How many moles of NH3 must be added to 1.00 L of solution to dissolve 0.979 g of CuCO3? For CuCO3, Ksp = 2.3 × 10-10. Ignore hydrolysis of CO32-, but consider the formation of the complex ion Cu(NH3)42+.
How many moles of NH3 must be added to 1.00 L of solution to dissolve 1.39 g of CuCO3? For CuCO3, Ksp = 2.3 × 10-10. Ignore hydrolysis of CO32-, but consider the formation of the complex ion Cu(NH3)42+.
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To solve this problem, we need to consider the solubility equilibrium of CuCO3 in water. CuCO3 dissociates into Cu2+ and CO32- ions according to the equation:
CuCO3 <--> Cu2+ + CO32-
We also need to take into account the formation of the complex ion Cu(NH3)42+:
Cu2+ + 4NH3 <--> Cu(NH3)42+
In this equilibrium, the formation constant (Kf) for Cu(NH3)42+ is not given. However, we can assume that this formation is favored by the presence of excess NH3. Therefore, we can assume that the concentration of Cu(NH3)42+ is equal to the concentration of Cu2+ since all the Cu2+ ions will bind to NH3 to form Cu(NH3)42+.
Let's break down the steps to get the answer:
Step 1: Calculate the moles of CuCO3.
Given: Mass of CuCO3 = 0.979 g, Molar mass of CuCO3 = 123.55 g/mol
Moles of CuCO3 = Mass of CuCO3 / Molar mass of CuCO3
= 0.979 g / 123.55 g/mol
= 0.00792 mol
Step 2: Use the solubility product expression to calculate the concentration of Cu2+.
Given: Ksp = 2.3 × 10^-10
Cu2+ concentration = Square root of (Ksp)
= Square root of (2.3 × 10^-10)
= 4.8 × 10^-6 M
Step 3: Calculate the moles of Cu(NH3)42+ required to react with all Cu2+ ions.
Since the concentration of Cu(NH3)42+ is assumed to be equal to the concentration of Cu2+ (from the assumption stated earlier), the moles of Cu(NH3)42+ is also equal to the moles of Cu2+.
Moles of Cu(NH3)42+ = 0.00792 mol (same as the moles of Cu2+)
Step 4: Calculate the concentration of NH3 required to react with Cu2+.
From the balanced equation:
Cu2+ + 4NH3 <--> Cu(NH3)42+
We know that the ratio is 1:4 between Cu2+ and NH3. Therefore, we need four times the moles of Cu2+ in NH3.
Moles of NH3 = 4 * moles of Cu2+
= 4 * 0.00792 mol
= 0.0317 mol
Step 5: Calculate the concentration of NH3 in the 1.00 L solution.
Concentration of NH3 = Moles of NH3 / Volume of solution
= 0.0317 mol / 1.00 L
= 0.0317 M
So, 0.0317 moles of NH3 must be added to 1.00 L of solution to dissolve 0.979 g of CuCO3.