Final answer:
To find the number of sucrose molecules in 125g, calculate the moles of sucrose by dividing the mass by the molar mass, and then multiply by Avogadro's number. There are approximately 2.198 × 10^23 sucrose molecules in 125 grams of sugar.
Step-by-step explanation:
To calculate the number of molecules of sucrose (C12H22O11) in 125 grams, we first need to find the molar mass of sucrose. By adding the atomic masses of carbon (C), hydrogen (H), and oxygen (O), we get:
- 12 C atoms = 12 × 12.01 g/mol = 144.12 g/mol
- 22 H atoms = 22 × 1.008 g/mol = 22.176 g/mol
- 11 O atoms = 11 × 16.00 g/mol = 176.00 g/mol
The molar mass of sucrose is thus 342.296 g/mol (144.12 + 22.176 + 176.00). To find the number of moles of sucrose in 125 grams, divide the mass by the molar mass:
125 g ÷ 342.296 g/mol = 0.365 moles of sucrose (approximately)
Since one mole of any substance contains Avogadro's number of molecules (6.022 × 1023 molecules/mol), we multiply the moles of sucrose by Avogadro's number to find the number of molecules:
0.365 moles × 6.022 × 1023 molecules/mol = 2.198 × 1023 sucrose molecules (approximately)
This result is consistent with our rough estimate.