A sugar crystal contains approximately 1.8×10¹⁷ sucrose (C₁₂H₂₂O₁₁) molecules. What is its mass in mg?

Verified step by step guidance

1. First, we need to calculate the molar mass of sucrose (C12H22O11). The molar mass is the sum of the atomic masses of all the atoms in a molecule. For sucrose, this would be 12 atoms of Carbon (C), 22 atoms of Hydrogen (H), and 11 atoms of Oxygen (O). The atomic masses of C, H, and O are approximately 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol respectively.
2. Next, multiply the number of each atom by their respective atomic masses and add them all together to get the molar mass of sucrose. The molar mass of sucrose is (12*12.01 g/mol) + (22*1.01 g/mol) + (11*16.00 g/mol).
3. Then, we need to convert the number of molecules to moles. We can do this by using Avogadro's number, which is approximately 6.022 * 10^23 molecules/mol. So, the number of moles of sucrose is 1.8 * 10^17 molecules divided by 6.022 * 10^23 molecules/mol.
4. After that, we can find the mass of the sugar crystal in grams by multiplying the number of moles of sucrose by the molar mass of sucrose.
5. Finally, to convert the mass from grams to milligrams, multiply by 1000, since there are 1000 milligrams in a gram.

Key Concepts

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For sucrose (C12H22O11), the molar mass can be calculated by summing the atomic masses of all the constituent atoms: 12 carbon (C), 22 hydrogen (H), and 11 oxygen (O) atoms. This value is essential for converting between the number of molecules and mass.

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 allows chemists to relate the macroscopic scale of substances (grams) to the microscopic scale (molecules). In this problem, it helps to determine how many moles of sucrose correspond to the given number of molecules.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this context, converting the mass of sucrose from grams to milligrams is necessary, as the final answer is requested in milligrams (mg). Understanding how to perform these conversions is crucial for accurately reporting measurements in chemistry.