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20.95 g of caffeine, C₈H₁₀N₄O₂

Explanation:

From the question given above, the following data were obtained:

Number of molecules of C₈H₁₀N₄O₂ = 6.5×10²² molecules

Mass of C₈H₁₀N₄O₂ =?

From Avogadro's hypothesis,

1 mole of C₈H₁₀N₄O₂ = 6.02×10²³ molecules

Next, we shall determine the mass of 1 mole of C₈H₁₀N₄O₂. This can be obtained as follow:

1 mole of C₈H₁₀N₄O₂ = (8×12) + (10×1) + (4×14) + (2×16)

= 96 + 10 + 56 + 32

1 mole of C₈H₁₀N₄O₂ = 194 g

Thus,

194 g of C₈H₁₀N₄O₂ = 6.02×10²³ molecules

Finally, we shall determine the mass of caffeine, C₈H₁₀N₄O₂ that contains 6.5×10²² molecules. This can be obtained as follow:

6.02×10²³ molecules = 194 g of C₈H₁₀N₄O₂

Therefore,

6.5×10²² molecules = (6.5×10²² × 194) / 6.02×10²³

6.5×10²² molecules = 20.95 g of C₈H₁₀N₄O₂.

Therefore, 20.95 g of caffeine, C₈H₁₀N₄O₂ contains 6.5×10²² molecules

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