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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 6.49 x 10²4 oxygen atoms.

Step by step solution

01

Calculate the cube's volume

We are given that the cube has an edge length of 2.005 in. First, convert this length to centimeters: \(1 \mathrm{~in} = 2.54 \mathrm{~cm}\) (2.005 in.) x (2.54 cm/in.) = 5.0927 cm Now, calculate the volume of the cube: (volume of a cube) = (edge length)³ volume = (5.0927 cm)³ = 132.6316 cm³
02

Find the mass of the sample using its volume and density

Use the formula: mass = (volume) x (density) mass = (132.6316 cm³) x (2.71 g/cm³) = 359.6320 g
03

Calculate the number of moles of calcium carbonate in the sample

Use the molar mass of calcium carbonate (CaCO₃) to convert the mass to moles: molar mass of CaCO₃ = 40.08 g (Ca) + 12.01 g (C) + (3 x 16.00 g (O)) = 100.09 g/mol number of moles of CaCO₃ = (mass of CaCO₃) / (molar mass of CaCO₃) number of moles of CaCO₃ = (359.6320 g) / (100.09 g/mol) = 3.5953 mol
04

Calculate the number of moles of oxygen in the sample

In one mole of calcium carbonate, there are three moles of oxygen (due to the formula CaCO₃). Multiply the moles of CaCO₃ by three to find the moles of oxygen: number of moles of O = (3.5953 mol of CaCO₃) x (3 mol of O per mol of CaCO₃) = 10.7860 mol of O
05

Convert moles of oxygen to the number of oxygen atoms using Avogadro's constant

Use Avogadro's constant (6.022 x 10²³ atoms/mol) to convert moles of oxygen to atoms: number of oxygen atoms = (10.7860 mol of O) x (6.022 x 10²³ atoms/mol) = 6.492 x 10²4 atoms The sample of calcium carbonate contains approximately 6.49 x 10²4 oxygen atoms.

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Most popular questions from this chapter

(a) What is the mass, in grams, of \(2.50 \times 10^{-3} \mathrm{~mol}\) of ammonium phosphate? (b) How many moles of chloride ions are in \(0.2550 \mathrm{~g}\) of aluminum chloride? (c) What is the mass, in grams, of \(7.70 \times 10^{20}\) molecules of caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2} ?\) (d) What is the molar mass of cholesterol if \(0.00105 \mathrm{~mol}\) has a mass of \(0.406 \mathrm{~g}\) ?

(a) When a compound containing C, H, and O is completely combusted in air, what reactant besides the hydrocarbon is involved in the reaction? (b) What products form in this reaction? (c) What is the sum of the coefficients in the balanced chemical equation for the combustion of one mole of acetone, \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}(l),\) in air?

Write a balanced chemical equation for the reaction that occurs when (a) \(\mathrm{Mg}(s)\) reacts with \(\mathrm{Cl}_{2}(g) ;(\mathbf{b})\) barium carbonate decomposes into barium oxide and carbon dioxide gas when heated; \((\mathbf{c})\) the hydrocarbon styrene, \(\mathrm{C}_{8} \mathrm{H}_{8}(l),\) is combusted in air; \((\mathbf{d})\) dimethylether, $\mathrm{CH}_{3} \mathrm{OCH}_{3}(g),$ is combusted in air.

Solutions of sodium carbonate and silver nitrate react to form solid silver carbonate and a solution of sodium nitrate. A solution containing $3.50 \mathrm{~g}\( of sodium carbonate is mixed with one containing \)5.00 \mathrm{~g}$ of silver nitrate. How many grams of sodium carbonate, silver nitrate, silver carbonate, and sodium nitrate are present after the reaction is complete?

Determine the empirical and molecular formulas of each of the following substances: (a) Styrene, a compound used to make Styrofoam \(^{*}\) cups and insulation, contains \(92.3 \% \mathrm{C}\) and \(7.7 \% \mathrm{H}\) by mass and has a molar mass of \(104 \mathrm{~g} / \mathrm{mol}\). (b) Caffeine, a stimulant found in coffee, contains \(49.5 \% \mathrm{C}\), \(5.15 \% \mathrm{H}, 28.9 \% \mathrm{~N},\) and \(16.5 \% \mathrm{O}\) by mass and has a molar mass of \(195 \mathrm{~g} / \mathrm{mol}\) (c) Monosodium glutamate (MSG), a flavor enhancer in certain foods, contains \(35.51 \% \mathrm{C}, 4.77 \% \mathrm{H}, 37.85 \% \mathrm{O},\) $8.29 \% \mathrm{~N},\( and \)13.60 \% \mathrm{Na},\( and has a molar mass of \)169 \mathrm{~g} / \mathrm{mol} .$
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