A pure copper sphere has a radius of 0.935 in. How many copper atoms does it contain? [The volume of a sphere is (4/3)πr³ and the density of copper is 8.96 g/cm³.]

검증된 단계별 안내

Convert the radius from inches to centimeters using the conversion factor 1 inch = 2.54 cm.

Calculate the volume of the sphere using the formula \( V = \frac{4}{3} \pi r^3 \), where \( r \) is the radius in centimeters.

Determine the mass of the copper sphere by multiplying the volume by the density of copper (8.96 g/cm³).

Calculate the number of moles of copper by dividing the mass of the copper sphere by the molar mass of copper (approximately 63.55 g/mol).

Find the number of copper atoms by multiplying the number of moles by Avogadro's number (approximately \( 6.022 \times 10^{23} \) atoms/mol).

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주요 개념

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Volume of a Sphere

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius. This formula allows us to determine the space occupied by the sphere, which is essential for calculating the mass of the copper sphere when combined with its density.

Density

Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³) for solids. For copper, the density is 8.96 g/cm³, which means that each cubic centimeter of copper weighs 8.96 grams. This property is crucial for converting the volume of the sphere into mass.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10²³, is the number of atoms or molecules in one mole of a substance. Once the mass of the copper sphere is determined, this concept allows us to calculate the number of copper atoms by converting the mass into moles and then using Avogadro's number to find the total atom count.

A pure copper sphere has a radius of 0.935 in. How many copper atoms does it contain? [The volume of a sphere is (4/3)πr3 and the density of copper is 8.96 g/cm3.]