Question

How many grams of caffeine are found in 6.500 x 10^22 molecules of caffeine?

Answer 1

21.614 grams are found in
`6.5 * 10^(22)` molecules of caffeine.

Step-by-step explanation:

The chemical formula for caffeine is
`C_(8)H_(10)N_(4)O_(2)`, the molar weight of caffeine is:

`M = 8\cdot \left(12.011\,(g)/(mol) \right) + 16\cdot \left(1.008\,(g)/(mol) \right)+4\cdot \left(14.007\,(g)/(mol) \right)+2\cdot \left(15.999\,(g)/(mol) \right)`

`M = 200.242\,(g)/(mol)`

According to Avogadro's Law, a mol of caffeine contains
`6.022* 10^(23)` molecules. The number of grams contained in
`6.5 * 10^(22)` molecules is determined by simple rule of three:

`x = (6.5* 10^(22)\,molecules)/(6.022* 10^(23)\,molecules) * 200.242\,g`

`x = 21.614\,g`

21.614 grams are found in
`6.5 * 10^(22)` molecules of caffeine.