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Chapter 3: Problem 74

In 1987 the first substance to act as a superconductor at a temperature above that of liquid nitrogen \((77 \mathrm{~K})\) was discovered. The approximate formula of this substance is \(\mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7}\). Calculate the percent composition by mass of this material.

Short Answer

Expert verified
The percent composition by mass of the superconductor YBa2Cu3O7 is approximately Y: 13.36%, Ba: 41.20%, Cu: 28.60%, and O: 16.84%.

Step by step solution

01

Find the molar mass of each element in the formula

First, we need to find the molar mass for each element: Y (yttrium), Ba (barium), Cu (copper), and O (oxygen). From the periodic table, their respective molar masses are: - Yttrium (Y): 89 g/mol - Barium (Ba): 137.3 g/mol - Copper (Cu): 63.5 g/mol - Oxygen (O): 16 g/mol
02

Calculate molar mass of YBa2Cu3O7

To calculate the molar mass of the compound, we multiply the molar mass of each element with its respective number of moles and then sum up the results. Molar mass of YBa2Cu3O7 = (1 × 89) + (2 × 137.3) + (3 × 63.5) + (7 × 16) = 89 + 274.6 + 190.5 + 112 = 666.1 g/mol
03

Calculate the mass fraction of each element

Now we can compute the mass fraction of each element in the compound. The mass fraction is the mass of an element divided by the molar mass of the compound: Mass fraction of Y = Mass of Y / Molar mass of YBa2Cu3O7 = (1 × 89) / 666.1≈ 0.1336 Mass fraction of Ba = Mass of Ba / Molar mass of YBa2Cu3O7 = (2 × 137.3) / 666.1≈ 0.4120 Mass fraction of Cu = Mass of Cu / Molar mass of YBa2Cu3O7 = (3 × 63.5) / 666.1≈ 0.2860 Mass fraction of O = Mass of O / Molar mass of YBa2Cu3O7 = (7 × 16) / 666.1≈ 0.1684
04

Calculate the percent composition by mass

Finally, we can express the mass fractions as percentages. Percent composition of Y = Mass fraction of Y × 100 ≈ 0.1336 × 100 = 13.36% Percent composition of Ba = Mass fraction of Ba × 100 ≈ 0.4120 × 100 = 41.20% Percent composition of Cu = Mass fraction of Cu × 100 ≈ 0.2860 × 100 = 28.60% Percent composition of O = Mass fraction of O × 100 ≈ 0.1684 × 100 = 16.84% Thus, the percent composition by mass of YBa2Cu3O7 is approximately Y: 13.36%, Ba: 41.20%, Cu: 28.60%, and O: 16.84%.

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Most popular questions from this chapter

Ammonia reacts with \(\mathrm{O}_{2}\) to form either \(\mathrm{NO}(g)\) or \(\mathrm{NO}_{2}(g) \mathrm{ac}-\) cording to these unbalanced equations: $$ \begin{array}{l} \mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{H}_{2} \mathrm{O}(g) \\ \mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g) \end{array} $$ In a certain experiment \(2.00\) moles of \(\mathrm{NH}_{3}(g)\) and \(10.00 \mathrm{moles}\) of \(\mathrm{O}_{2}(g)\) are contained in a closed flask. After the reaction is complete, \(6.75\) moles of \(\mathrm{O}_{2}(g)\) remains. Calculate the number of moles of \(\mathrm{NO}(g)\) in the product mixture: (Hint: You cannot do this problem by adding the balanced equations because you cannot assume that the two reactions will occur with equal probability.)

Vitamin A has a molar mass of \(286.4 \mathrm{~g} / \mathrm{mol}\) and a general molecular formula of \(\mathrm{C}_{x} \mathrm{H}_{2} \mathrm{E}\), where \(\mathrm{E}\) is an unknown element. If vitamin \(\mathrm{A}\) is \(83.86 \% \mathrm{C}\) and \(10.56 \% \mathrm{H}\) by mass, what is the molecular formula of vitamin \(\mathrm{A}\) ?

Silver sulfadiazine burn-treating cream creates a barrier against bacterial invasion and releases antimicrobial agents directly into the wound. If \(25.0 \mathrm{~g} \mathrm{Ag}_{2} \mathrm{O}\) is reacted with \(50.0 \mathrm{~g} \mathrm{C}_{10} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{SO}_{2}\), what mass of silver sulfadiazine, \(\mathrm{AgC}_{10} \mathrm{H}_{9} \mathrm{~N}_{4} \mathrm{SO}_{2}\), can be produced, assuming \(100 \%\) yield? $$ \mathrm{Ag}_{2} \mathrm{O}(s)+2 \mathrm{C}_{10} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{SO}_{2}(s) \longrightarrow 2 \mathrm{AgC}_{10} \mathrm{H}_{9} \mathrm{~N}_{4} \mathrm{SO}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(l) $$

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Freon- \(12\left(\mathrm{CCl}_{2} \mathrm{~F}_{2}\right)\) is used as a refrigerant in air conditioners and as a propellant in aerosol cans. Calculate the number of molecules of Freon-12 in \(5.56 \mathrm{mg}\) of Freon-12. What is the mass of chlorine in \(5.56 \mathrm{mg}\) of Freon- \(12 ?\)
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