Caffeine is found in your coffee and your tea. Its molecular formula is C8H10N4O2. (a) Calculate the molar mass of caffeine. (b) Calculate the percent composition by mass of C, H, N, and O in caffeine. (c) Red Bull contains 80 mg of caffeine. How many molecules of caffeine are there in Red Bull? [C 12.011 amu; H 1.008 amu; N 14.008 amu; O 15.999 amu]
The Correct Answer and Explanation is:
Answer:
(a) Molar Mass of Caffeine (C₈H₁₀N₄O₂):
= (8 × 12.011) + (10 × 1.008) + (4 × 14.008) + (2 × 15.999)
= 96.088 + 10.080 + 56.032 + 31.998
= 194.198 g/mol
(b) Percent Composition by Mass:
- %C = (96.088 / 194.198) × 100 = 49.47%
- %H = (10.080 / 194.198) × 100 = 5.19%
- %N = (56.032 / 194.198) × 100 = 28.86%
- %O = (31.998 / 194.198) × 100 = 16.48%
(c) Molecules of Caffeine in 80 mg (0.080 g):
Moles of caffeine = 0.080 g / 194.198 g/mol = 0.000412 moles
Molecules = 0.000412 mol × 6.022 × 10²³ mol⁻¹ = 2.48 × 10²⁰ molecules
Explanation
Caffeine is a stimulant commonly found in coffee, tea, and energy drinks. To understand how much caffeine is present and how it behaves chemically, we first calculate its molar mass, which is the mass of one mole of its molecules. The molecular formula of caffeine is C₈H₁₀N₄O₂, meaning it contains 8 carbon atoms, 10 hydrogen atoms, 4 nitrogen atoms, and 2 oxygen atoms. Using the atomic masses (C = 12.011, H = 1.008, N = 14.008, O = 15.999), we multiply each by the number of atoms and sum them:
(8×12.011) + (10×1.008) + (4×14.008) + (2×15.999) = 194.198 g/mol.
Next, we determine the percent composition by mass, which tells us how much of each element contributes to the total mass of the compound. This is useful in chemical analysis and quality control. We calculate this by dividing the total mass contributed by each element by the molar mass and multiplying by 100%. For example, carbon contributes 96.088 g, so (96.088 / 194.198) × 100 = 49.47%. We do the same for hydrogen (5.19%), nitrogen (28.86%), and oxygen (16.48%).
Finally, we determine how many molecules of caffeine are in an 80 mg sample (as in a can of Red Bull). We convert 80 mg to grams (0.080 g), divide by the molar mass to find moles, then multiply by Avogadro’s number (6.022×10²³) to get the number of molecules: 0.000412 mol × 6.022×10²³ = approximately 2.48×10²⁰ molecules. This large number reflects the tiny size and vast quantity of molecules in even small amounts of substance.
