(c) What is the mass, in grams, of 7.70⨉10²⁰ molecules of caffeine, C₈H₁₀N₄O₂?

Verified step by step guidance

1. Determine the molar mass of caffeine (C_8H_10N_4O_2) by adding the atomic masses of all the atoms in the formula.
2. Calculate the number of moles of caffeine using Avogadro's number (6.022 \(\times\) 10^{23} molecules/mol) to convert molecules to moles.
3. Use the number of moles calculated in the previous step to find the mass in grams by multiplying it by the molar mass of caffeine.
4. Set up the conversion factor to go from molecules to grams, ensuring units cancel appropriately.
5. Perform the calculation to find the mass in grams of the given number of caffeine molecules.

Key Concepts

Molecular Weight

Molecular weight, or molar mass, is the mass of one mole of a substance, expressed in grams per mole (g/mol). For caffeine (C8H10N4O2), the molecular weight is calculated by summing the atomic weights of all the atoms in its formula: 8 carbon (C), 10 hydrogen (H), 4 nitrogen (N), and 2 oxygen (O) atoms. This value is essential for converting between the number of molecules and mass.

Avogadro's Number

Avogadro's number, approximately 6.022 × 10^23, is the number of atoms, ions, or molecules in one mole of a substance. This constant allows chemists to relate the macroscopic scale of substances (grams) to the microscopic scale (molecules). In this question, it is used to convert the given number of caffeine molecules into moles, which can then be converted to mass.

Conversion from Molecules to Grams

To find the mass of a substance from the number of molecules, one must first convert the number of molecules to moles using Avogadro's number, and then multiply the number of moles by the molecular weight. This two-step conversion is crucial for solving the problem, as it bridges the gap between the microscopic quantity of molecules and the macroscopic quantity of mass.