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.
Why did the titanium go to the Cobalt's party? Because it wanted to get a "Ti-tanium" of the fun! But let's get serious now and calculate the concentration of titanium in the original unknown solution.
First, we need to calculate the atomic absorption ratio for titanium (Ti) and cobalt (Co) in the standard mixture. Based on the given signal-to-signal ratio of 2.65 Ti: 1.00 Co, we can calculate the atomic absorption ratio as 2.65/1.00 = 2.65.
Now, let's calculate the concentration of titanium in the unknown solution.
Given:
Volume of Ti solution = 4.00 mL
Volume of Co solution = 3.00 mL
Atomic absorbance of Ti = 0.128
Atomic absorbance of Co = 0.218
First, let's calculate the concentration of cobalt in the unknown solution:
Cobalt concentration = Atomic absorbance of Co / Atomic absorption ratio
= 0.218 / 2.65
≈ 0.082 molar
Next, let's calculate the concentration of titanium:
Titanium concentration = (Atomic absorbance of Ti / Atomic absorption ratio) * Co concentration
= (0.128 / 2.65) * 0.082
≈ 0.0039 molar
Therefore, the concentration of titanium in the original unknown solution is approximately 0.0039 moles/L.
To determine the concentration of titanium in the original unknown solution, we will use the method of standard addition. This method involves adding a known amount of standard solution to the unknown solution and measuring the resulting signal. By comparing the signal of the unknown sample to that of a reference standard, we can calculate the concentration of the analyte in the original solution.
First, let's calculate the moles of cobalt (Co) in the mixture. We know that the atomic absorbance (A) of Co is 0.218, and the concentration of Co in the mixture is 11.7 micrograms/mL.
moles of Co = (A Co / A ref) * (C ref / V ref)
moles of Co = (0.218 / 2.65) * (11.7 micrograms/mL / 3.00 mL)
moles of Co = 9.302 micrograms / 7.95 micrograms/mole
moles of Co = 1.17 x 10^-3 moles
Next, let's calculate the moles of titanium (Ti) in the mixture. We know that the atomic absorbance of Ti is 0.128.
moles of Ti = (A Ti / A ref) * (C ref / V ref)
moles of Ti = (0.128 / 2.65) * (2.31 micrograms/mL / 3.00 mL)
moles of Ti = 5.017 micrograms / 7.95 micrograms/mole
moles of Ti = 6.31 x 10^-4 moles
Now, we can calculate the moles of Ti in the original unknown solution by subtracting the moles of Ti in the mixture from the moles of Ti added (4.00 mL * C unknown).
moles of Ti unknown = (4.00 mL - 3.00 mL) * C unknown
moles of Ti unknown = 1.00 mL * C unknown
moles of Ti unknown = 1.00 mL * C unknown
Since we have the moles of Ti in the mixture and the moles of Ti in the unknown solution, we can set up an equation.
moles of Ti unknown + moles of Ti mixture = moles of Ti added
C unknown = (moles of Ti mixture - moles of Ti added) / volume of unknown solution
C unknown = (6.31 x 10^-4 moles - 1.17 x 10^-3 moles) / 1.00 mL
C unknown = - 5.24 x 10^-4 moles / 1.00 mL
However, the concentration needs to be in moles/L, so we need to convert 1.00 mL to L.
C unknown = - 5.24 x 10^-4 moles / 1.00 L
C unknown = - 5.24 x 10^-4 M
The concentration of titanium in the original unknown solution is approximately - 5.24 x 10^-4 M. The negative sign indicates that the concentration is below the detection limit of the instrument or that there might have been an error in the calculations. It is important to double-check the calculations and ensure the accuracy of the measurements.