A 24-h urine specimen was diluted to 2.000L and buffered to pH 10.0. A 10.00 mL aliquot was titrated with 27.32 mL of 0.003960 M EDTA. The calcium in a second 10.00 mL aliquot was iso;ated as solid CaC2O4, redissolved and titrated with 12.21 mL of the EDTA solution.
a) Calculate the conditional formation constants for complexation of Ca2+ and Mg2+ with EDTA at pH 10.0
b) Assuming that 15-300 mg magnesium and 50-400 mg calcium per day are normal, did this specimen fall within the normal ranges?
To solve this problem, we need to use the concept of conditional formation constants for complexation reactions and perform calculations involving titrations.
a) The conditional formation constant (Kf) represents the stability of a complex formed between a metal ion and a ligand at a given pH. In this case, we are interested in calculating the Kf values for the complexation of Ca2+ and Mg2+ with EDTA at pH 10.0.
The titration of the 10.00 mL aliquot with the EDTA solution allows us to determine the concentration of the metal ions in the solution. From the given information, we can write the following balanced chemical equations for the titration reactions:
1. Ca2+ + EDTA ⇌ CaEDTA2- (Complexation of Calcium)
2. Mg2+ + EDTA ⇌ MgEDTA2- (Complexation of Magnesium)
Using the given volumes and concentrations of the titrant and the balanced equations, we can use the stoichiometry of the reactions to determine the moles of metal ions reacted with EDTA.
For Calcium:
Moles of Ca2+ = (27.32 mL) * (0.003960 M)
For Magnesium:
Moles of Mg2+ = (12.21 mL) * (0.003960 M)
Now, we can determine the concentration of Ca2+ and Mg2+ in the original 24-h urine specimen.
For Calcium:
Concentration of Ca2+ = (moles of Ca2+) / (volume of diluted urine specimen)
For Magnesium:
Concentration of Mg2+ = (moles of Mg2+) / (volume of diluted urine specimen)
Finally, we can calculate the conditional formation constants (Kf) using the equation:
Kf = (concentration of metal ion) / (concentration of metal-ligand complex)
b) To determine if the specimen falls within the normal ranges for magnesium and calcium, compare the calculated concentrations to the given normal ranges (15-300 mg for magnesium and 50-400 mg for calcium). Convert the calculated concentrations to mg if necessary. If the calculated concentrations are within the given normal ranges, then the specimen is within the normal limits.
Note: The actual calculations involving the given numbers are not provided in the question, so you would need to substitute the relevant numbers into the equations to obtain the final results.
To calculate the conditional formation constants for complexation of Ca2+ (calcium) and Mg2+ (magnesium) with EDTA (ethylenediaminetetraacetic acid) at pH 10.0, we need to analyze the titration data provided.
Step 1: Calculate the number of moles of EDTA used in each titration:
- For the titration with calcium (Ca), 27.32 mL of 0.003960 M EDTA was used.
Number of moles of EDTA = volume (in L) x concentration
= 27.32 mL / 1000 mL/L x 0.003960 M
- For the titration with magnesium (Mg), 12.21 mL of the same EDTA solution was used.
Number of moles of EDTA = 12.21 mL / 1000 mL/L x 0.003960 M
Step 2: Calculate the number of moles of Ca2+ and Mg2+ in each aliquot used for titration.
- The volume of the aliquot used for titration is 10.00 mL.
- Convert volume to L: 10.00 mL / 1000 mL/L
- Multiply by the concentrations of Ca2+ and Mg2+ in the urine specimen to get moles.
Number of moles of Ca2+ or Mg2+ = volume (in L) x concentration
= 10.00 mL / 1000 mL/L x (concentration in urine specimen)
Step 3: Calculate the moles of EDTA that reacted with Ca2+ and Mg2+ in each titration.
- Moles of EDTA reacted with Ca2+ = Number of moles of Ca2+ in aliquot for Ca titration
- Moles of EDTA reacted with Mg2+ = Number of moles of Mg2+ in aliquot for Mg titration
Step 4: Calculate the ratio of moles of Ca2+ and Mg2+ to moles of EDTA in each titration.
- For the Ca titration, divide moles of Ca2+ by moles of EDTA.
- For the Mg titration, divide moles of Mg2+ by moles of EDTA.
Step 5: Use the ratio obtained in Step 4 to calculate the conditional formation constants for complexation of Ca2+ and Mg2+ with EDTA.
- The formula for conditional formation constant (K') is: K' = [Ca2+ (or Mg2+)] / [EDTA]
Repeat Steps 1-5 for both calcium and magnesium to get their respective conditional formation constants.
To determine if the specimen falls within the normal ranges for magnesium and calcium levels, we need to compare the calculated values to the ranges provided (15-300 mg for magnesium and 50-400 mg for calcium). Convert the moles obtained in Step 2 back to mass (mg) using the molar mass of magnesium and calcium, and check if they fall within the normal ranges.