For a mixture of 12.0mL of 0.004. M AgNO3 and 8.0mL of 0.0025 M K2CrO4, a colorimetric measurement of CrO4-2 in the equilibrium supernatant liquid found its concentration to be 1.5*10^-4 M. Calculate the Ksp of Ag2CrO4.
To calculate the Ksp of Ag2CrO4, we first need to determine the concentration of Ag+ and CrO4^2- ions in the equilibrium supernatant liquid.
1. Calculate the moles of AgNO3:
- Moles of AgNO3 = Volume (in L) x Concentration (in M)
- Moles of AgNO3 = 12.0 mL x (1 L / 1000 mL) x 0.004 M
2. Calculate the moles of K2CrO4:
- Moles of K2CrO4 = Volume (in L) x Concentration (in M)
- Moles of K2CrO4 = 8.0 mL x (1 L / 1000 mL) x 0.0025 M
3. Determine the limiting reagent:
- Compare the moles of AgNO3 and K2CrO4 to identify the limiting reagent.
- The limiting reagent is the one that produces fewer moles of the desired product. In this case, it is AgNO3 since it produces 2 moles of Ag+ ions per 1 mole of Ag2CrO4.
4. Calculate the moles of Ag+ ions produced:
- Moles of Ag+ ions = Moles of AgNO3 x 2
5. Calculate the moles of CrO4^2- ions consumed:
- Moles of CrO4^2- ions = Moles of Ag+ ions
6. Calculate the concentration of CrO4^2- ions in the equilibrium supernatant liquid:
- Concentration of CrO4^2- ions = Moles of CrO4^2- ions / Total volume (in L)
- Total volume = Volume of AgNO3 + Volume of K2CrO4 = 12.0 mL + 8.0 mL = 20.0 mL = 0.020 L
- Concentration of CrO4^2- ions = Moles of CrO4^2- ions / 0.020 L
7. Substitute the values into the formula for Ksp:
- Ksp = [Ag+]^2 x [CrO4^2-]
- Ksp = (2 x [Ag+ ions])^2 x [CrO4^2- ions]
- Ksp = (2 x Moles of Ag+ ions / 0.020 L)^2 x (Moles of CrO4^2- ions / 0.020 L)
8. Substitute the known values and calculate the Ksp of Ag2CrO4.
Note: It is important to convert all volumes to liters (L) and double-check unit conversions and significant figures to ensure accurate results.
I think the easiest way to handle this is to set up an ICE chart.
Each soln has been diluted so the concns are as followws:
(Ag^+) = 0.004M x (12/20) = 0.0024M
(CrO4^2-) = 0.0025 x (8/20) = 0.0010
.......2Ag^+ + CrO4^2- ==> Ag2CrO4
I...0.0024M....0.0010.......----
C..-0.0020.....-0.0010..........----
E...0.0004......1.5E-4....
Substitute into the Ksp expression and solve for Ksp.