Textbook Question
The mass of an average blueberry is 0.75 g and the mass of an automobile is 2.0×103 kg. Find the number of automobiles whose total mass is the same as 1.0 mol of blueberries.
Ch.2 - Atoms & Elements
Chapter 2, Problem 113
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.]
Verified step by step guidance1
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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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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.
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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.
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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.
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Related Practice
Textbook Question
A pure titanium cube has an edge length of 2.78 in. How many titanium atoms does it contain? Titanium has a density of 4.50 g/cm3.
Textbook Question
What is the edge length (in cm) of a titanium cube that contains 2.55 * 1024 titanium atoms? The density of titanium is 4.50 g/cm3.
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Textbook Question
Boron has only two naturally occurring isotopes. The mass of boron-10 is 10.01294 amu and the mass of boron-11 is 11.00931 amu. Calculate the relative abundances of the two isotopes.
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