C₈H₁₄N₂O₂ in 15 mg of C₈H₁₄N₂O₂ = 8.423 × 10¹⁹ molecules

Therefore;

The number of oxygen atom per 15 mg of C₈H₁₄N₂O₂ = 2 × 8.423 × 10¹⁹  oxygen atoms

The number of oxygen atom per 15 mg of C₈H₁₄N₂O₂  = 1.685 × 10²⁰ atoms of oxygen

e. The number of nitrogen atoms are equal to the number of oxygen atoms per molecule of C₈H₁₄N₂O₂, therefore;

The number of nitrogen atoms = 1.685 × 10²⁰ atoms of nitrogen.