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.

First, we need to find the molar mass of the given substance (YBa\(_{2}\)Cu\(_{3}\)O\(_{7}\)). We can do this by using the periodic table and adding the molar masses of each element in the formula. \[ \begin{aligned} \mathrm{Molar\ Mass} &= 1(\mathrm{Molar\ Mass\ of\ Y}) + 2(\mathrm{Molar\ Mass\ of\ Ba}) + 3(\mathrm{Molar\ Mass\ of\ Cu}) + 7(\mathrm{Molar\ Mass\ of\ O}) \\ &= 1(88.91 \mathrm{~g/mol}) + 2(137.33 \mathrm{~g/mol}) + 3(63.55 \mathrm{~g/mol}) + 7(16.00 \mathrm{~g/mol}) \end{aligned} \]

Now, let's calculate the individual masses of the elements in the substance's formula: \[ \begin{aligned} \mathrm{Mass\ of\ Y} &= 1(88.91 \mathrm{~g/mol}) \\ \mathrm{Mass\ of\ Ba} &= 2(137.33 \mathrm{~g/mol}) \\ \mathrm{Mass\ of\ Cu} &= 3(63.55 \mathrm{~g/mol}) \\ \mathrm{Mass\ of\ O} &= 7(16.00 \mathrm{~g/mol}) \end{aligned} \]

Finally, we can determine the percent composition by mass for each element in the substance. For this, we need to divide the individual mass of each element by the molar mass of the substance and multiply the result by 100. \[ \begin{aligned} \mathrm{Percent\ Composition\ of\ Y} & = \frac{\mathrm{Mass\ of\ Y}}{\mathrm{Molar\ Mass}} \times 100\% \\ \mathrm{Percent\ Composition\ of\ Ba} & = \frac{\mathrm{Mass\ of\ Ba}}{\mathrm{Molar\ Mass}} \times 100\% \\ \mathrm{Percent\ Composition\ of\ Cu} & = \frac{\mathrm{Mass\ of\ Cu}}{\mathrm{Molar\ Mass}} \times 100\% \\ \mathrm{Percent\ Composition\ of\ O} & = \frac{\mathrm{Mass\ of\ O}}{\mathrm{Molar\ Mass}} \times 100\% \end{aligned} \] Calculate the values for each element to find their percent compositions by mass.