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. Determine the molar mass of caffeine (C_8H_{10}N_4O_2) by adding the atomic masses of all the atoms in the formula.
2. Calculate the total molar mass: (8 \times \text{atomic mass of C}) + (10 \times \text{atomic mass of H}) + (4 \times \text{atomic mass of N}) + (2 \times \text{atomic mass of O}).
3. Convert the mass of caffeine from milligrams to grams by dividing by 1000, since there are 1000 mg in a gram.
4. Use the formula $\text{moles}=\frac{\text{mass in grams}}{\text{molar mass}}$ to find the number of moles of caffeine.
5. Substitute the values into the formula to calculate the moles of caffeine in the cup of coffee.

Key Concepts

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For caffeine (C8H10N4O2), the molar mass can be calculated by summing the atomic masses of all the atoms in its molecular formula. This value is essential for converting between grams and moles, allowing us to determine how many moles are present in a given mass of caffeine.

Moles

A mole is a unit in chemistry that represents a specific quantity of particles, typically atoms or molecules. One mole contains approximately 6.022 x 10^23 entities, known as Avogadro's number. Understanding moles is crucial for stoichiometric calculations, as it allows chemists to relate mass to the number of particles in a substance, facilitating conversions in chemical reactions.

Conversion from Mass to Moles

To convert mass to moles, the formula used is: moles = mass (g) / molar mass (g/mol). This relationship is fundamental in chemistry, as it enables the calculation of how many moles of a substance are present when given its mass. In the context of caffeine, knowing the mass of caffeine in a cup of coffee allows us to determine the number of moles, which is essential for various chemical analyses.