Cobalt was used as an internal standard to analyze a sample of titanium with atomic absorption spectroscopy. A mixture was prepared by combining a 4.00 mL Ti solution of unknown concentration with 3.00 mL of a 11.7 micrograms/mL solution of Co. The atomic absorbances were measured as 0.128 and 0.218 for Ti and Co, respectively.
As a reference, a standard mixture containing 1.58 micrograms Co/mL and 2.31 micrograms Ti/mL was prepared and measured to have a signal-to-signal ratio of 2.65 Ti: 1.00 Co.
Determine the concentration (moles/L) of titanium in the original unknown solution.
To determine the concentration of titanium in the original unknown solution, we can use the information provided about the samples and the standard mixture.
First, let's calculate the moles of cobalt (Co) in the unknown sample and the standard mixture:
1. Moles of Co in the unknown sample:
Concentration of Co in the unknown mixture = 11.7 μg/mL
Volume of the unknown mixture = 3.00 mL
Moles of Co = (concentration of Co) x (volume of unknown mixture) / molecular weight of Co
Assuming the molecular weight of Co is 59.93 g/mol:
Moles of Co in the unknown sample = (11.7 μg/mL) x (3.00 mL) / (59.93 g/mol) = 0.584 μmol
2. Moles of Co in the standard mixture:
Concentration of Co in the standard mixture = 1.58 μg/mL
Volume of the standard mixture = 3.00 mL
Moles of Co in the standard mixture = (1.58 μg/mL) x (3.00 mL) / (59.93 g/mol) = 0.079 μmol
Next, we need to calculate the signal ratio for titanium (Ti) in the unknown sample using the measured atomic absorbances:
Signal ratio for Ti = Atomic absorbance of Ti / Atomic absorbance of Co
Signal ratio for Ti = 0.128 / 0.218 = 0.587
Now, let's use the signal-to-signal ratio from the standard mixture to find the moles of Ti in the unknown sample:
Signal ratio for Ti in standard mixture = 2.65 Ti : 1.00 Co
Moles of Ti in standard mixture = (Signal ratio for Ti in standard mixture) x (Moles of Co in standard mixture)
Moles of Ti in standard mixture = 2.65 x 0.079 μmol = 0.209 μmol
Finally, we can determine the concentration of titanium in the original unknown solution by dividing the moles of Ti in the unknown sample by the volume of the unknown mixture:
Concentration of Ti in unknown solution = (Moles of Ti in unknown sample) / (Volume of unknown mixture)
Concentration of Ti in unknown solution = 0.209 μmol / 4.00 mL
Note that the volume should be converted to liters for consistency. Assuming 1 mL = 1 cm³ and converting to liters (L), we have:
Concentration of Ti in unknown solution = 0.209 μmol / 4.00 x 10^-6 L = 5.23 x 10^-2 mol/L