The YBa₂Cu₃O₇ superconductor can be synthesized by the solgel method from a stoichiometric mixture of metal ethoxides followed by heating in oxygen. How many grams of Y(OCH₂CH₃)₃ and how many grams of Ba(OCH₂CH₃)₂ are required to react with 75.4 g of Cu(OCH₂CH₃)₂ and an excess of water? Assuming a 100% yield, how many grams of YBa₂Cu₃O₇ are obtained?

Verified step by step guidance

1. Step 1: Write down the balanced chemical equation for the reaction. The reaction is between Y(OCH2CH3)3, Ba(OCH2CH3)2, Cu(OCH2CH3)2, and water to form YBa2Cu3O7 and ethanol (C2H5OH).
2. Step 2: Calculate the molar mass of each reactant and product. You can do this by adding up the atomic masses of each element in the compound. For example, the molar mass of Cu(OCH2CH3)2 is the atomic mass of copper plus twice the sum of the atomic masses of oxygen, carbon, and hydrogen.
3. Step 3: Convert the mass of Cu(OCH2CH3)2 given in the problem (75.4 g) to moles using its molar mass. This is done by dividing the mass by the molar mass.
4. Step 4: Use the stoichiometry of the balanced chemical equation to calculate the moles of Y(OCH2CH3)3 and Ba(OCH2CH3)2 required. For example, the balanced equation tells you that for every 3 moles of Cu(OCH2CH3)2, you need 1 mole of Y(OCH2CH3)3 and 2 moles of Ba(OCH2CH3)2.
5. Step 5: Convert the moles of Y(OCH2CH3)3 and Ba(OCH2CH3)2 calculated in step 4 to grams using their respective molar masses. This is done by multiplying the number of moles by the molar mass. Similarly, calculate the mass of YBa2Cu3O7 produced by converting the moles of Cu(OCH2CH3)2 to moles of YBa2Cu3O7 using the stoichiometry of the balanced equation, and then to grams using its molar mass.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the conservation of mass. It involves using balanced chemical equations to determine the proportions of substances involved. In this question, stoichiometry is essential for calculating the required amounts of Y(OCH2CH3)3 and Ba(OCH2CH3)2 needed to react with a given mass of Cu(OCH2CH3)2.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is crucial for converting between the mass of a substance and the number of moles, which is necessary for stoichiometric calculations. In this problem, determining the molar masses of Y(OCH2CH3)3, Ba(OCH2CH3)2, and Cu(OCH2CH3)2 will allow for accurate calculations of the required reactants.

Yield and Theoretical Yield

Yield refers to the amount of product obtained from a chemical reaction, while theoretical yield is the maximum amount of product that could be formed from given amounts of reactants, assuming complete conversion. In this question, the assumption of 100% yield simplifies the calculation of the mass of YBa2Cu3O7 produced, allowing for a direct application of stoichiometric ratios derived from the balanced equation.