The molecular formula of allicin, the compound responsible for the characteristic smell of garlic, is C₆H₁₀OS₂. (c) How many molecules of allicin are in 5.00 mg of this substance?

Verified step by step guidance

1. <Calculate the molar mass of allicin by adding the atomic masses of all the atoms in its molecular formula: C_6H_10OS_2.>
2. <Convert the mass of allicin from milligrams to grams by dividing by 1000.>
3. <Use the molar mass to convert the mass of allicin in grams to moles by dividing the mass by the molar mass.>
4. <Use Avogadro's number (6.022 \times 10^{23} molecules/mol) to convert the number of moles of allicin to the number of molecules by multiplying the moles by Avogadro's number.>
5. <The result from the previous step gives the number of molecules of allicin in 5.00 mg of the substance.>

Key Concepts

Molecular Formula

A molecular formula indicates the number and type of atoms in a molecule. For allicin, C6H10OS2, it shows there are 6 carbon atoms, 10 hydrogen atoms, 1 oxygen atom, and 2 sulfur atoms. Understanding the molecular formula is essential for calculating the molar mass and determining the number of molecules in a given mass of the substance.

Molar Mass

The molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the number of molecules in a sample, you first calculate the molar mass of allicin using its molecular formula. This value allows you to convert the mass of the sample (in mg) to moles, which can then be used to find the number of molecules.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of particles (atoms, molecules, etc.) in one mole of a substance. This constant is crucial for converting moles of a substance into the actual number of molecules. Once the number of moles of allicin is determined from the mass, multiplying by Avogadro's number gives the total number of molecules present in the sample.