Find the total number of atoms in a sample of cocaine hydrochloride, C₁₇H₂₂ClNO₄, of mass 23.5 mg.

검증된 단계별 안내

Convert the mass of the cocaine hydrochloride from milligrams to grams. Remember that 1 mg equals 0.001 grams.

Calculate the molar mass of cocaine hydrochloride, C17H22ClNO4. Use the atomic masses of carbon (C), hydrogen (H), chlorine (Cl), nitrogen (N), and oxygen (O) from the periodic table to find the sum.

Use the molar mass to convert the mass of the cocaine hydrochloride sample from grams to moles. Use the formula: \( \text{moles} = \frac{\text{mass in grams}}{\text{molar mass}} \).

Calculate the total number of molecules in the sample by using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules per mole. Multiply the number of moles by Avogadro's number.

Determine the total number of atoms in a molecule of cocaine hydrochloride. Since the formula is C17H22ClNO4, add up the atoms: 17 carbon atoms, 22 hydrogen atoms, 1 chlorine atom, 1 nitrogen atom, and 4 oxygen atoms. Multiply the total number of molecules by the total number of atoms per molecule to find the total number of atoms in the sample.

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주요 개념

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Molecular Formula

The molecular formula of a compound provides the types and numbers of atoms present in a molecule. For cocaine hydrochloride, C17H22ClNO4, the formula indicates it contains 17 carbon (C) atoms, 22 hydrogen (H) atoms, 1 chlorine (Cl) atom, 1 nitrogen (N) atom, and 4 oxygen (O) atoms. Understanding the molecular formula is essential for determining the total number of atoms in a given mass of the substance.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the total number of atoms in a sample, one must first calculate the molar mass of cocaine hydrochloride by summing the atomic masses of all atoms in its molecular formula. This value allows for the conversion of the sample's mass into moles, which is crucial for further calculations.

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. Once the number of moles of cocaine hydrochloride is determined from the sample's mass and its molar mass, Avogadro's number can be used to calculate the total number of individual atoms in the sample. This concept is fundamental in bridging the macroscopic and microscopic worlds in chemistry.

Find the total number of atoms in a sample of cocaine hydrochloride, C17H22ClNO4, of mass 23.5 mg.