At least 25 mg of tetrahydrocannabinol (THC), the active ingredient in marijuana, is required to produce intoxication. The molecular formula of THC is C₂₁H₃₀O₂. How many molecules?

Verified step by step guidance

1. Identify the given information: 25 mg of THC and its molecular formula C_{21}H_{30}O_2.
2. Convert the mass of THC from milligrams to grams by dividing by 1000.
3. Calculate the molar mass of THC by adding the atomic masses of all the atoms in the molecular formula: (21 \times \text{atomic mass of C}) + (30 \times \text{atomic mass of H}) + (2 \times \text{atomic mass of O}).
4. Convert the mass of THC in grams to moles by dividing by the molar mass of THC.
5. Use Avogadro's number (6.022 \times 10^{23} molecules/mol) to convert the moles of THC to the number of molecules by multiplying the moles by Avogadro's number.

Key Concepts

Molecular Formula

A molecular formula represents the number and type of atoms in a molecule. For THC, the molecular formula C21H30O2 indicates it contains 21 carbon atoms, 30 hydrogen atoms, and 2 oxygen atoms. Understanding molecular formulas is essential for calculating the number of molecules in a given mass.

Molar Mass

The molar mass of a compound is the mass of one mole of its molecules, typically expressed in grams per mole (g/mol). For THC, the molar mass can be calculated by summing the atomic masses of all atoms in its molecular formula. This value is crucial for converting between mass and the number of molecules using Avogadro's number.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of molecules 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 the question, it is used to determine how many molecules correspond to the specified mass of THC.