Answer
There are $ 6.44\times 10^{- 4}$ moles of caffeine in a cup, which is equal to $3.88 \times 10^{20}$ molecules.
Work Step by Step
1. Calculate the molar mass $(C_8H_{10}N_4O_2)$:
12.01* 8 + 1.008* 10 + 14.01* 4 + 16* 2 = 194.2g/mol
2. Calculate the number of moles $(C_8H_{10}N_4O_2)$
** 125 mg = $125 \times 10^{-3} g = 0.125 g$
$n(moles) = \frac{mass(g)}{mm(g/mol)}$
$n(moles) = \frac{ 0.125}{ 194.2}$
$n(moles) = 6.44\times 10^{- 4}$
3. Find the number of molecules:
$6.44\times 10^{- 4} mol \times \frac{6.022 \times 10^{23} molecules}{1 mol} = 3.88 \times 10^{20}$
