Question

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

The percent composition by mass of YBa2Cu3O7 is approximately Y: 13.34%, Ba: 41.23%, Cu: 28.63%, and O: 16.81%.

Step-by-step solution

Calculate the molar masses of each element in the compound

We will need the molar masses of Y (Yttrium), Ba (Barium), Cu (Copper), and O (Oxygen) to do this. You can find the molar masses of the elements in the periodic table. Molar mass of Y = 88.91 g/mol Molar mass of Ba = 137.33 g/mol Molar mass of Cu = 63.55 g/mol Molar mass of O = 16.00 g/mol

Calculate the molar mass of the compound YBa2Cu3O7

To find the molar mass of the compound, we'll multiply the molar mass of each element by the number of atoms in the compound and then sum them up. Molar mass of YBa2Cu3O7 = (1 × 88.91) + (2 × 137.33) + (3 × 63.55) + (7 × 16.00) Molar mass of YBa2Cu3O7 = 88.91 + 274.66 + 190.65 + 112.00 Molar mass of YBa2Cu3O7 = 666.22 g/mol

Calculate the mass percentage of each element in the compound

To find the mass percentage of each element in the compound, divide the product of the molar mass of the element and the number of atoms of the element by the molar mass of the compound, and then multiply by 100. Percent Y = (mass of Y / molar mass of YBa2Cu3O7) × 100 Percent Y = (88.91 / 666.22) × 100 = 13.34 % Percent Ba = (mass of 2Ba / molar mass of YBa2Cu3O7) × 100 Percent Ba = (274.66 / 666.22) × 100 = 41.23 % Percent Cu = (mass of 3Cu / molar mass of YBa2Cu3O7) × 100 Percent Cu = (190.65 / 666.22) × 100 = 28.63 % Percent O = (mass of 7O / molar mass of YBa2Cu3O7) × 100 Percent O = (112.00 / 666.22) × 100 = 16.81 % So, the percent composition by mass of YBa2Cu3O7 is approximately Y: 13.34 %, Ba: 41.23 %, Cu: 28.63 %, and O: 16.81 %.