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. Step 1: Determine the molar mass of caffeine (C₈H₁₀N₄O₂). To do this, sum the atomic masses of all the atoms in the formula: 8 carbon (C), 10 hydrogen (H), 4 nitrogen (N), and 2 oxygen (O). Use the periodic table to find the atomic masses: C = 12.01 g/mol, H = 1.008 g/mol, N = 14.01 g/mol, O = 16.00 g/mol.
2. Step 2: Calculate the total molar mass of caffeine by multiplying the atomic mass of each element by the number of atoms of that element in the formula and then summing the results. For example, the contribution of carbon is 8 × 12.01 g/mol, hydrogen is 10 × 1.008 g/mol, and so on.
3. Step 3: Convert the mass of caffeine in the coffee cup from milligrams (mg) to grams (g). Since 1 g = 1000 mg, divide the given mass (125 mg) by 1000 to express it in grams.
4. Step 4: Use the formula for moles: \( \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \). Substitute the mass of caffeine in grams (from Step 3) and the molar mass of caffeine (from Step 2) into this formula.
5. Step 5: Perform the division to calculate the number of moles of caffeine in one cup of coffee. This will give you the final answer in moles.

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 calculation is fundamental in chemistry, as it enables the determination of how many moles of a substance are present in a given mass. In the context of caffeine, knowing the mass of caffeine in a cup of coffee allows us to calculate the number of moles, which is essential for understanding its effects and interactions in biological systems.