If 2.50 g of CuSO4 are dissolved in 8.9 *102 mL of 0.21 M NH3, what are the concentrations of Cu(NH3)4^2+, NH3 and Cu^2+ at equilibrium?
To determine the equilibrium concentrations of Cu(NH3)4^2+, NH3, and Cu^2+, we will need to use the concept of stoichiometry and equilibrium calculations. Here are the step-by-step calculations:
Step 1: Convert the given mass of CuSO4 to moles.
- Molar mass of CuSO4 = 63.55 g/mol + 32.07 g/mol + (4 × 16.00 g/mol) = 159.60 g/mol
- Moles of CuSO4 = Given mass / Molar mass = 2.50 g / 159.60 g/mol = 0.01567 mol
Step 2: Convert the given volume of NH3 to moles.
- Concentration of NH3 = 0.21 M (given)
- Moles of NH3 = Concentration × Volume = 0.21 mol/L × (8.9 × 10^2 mL / 1000 mL/L) = 0.1869 mol
Step 3: Determine the limiting reactant.
- CuSO4 is the limiting reactant because it is present in a smaller amount compared to NH3. The mole ratio between CuSO4 and Cu(NH3)4^2+ is 1:1.
Step 4: Calculate the amount of Cu(NH3)4^2+ formed.
- Moles of Cu(NH3)4^2+ = Moles of limiting reactant (CuSO4) = 0.01567 mol
Step 5: Calculate the concentration of Cu(NH3)4^2+ at equilibrium.
- Volume of solution = 8.9 × 10^2 mL / 1000 mL/L = 0.89 L
- Concentration of Cu(NH3)4^2+ = Moles of Cu(NH3)4^2+ / Volume = 0.01567 mol / 0.89 L = 0.0176 M
Step 6: Calculate the concentration of NH3 at equilibrium.
- The stoichiometric coefficient for NH3 in the balanced equation is 4.
- Moles of NH3 used = 4 × Moles of Cu(NH3)4^2+ = 4 × 0.01567 mol = 0.0627 mol
- Moles of NH3 remaining = Initial moles of NH3 - Moles of NH3 used = 0.1869 mol - 0.0627 mol = 0.1242 mol
- Volume of solution = 0.89 L
- Concentration of NH3 = Moles of NH3 remaining / Volume = 0.1242 mol / 0.89 L = 0.1397 M
Step 7: Calculate the concentration of Cu^2+ at equilibrium.
- The stoichiometric coefficient for CuSO4 in the balanced equation is 1.
- Moles of Cu^2+ = Moles of CuSO4 reacted = Moles of limiting reactant (CuSO4) = 0.01567 mol
- Volume of solution = 0.89 L
- Concentration of Cu^2+ = Moles of Cu^2+ / Volume = 0.01567 mol / 0.89 L = 0.0176 M
So, at equilibrium, the concentrations are:
- [Cu(NH3)4^2+] = 0.0176 M
- [NH3] = 0.1397 M
- [Cu^2+] = 0.0176 M
To find the concentrations of Cu(NH3)4^2+, NH3, and Cu^2+ at equilibrium, we need to analyze the reaction and use the principles of stoichiometry.
The reaction between CuSO4 and NH3 can be represented as follows:
CuSO4 + 4NH3 ⇌ Cu(NH3)4^2+ + SO4^2-
Given that 2.50 g of CuSO4 are dissolved in 8.9 * 102 mL of 0.21 M NH3, we first need to determine the number of moles of CuSO4:
The molar mass of CuSO4 is 159.61 g/mol.
Using the formula: moles = mass / molar mass, we can find the number of moles:
moles of CuSO4 = 2.50 g / 159.61 g/mol
Next, we need to convert the volume of NH3 from milliliters to liters:
volume of NH3 = 8.9 * 102 mL = 8.9 * 10^-1 L
Using the molarity of NH3, we can calculate the number of moles of NH3:
moles of NH3 = molarity * volume
moles of NH3 = 0.21 mol/L * 8.9 * 10^-1 L
Now, let's use stoichiometry to determine the concentrations at equilibrium:
Since the balanced equation indicates a 1:4 ratio between CuSO4 and Cu(NH3)4^2+, the moles of Cu(NH3)4^2+ at equilibrium will be equal to moles of CuSO4 at the start.
Concentration of Cu(NH3)4^2+ = moles of Cu(NH3)4^2+ / volume of solution
To calculate the moles of Cu(NH3)4^2+:
moles of Cu(NH3)4^2+ = moles of CuSO4
Next, we need to determine the moles of NH3 present at equilibrium using the stoichiometric ratio of 1:4:
moles of NH3 = (4 * moles of Cu(NH3)4^2+) / volume of solution
Finally, to find the concentration of Cu^2+, we use the stoichiometric ratio of 1:1 between Cu(NH3)4^2+ and Cu^2+:
Concentration of Cu^2+ = moles of Cu(NH3)4^2+ / volume of solution
By substituting the values into the equations, you can find the concentrations of Cu(NH3)4^2+, NH3, and Cu^2+ at equilibrium.
mols CuSO4 initially = g/molar mass = 2.50/159.5 = 0.0157. millimols = 15.7 .millimols NH3 = mL x M = 890 x 0.21 = about 187
.............CuSO4 + 4NH3 ==> [Cu(NH3)4]^2+ + [SO4]^2-
I................15.7......187................0.........................0
C.............-15.7.....-62.8.........+15.7.....................15.7
E.................0..........124.2........15.7.....................15.7
So your solution now is 0 mmols CuSO4, 124.2 mmols NH3 and 15.7 mmols Cu complex. You want concentrations which is M = mmols/mL = ?
You do the rest.
NOTE: I rounded here and there and estimated most of the molar masses so you should check everything and round to your satisfaction. Post your work if you get stuck.