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Answer:
21.614 grams are found in [tex]6.5 \times 10^{22}[/tex] molecules of caffeine.
Explanation:
The chemical formula for caffeine is [tex]C_{8}H_{10}N_{4}O_{2}[/tex], the molar weight of caffeine is:
[tex]M = 8\cdot \left(12.011\,\frac{g}{mol} \right) + 16\cdot \left(1.008\,\frac{g}{mol} \right)+4\cdot \left(14.007\,\frac{g}{mol} \right)+2\cdot \left(15.999\,\frac{g}{mol} \right)[/tex]
[tex]M = 200.242\,\frac{g}{mol}[/tex]
According to Avogadro's Law, a mol of caffeine contains [tex]6.022\times 10^{23}[/tex] molecules. The number of grams contained in [tex]6.5 \times 10^{22}[/tex] molecules is determined by simple rule of three:
[tex]x = \frac{6.5\times 10^{22}\,molecules}{6.022\times 10^{23}\,molecules} \times 200.242\,g[/tex]
[tex]x = 21.614\,g[/tex]
21.614 grams are found in [tex]6.5 \times 10^{22}[/tex] molecules of caffeine.