Final answer:
To calculate the theoretical yield of Cu(NO3)2, we convert the given mass of silver nitrate to moles, use the stoichiometry of the balanced reaction equation, and then convert back to the mass of Cu(NO3)2 to arrive at the theoretical yield of 40.55g.
Step-by-step explanation:
The student asked how to determine the theoretical yield of Cu(NO3)2 when copper reacts with 36.7g of silver nitrate. To solve this, we first need to use the molar mass of AgNO3 to convert the mass of AgNO3 to moles. Since the reaction is:
Cu(s) + 2 AgNO3(aq) → Cu(NO3)₂(aq) + 2 Ag(s),
according to the stoichiometry of the reaction, one mole of Cu produces one mole of Cu(NO3)2. Using this stoichiometry and the molar mass of Cu(NO3)2, we can find the mass of Cu(NO3)2 that forms, which is the theoretical yield.
The molar mass of AgNO3 is approximately 169.88 g/mol, and the molar mass of Cu(NO3)₂ is approximately 187.55 g/mol. Therefore, the calculation goes as follows:
- Calculate moles of AgNO3: 36.7g AgNO3 / 169.88 g/mol = 0.216 moles AgNO3
- Using the mole ratio from the balanced equation, moles of Cu(NO3)2 = moles of AgNO3 (since 2 mol AgNO3 produces 1 mol Cu(NO3)2, the amount of AgNO3 moles will be half that of AgNO3).
- Calculate mass of Cu(NO3)2: 0.216 moles Cu(NO3)2 * 187.55 g/mol = 40.55g Cu(NO3)2
Therefore, the theoretical yield of Cu(NO3)2 is 40.55g.