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Chapter 5: 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 YBa\(_2\)Cu\(_3\)O\(_7\) compound is: Yttrium (Y) - \(13.50\%\), Barium (Ba) - \(41.22\%\), Copper (Cu) - \(28.61\%\), and Oxygen (O) - \(16.67\%\).

Step by step solution

01

Determine the molar mass of each element

To find the percent composition, we will need the molar mass of each element in the compound (Y, Ba, Cu, and O). Using the periodic table, we find the molar mass of each element: Yttrium (Y): \(89.905\, \mathrm{g/mol}\) Barium (Ba): \(137.33\, \mathrm{g/mol}\) Copper (Cu): \(63.546\, \mathrm{g/mol}\) Oxygen (O): \(16.00\, \mathrm{g/mol}\)
02

Calculate the total molar mass of the compound YBa\(_2\)Cu\(_3\)O\(_7\)

Use the molar masses and their respective proportions in the compound to find the total molar mass: Total molar mass = (1 x molar mass of Y) + (2 x molar mass of Ba) + (3 x molar mass of Cu) + (7 x molar mass of O) Total molar mass = \[ (1 x 89.905) + (2 x 137.33) + (3 x 63.546) + (7 x 16.00) \mathrm{g/mol} \] Total molar mass = \( 666.262 \, \mathrm{g/mol} \)
03

Calculate the percent composition by mass of each element in the compound

Use the individual molar mass of each element and divide it by the total molar mass of the compound, then multiply by 100% to obtain the percent composition of each element: Percent composition (Y) = \(\frac{89.905}{666.262} \times 100\% = 13.50\%\) Percent composition (Ba) = \(\frac{2 \times 137.33}{666.262} \times 100\% = 41.22\%\) Percent composition (Cu) = \(\frac{3 \times 63.546}{666.262} \times 100\% = 28.61\%\) Percent composition (O) = \(\frac{7 \times 16.00}{666.262} \times 100\% = 16.67\%\)
04

Summarize the results

Finally, the percent composition by mass of YBa\(_2\)Cu\(_3\)O\(_7\) is as follows: Yttrium (Y): \(13.50\%\) Barium (Ba): \(41.22\%\) Copper (Cu): \(28.61\%\) Oxygen (O): \(16.67\%\)

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