"When 3.00 ml of a 0.00600 M K2CrO4 solution and 3.000 ml of a 0.0100 M Cu(NO3)2 solution are mixed, some solid forms. The mixture is centrifuged and the supernatant is removed. The absorbance of the supernatant, measured at 400 nm in a 1.00 cm cuvette, is 0.286. The extinction coefficient of Cr04^2- at 400 nm is 250.0 M^-1 cm^-1. Calculate Ksp for CuCrO4."
So, I'm not sure how to go about this. My teachers suggested strategy is to find the concentration of CrO4^2-, then the equilibrium amount, initial amount and amount of CrO4^2- used to form CuCrO4 and then move on to Cu^2+.
I rearranged the absorbance equation to get the concentration of CrO4^2- = 1.14x10^-3 M.
Then I attempted using C1V1 = C2V2 to figure out the equilibrium amount of CrO4^2-. I ended up with a V2=15 mls.
That's where I stopped because it didn't sound correct. Any advice would be appreciated.
You're right. (CrO4^2-) = 0.00114M
Your c1v1 = c2v2 is ok but you should be solving for c2 and not v. You know volume.
c1v1 = c2v2
0.01M*3.00mL = c2*6.00 mL.
c2 = 0.005 = [Cu(NO3)2] initially
Do the same for K2CrO4. You should get
1/2 * 0.006 = 0.003 = K2CrO4.
...Cu(NO3)2 + K2CrO4 ==> CuCrO4 + 2KNO3
I..0.005......0.003........0
C...-x..........-x
E..0.005-x...0.00114
You know Eq is 0.00114 for K2CrO4 you can calculate x and that will tell you how much Cu(NO3)2 was used and that will give you Eq for Cu(NO3)2.
Then plug in and calculate Ksp.
To find the Ksp for CuCrO4, you need to determine the concentration of Cu^2+ in the solution. Here's a step-by-step approach to solve this problem:
1. Start by calculating the moles of CrO4^2- in the solution:
- Given: volume = 3.00 ml and concentration = 0.00600 M
- Moles of CrO4^2- = volume x concentration = 3.00 ml x 0.00600 M
2. Use stoichiometry to determine the moles of CuCrO4 formed:
- The balanced equation for the reaction is:
2 K2CrO4 + 3 Cu(NO3)2 → CuCrO4 + 4 KNO3
- From the balanced equation, it is clear that 2 moles of K2CrO4 react with 3 moles of Cu(NO3)2 to form 1 mole of CuCrO4.
- So, the moles of CuCrO4 = (moles of CrO4^2-) / 2
3. Calculate the volume of the solution at equilibrium after adding Cu(NO3)2:
- Use the dilution formula C1V1 = C2V2, where C1 and V1 are the initial concentration and volume of Cu(NO3)2 solution, and C2 and V2 are the final concentration and volume at equilibrium.
- Given: C1 = 0.0100 M, V1 = 3.00 ml, C2 = ?
- Solve for V2 using the formula: V2 = (C1 x V1) / C2
4. Calculate the concentration of Cu^2+ formed:
- To find the concentration of Cu^2+, divide the moles of CuCrO4 calculated in step 2 by the volume at equilibrium obtained in step 3.
5. Finally, use the concentration of Cu^2+ and the absorbance of the supernatant to calculate the Ksp:
- Given: absorbance = 0.286, extinction coefficient = 250.0 M^-1 cm^-1, path length (cuvette width) = 1.00 cm
- Use the Beer-Lambert Law: absorbance = ε x concentration x path length
- Rearrange the equation to find the concentration: concentration = absorbance / (ε x path length)
6. Substitute the concentration of Cu^2+ obtained in step 4 into the equation from step 5 and solve for Ksp.
By following these steps, you should be able to calculate the Ksp for CuCrO4. Let me know if you need further assistance!