An average cup of coffee contains about 125 mg of caffeine, C8H10N4O2. How many moles of caffeine are in a cup? How many molecules of caffeine?

검증된 단계별 안내

Calculate the molar mass of caffeine, C_8H_{10}N_4O_2, by adding the atomic masses of all the atoms in the formula.

Convert the mass of caffeine in the coffee cup from milligrams to grams by dividing by 1000.

Use the formula: number of moles = mass (g) / molar mass (g/mol) to find the number of moles of caffeine.

Use Avogadro's number, 6.022 \(\times\) 10^{23} molecules/mol, to convert the number of moles of caffeine to the number of molecules.

Multiply the number of moles by Avogadro's number to find the total number of caffeine molecules in the cup.

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주요 개념

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Moles and Molar Mass

A mole is a unit in chemistry that represents 6.022 x 10^23 entities, such as atoms or molecules. The molar mass of a substance, measured in grams per mole (g/mol), is the mass of one mole of that substance. For caffeine (C8H10N4O2), the molar mass can be calculated by summing the atomic masses of its constituent elements, which is essential for converting grams to moles.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of particles in one mole of a substance. This constant allows chemists to relate the mass of a substance to the number of molecules it contains. In the context of caffeine, once the number of moles is determined, Avogadro's number can be used to calculate the total number of caffeine molecules in a cup of coffee.

Dimensional Analysis

Dimensional analysis is a mathematical technique used to convert units from one system to another. In chemistry, it is often employed to relate mass, moles, and number of particles. By using conversion factors, such as molar mass and Avogadro's number, one can systematically convert the mass of caffeine in a cup of coffee to moles and then to the number of molecules.