Filter coffee contains caffeine at a concentration of 3.361x10^-3 mol dm^-3. What is the mass of caffeine in a 250ml mug of the coffee?

Molar mass of C₈H₁₀N₄O₂ (caffeine)
= (12.0×8 + 1.0×10 + 14.0×4 + 16.0×2) g/mol
= 194.0 g/mol

Mass of caffeine
= (3.361 × 10⁻³ mol/L) × (250/1000 L) × (194.0 g/mol)
= 0.163 g

https://pubchem.ncbi.nlm.nih.gov/search/#collection=compounds&query_type=mf&query=C8H10N4O2&sort=mw&sort_dir=asc

According to the website above, this is the formula of caffeine.
C8H10N4O2
Let’s determine the mass of one mole of this compound.

Molar mass = 12 * 8 + 10 + 14 * 4 + 16 * 2 = 194 grams

3.36 * 10^-2 mol dm^-3

One cubic decimeter is the same as one liter. The information above means one liter of this solution contains 3.36 * 10^-3 mole of caffeine. Let’s determine the mass of caffeine in one liter of this solution.

Mass per liter = 3.36 * 10^-3 * 194 = 0.65184 grams
250 milliters is one fourth of a liter.

Mass = ¼ * 0.65184 = 0.16296 gram

If you need to round the answer to three significant digits, the mass is 0.163gram. I hope this is helpful for you.