What is the mass in grams of a single molecule of sucrose (C_{12}H_{22}O_{11})?

• A. 1.66 imes 10^{-23} grams
• B. 5.68 imes 10^{-22} grams
• C. 3.42 imes 10^{-24} grams
• D. 1.99 imes 10^{-20} grams

Answer: (B)

Verified step by step guidance

1. Identify the molecular formula of sucrose, which is C_{12}H_{22}O_{11}. This means one molecule contains 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms.
2. Calculate the molar mass of sucrose by summing the atomic masses of all atoms in the formula: use approximately 12.01 g/mol for carbon, 1.008 g/mol for hydrogen, and 16.00 g/mol for oxygen. The formula is: \(M = 12 \times 12.01 + 22 \times 1.008 + 11 \times 16.00\).
3. Recall that the molar mass (in grams per mole) represents the mass of one mole of molecules. To find the mass of a single molecule, divide the molar mass by Avogadro's number, \(N_A = 6.022 \times 10^{23}\) molecules/mol.
4. Set up the calculation for the mass of one molecule as: \(m = \frac{M}{N_A}\), where \(m\) is the mass of one molecule in grams.
5. Perform the division to find the mass of a single sucrose molecule in grams, which will give you the answer closest to one of the provided options.