The molecular formula of allicin, the compound responsible for the characteristic smell of garlic, is C6H10OS2.
(a) What is the molar mass of allicin?
__ g/mol
(b) How many moles of allicin are present in 6.60 mg of this substance?
__ mol
(c) How many molecules of allicin are in 6.60 mg of this substance?
__ allicin molecules
(d) How many H atoms are present in 6.60 mg of allicin?
__ H atoms
The Correct Answer and Explanation is:
To solve this problem, we will go through each part step by step, using the molecular formula of allicin: C₆H₁₀OS₂.
(a) Molar Mass of Allicin
To calculate the molar mass, sum the atomic masses of each element in the formula:
- Carbon (C): 12.01 g/mol × 6 = 72.06 g/mol
- Hydrogen (H): 1.008 g/mol × 10 = 10.08 g/mol
- Oxygen (O): 16.00 g/mol × 1 = 16.00 g/mol
- Sulfur (S): 32.07 g/mol × 2 = 64.14 g/mol
Total molar mass = 72.06 + 10.08 + 16.00 + 64.14 = 162.28 g/mol
✅ Answer (a): 162.28 g/mol
(b) Moles of Allicin in 6.60 mg
Convert mg to grams:
6.60 mg = 0.00660 g
Use the formula:
moles = mass / molar mass moles=0.00660 g162.28 g/mol=4.07×10−5 mol\text{moles} = \frac{0.00660\ \text{g}}{162.28\ \text{g/mol}} = 4.07 \times 10^{-5}\ \text{mol}
✅ Answer (b): 4.07 × 10⁻⁵ mol
(c) Molecules of Allicin in 6.60 mg
Use Avogadro’s number:
1 mol = 6.022 × 10²³ molecules molecules=4.07×10−5 mol×6.022×1023 molecules/mol=2.45×1019 molecules\text{molecules} = 4.07 \times 10^{-5}\ \text{mol} \times 6.022 \times 10^{23}\ \text{molecules/mol} = 2.45 \times 10^{19}\ \text{molecules}
✅ Answer (c): 2.45 × 10¹⁹ allicin molecules
(d) Hydrogen Atoms in 6.60 mg of Allicin
Each molecule of allicin contains 10 hydrogen atoms. H atoms=2.45×1019 molecules×10=2.45×1020 H atoms\text{H atoms} = 2.45 \times 10^{19}\ \text{molecules} \times 10 = 2.45 \times 10^{20}\ \text{H atoms}
✅ Answer (d): 2.45 × 10²⁰ H atoms
Summary & Explanation
Allicin (C₆H₁₀OS₂) is an organosulfur compound that gives garlic its characteristic aroma. Understanding the molecular composition allows chemists to calculate various quantitative properties, such as mass, moles, and atomic content.
First, we calculate the molar mass by summing the atomic masses of the atoms in the molecular formula: carbon (C), hydrogen (H), oxygen (O), and sulfur (S). Each element’s contribution is multiplied by the number of atoms in the molecule. The result is a molar mass of 162.28 g/mol, which tells us the mass of one mole of allicin molecules.
Next, to find the number of moles in 6.60 mg (0.00660 g), we divide the mass by the molar mass. This gives 4.07 × 10⁻⁵ mol, a small amount, typical for laboratory-scale samples.
To determine how many individual molecules this amount represents, we multiply the number of moles by Avogadro’s number (6.022 × 10²³), the number of particles in one mole. The result, 2.45 × 10¹⁹ molecules, shows the enormous number of molecules even in tiny masses.
Finally, each allicin molecule contains 10 hydrogen atoms, so the total number of hydrogen atoms is the number of molecules multiplied by 10, giving 2.45 × 10²⁰ H atoms.
These calculations are essential in chemistry and biochemistry for understanding reactivity, dosage, and molecular interactions.
