A sugar crystal contains approximately 6.55 * 1017 sucrose (C12H22O11) molecules. What is its mass in mg?

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Identify the molar mass of sucrose (C_{12}H_{22}O_{11}) by adding the atomic masses of its constituent atoms: 12 carbon (C), 22 hydrogen (H), and 11 oxygen (O) atoms.

Calculate the molar mass of sucrose using the periodic table: \( M = 12 \times M_C + 22 \times M_H + 11 \times M_O \), where \( M_C \), \( M_H \), and \( M_O \) are the atomic masses of carbon, hydrogen, and oxygen, respectively.

Use Avogadro's number (\( 6.022 \times 10^{23} \) molecules/mol) to find the number of moles of sucrose in the crystal: \( \text{moles of sucrose} = \frac{6.55 \times 10^{17}}{6.022 \times 10^{23}} \).

Calculate the mass of sucrose in grams by multiplying the number of moles by the molar mass: \( \text{mass in grams} = \text{moles of sucrose} \times M \).

Convert the mass from grams to milligrams by multiplying by 1000 (since 1 g = 1000 mg).

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주요 개념

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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 convert the number of sucrose molecules into moles.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this context, it involves converting the mass of sucrose from grams to milligrams (mg), where 1 gram equals 1000 milligrams. Understanding how to perform these conversions is crucial for accurately reporting mass in the desired units.