Final answer:
To find the mass of a sugar crystal containing approximately 1.8 x 10¹⁷ sucrose molecules, calculate the moles of sucrose using Avogadro's number and then multiply by the molar mass of sucrose to get the mass in grams. Convert the mass to milligrams for the final result.
Step-by-step explanation:
To calculate the mass of a sugar crystal with approximately 1.8 x 10¹⁷ sucrose molecules, we will first need to find the number of moles of sucrose present. Using Avogadro's number, which is 6.022 x 10¹⁼ molecules per mole, we can calculate the moles of sucrose.
Moles of sucrose = Number of molecules / Avogadro's number = 1.8 x 10¹⁷ molecules / (6.022 x 10¹⁼ molecules/mole)
After calculating the moles, we will then multiply it by the molar mass of sucrose (C₁₂H₂₂O₁₁), which is 342.297⁹ g/mol, to get the mass of sucrose in grams. Then we can convert the mass from grams to milligrams by multiplying it by 1,000 (since there are 1,000 milligrams in a gram).