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Chapter 3: Problem 108

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 sample of calcium carbonate contains approximately 6.50 × 10²4 oxygen atoms.

Step by step solution

01

Calculate the volume of the cube

We are given that each edge of the cube is 2.005 in. We first need to convert this length from inches to centimeters (1 inch = 2.54 cm). Then, we will calculate the volume of the cube by raising the length of one edge to the power of 3. Length in cm = \(2.005 \times 2.54\) cm = 5.0927 cm Volume of the cube = edge length³ = \(5.0927^3\) = 132.65 \(cm^3\)
02

Determine the mass of the cube using its density

The sample has a density of 2.71 g/ \(cm^3\). Density is defined as mass/volume, so we can calculate the mass by multiplying the density by the volume: Mass of the cube = density × volume = 2.71 g/ \(cm^3 \times 132.65\) \(cm^3\) = 359.63 g
03

Calculate the moles of calcium carbonate (CaCO3) present in the cube

First, we need to determine the molar mass of CaCO3. We know that the molar mass of Ca is 40.08 g/mol, C is 12.01 g/mol, and O is 16.00 g/mol. Therefore, the molar mass of CaCO3 is: Molar mass of CaCO₃ = 40.08 + 12.01 + (3 × 16.00) = 100.09 g/mol Now, we can calculate the moles of CaCO3 in the cube by dividing the mass by the molar mass: Moles of CaCO₃ = \( \frac{359.63 \, \text{g}}{100.09 \frac{\text{g}}{\text{mol}}} \) = 3.596 mol
04

Calculate the number of oxygen atoms using Avogadro's number

In a single molecule of CaCO₃, there are 3 oxygen atoms. So, to find the total number of oxygen atoms in the cube, we multiply the number of moles by Avogadro's number (6.022 × 10²³ atoms/mol) and then multiply by the 3 oxygen atoms: Number of oxygen atoms = moles of CaCO₃ × Avogadro's number × 3 = 3.596 mol × 6.022 × 10²³ atoms/mol × 3 = 6.50 × 10²4 oxygen atoms So, the sample of calcium carbonate contains 6.50 × 10²4 oxygen atoms.

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Most popular questions from this chapter

An element \(X\) forms an iodide \(\left(\mathrm{XI}_{3}\right)\) and a chloride \(\left(\mathrm{XCl}_{3}\right) .\) The iodide is quantitatively converted to the chloride when it is heated in a stream of chlorine: $$ 2 \mathrm{XI}_{3}+3 \mathrm{Cl}_{2} \longrightarrow 2 \mathrm{XCl}_{3}+3 \mathrm{I}_{2} $$ If 0.5000 \(\mathrm{g}\) of \(\mathrm{XI}_{3}\) is treated with chlorine, 0.2360 \(\mathrm{g}\) of \(\mathrm{XCl}_{3}\) is obtained. (a) Calculate the atomic weight of the element X. (b) Identify the element X.

Write a balanced chemical equation for the reaction that occurs when (a) titanium metal reacts with \(\mathrm{O}_{2}(g) ;(\mathbf{b})\) silver(I)oxide decomposes into silver metal and oxygen gas when heated; (c) propanol, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(l)\) burns in air; (d) methyl tert- butyl ether, \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}(l),\) burns in air.

(a) The characteristic odor of pineapple is due to ethyl butyrate, a compound containing carbon, hydrogen, and oxygen. Combustion of 2.78 mg of ethyl butyrate produces 6.32 \(\mathrm{mg}\) of \(\mathrm{CO}_{2}\) and 2.58 \(\mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula of the compound? (b) Nicotine, a component of tobacco, is composed of \(C, H,\) and \(N .\) A 5.250 -mg sample of nicotine was combusted, producing 14.242 \(\mathrm{mg}\) of \(\mathrm{CO}_{2}\) and 4.083 \(\mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula for nicotine? If nicotine has a molar mass of \(160 \pm 5 \mathrm{g} / \mathrm{mol},\) what is its molecular formula?

Determine the formula weights of each of the following compounds: (a) nitric acid, HNO \(_{3} ;\) (b) \(\mathrm{KMnO}_{4} ;\) (c) \(\mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) (d) quartz, SiO \(_{2} ;\) (e) gallium sulfide, (f) chromium(III) sulfate, (g) phosphorus trichloride.

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