Ch.2 - Atoms & Elements

Tro - Chemistry: A Molecular Approach 4th Edition

Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831당신이 사용하는 게 아니라요?교과서 변경

Tro 4th Edition

Ch.2 - Atoms & Elements

문제 118

2장, 문제 118

Common brass is a copper and zinc alloy containing 37.0% zinc by mass and having a density of 8.48 g/cm³. A fitting composed of common brass has a total volume of 112.5 cm³. How many atoms (copper and zinc) does the fitting contain?

검증된 단계별 안내

First, calculate the total mass of the brass fitting by multiplying its volume by its density. This will give you the mass in grams.

Next, calculate the mass of each element in the alloy. Since the alloy is 37.0% zinc by mass, multiply the total mass by 0.37 to find the mass of zinc. Subtract this from the total mass to find the mass of copper.

Convert the mass of each element to moles by dividing by the molar mass. The molar mass of copper (Cu) is approximately 63.55 g/mol and the molar mass of zinc (Zn) is approximately 65.38 g/mol.

Since 1 mole of any substance contains Avogadro's number (6.022 x 10^23) of entities (atoms in this case), multiply the number of moles of each element by Avogadro's number to find the number of atoms.

Finally, add the number of copper atoms and zinc atoms to find the total number of atoms in the brass fitting.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Density and Mass-Volume Relationship

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³). To find the mass of a substance when its density and volume are known, the formula mass = density × volume can be used. In this case, knowing the density of brass allows us to calculate the total mass of the fitting from its given volume.

Molar Mass and Composition of Alloys

An alloy's composition is crucial for determining its properties and behavior. Common brass, composed of copper and zinc, has specific molar masses (copper: 63.55 g/mol, zinc: 65.38 g/mol). By calculating the mass of each component based on the percentage by mass, we can find the number of moles of each metal in the fitting, which is essential for determining the number of atoms.

Avogadro's Number

Avogadro's number, approximately 6.022 × 10²³, is the number of atoms or molecules in one mole of a substance. This constant allows us to convert moles of a substance into the actual number of atoms. After calculating the moles of copper and zinc in the fitting, we can use Avogadro's number to find the total number of atoms present in the brass fitting.

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Common brass is a copper and zinc alloy containing 37.0% zinc by mass and having a density of 8.48 g/cm3. A fitting composed of common brass has a total volume of 112.5 cm3. How many atoms (copper and zinc) does the fitting contain?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Density and Mass-Volume Relationship

Molar Mass and Composition of Alloys

Avogadro's Number

Common brass is a copper and zinc alloy containing 37.0% zinc by mass and having a density of 8.48 g/cm³. A fitting composed of common brass has a total volume of 112.5 cm³. How many atoms (copper and zinc) does the fitting contain?