Caffeine has the formula C8H10N4O2. If an average cup of coffee contains approximately 125 mg of caffeine, how many moles of caffeine are in one cup?

Verified step by step guidance

1. Calculate the molar mass of caffeine (C_8H_{10}N_4O_2) by adding the atomic masses of all the atoms in the formula: 8 carbon atoms, 10 hydrogen atoms, 4 nitrogen atoms, and 2 oxygen atoms.
2. Use the atomic masses from the periodic table: Carbon (C) = 12.01 g/mol, Hydrogen (H) = 1.01 g/mol, Nitrogen (N) = 14.01 g/mol, Oxygen (O) = 16.00 g/mol.
3. Multiply the number of each type of atom by its atomic mass and sum them to find the molar mass of caffeine.
4. Convert the mass of caffeine in the coffee cup from milligrams to grams by dividing by 1000 (since 1 g = 1000 mg).
5. Use the formula: moles = mass (g) / molar mass (g/mol) to calculate the number of moles of caffeine in the cup.

Key Concepts

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To calculate the molar mass of caffeine (C8H10N4O2), you sum the atomic masses of all the atoms in its molecular formula: 8 carbon (C) atoms, 10 hydrogen (H) atoms, 4 nitrogen (N) atoms, and 2 oxygen (O) atoms. This value is essential for converting between grams and moles.

Moles

A mole is a unit in chemistry that represents a specific number of particles, typically atoms or molecules, equivalent to Avogadro's number, approximately 6.022 x 10^23. Moles provide a bridge between the atomic scale and macroscopic quantities, allowing chemists to count particles by weighing them. Understanding moles is crucial for stoichiometric calculations in chemical reactions.

Conversion from Mass to Moles

To find the number of moles from a given mass, you can use the formula: moles = mass (g) / molar mass (g/mol). In this case, you would take the mass of caffeine in the cup of coffee (125 mg, which is 0.125 g) and divide it by the molar mass of caffeine calculated earlier. This conversion is fundamental in determining the amount of substance present in a sample.