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Chapter 3: Problem 105

Consider a sample of calcium carbonate in the form of a cube measuring 2.005 in. on each edge. If the sample has a density of \(2.71 \mathrm{~g} / \mathrm{cm}^{3},\) how many oxygen atoms does it contain?

Short Answer

Expert verified
The calcium carbonate cube contains approximately 6.46 × 10²⁴ oxygen atoms.

Step by step solution

01

Calculate the volume of the cube in cm³

To find the volume, use the formula for the volume of a cube: \( Volume = edge^3 \). First, convert the edge length from inches to centimeters (1 inch = 2.54 cm) Edge length (in cm) = 2.005 in × 2.54 cm/in ≈ 5.0927 cm Now, compute the volume: Volume = (5.0927 cm)³ ≈ 132.1424 cm³
02

Calculate the mass of the cube

Next, calculate the mass of the sample with the given density: Density = Mass / Volume Rearrange to find mass: Mass = Density × Volume Mass ≈ 2.71 g/cm³ × 132.1424 cm³ ≈ 358.0658 g
03

Calculate the number of moles of calcium carbonate

To convert from mass to moles of calcium carbonate, use its molar mass of CaCO₃ = 40.08 g/mol (Ca) + 12.01 g/mol (C) + 16.00 g/mol × 3 (O) ≈ 100.09 g/mol: Moles of CaCO₃ = Mass of CaCO₃ / Molar Mass Moles of CaCO₃ ≈ 358.0658 g / 100.09 g/mol ≈ 3.5764 mol
04

Calculate the number of moles of oxygen

In one mole of calcium carbonate, there are 3 moles of oxygen atoms: Moles of O = 3 × Moles of CaCO₃ Moles of O ≈ 3 × 3.5764 mol ≈ 10.7292 mol
05

Calculate the number of oxygen atoms

Use Avogadro's number to find the number of oxygen atoms: Number of Oxygen atoms = Moles of oxygen × Avogadro's number Number of Oxygen atoms ≈ 10.7292 mol × 6.022 × 10²³ atoms/mol ≈ 6.46 × 10²⁴ oxygen atoms Therefore, the calcium carbonate cube contains approximately 6.46 × 10²⁴ oxygen atoms.

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Most popular questions from this chapter

Washing soda, a compound used to prepare hard water for washing laundry, is a hydrate, which means that a certain number of water molecules are included in the solid structure. Its formula can be written as \(\mathrm{Na}_{2} \mathrm{CO}_{3} \cdot x \mathrm{H}_{2} \mathrm{O},\) where \(x\) is the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) per mole of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\). When a \(2.558-\mathrm{g}\) sample of washing soda is heated at \(25^{\circ} \mathrm{C},\) all the water of hydration is lost, leaving \(0.948 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3} .\) What is the value of \(x ?\)

A bottling plant has 126,515 bottles with a capacity of \(355 \mathrm{~mL}\), 108,500 caps, and \(48,775 \mathrm{~L}\) of beverage. (a) How many bottles can be filled and capped? (b) How much of each item is left over? (c) Which component limits the production?

When ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) reacts with chlorine \(\left(\mathrm{Cl}_{2}\right)\), the main product is \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\), but other products containing \(\mathrm{Cl}\), such as \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2},\) are also obtained in small quantities. The formation of these other products reduces the yield of \(\mathrm{C}_{2} \mathrm{H}_{5}\) Cl. (a) Calculate the theoretical yield of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) when \(125 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{H}_{6}\) reacts with \(255 \mathrm{~g}\) of \(\mathrm{Cl}_{2}\), assuming that \(\mathrm{C}_{2} \mathrm{H}_{6}\) and \(\mathrm{Cl}_{2}\) react only to form \(\mathrm{C}_{2} \mathrm{H}_{2} \mathrm{Cl}\) and HCl. (b) Calculate the percent yield of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) if the reaction produces \(206 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\).

Calcium hydride reacts with water to form calcium hydroxide and hydrogen gas. (a) Write a balanced chemical equation for the reaction. (b) How many grams of calcium hydride are needed to form \(4.500 \mathrm{~g}\) of hydrogen?

A compound whose empirical formula is \(\mathrm{XF}_{3}\) consists of \(65 \%\) F by mass. What is the atomic mass of X?
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