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.

Question

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.

Answer 1

To determine the concentration of titanium (Ti) in the original unknown solution, we need to first calculate the molar absorptivity of titanium and cobalt at the given wavelength.

The molar absorptivity (ε) is a measure of how strongly a substance absorbs light at a specific wavelength. It is usually given in units of L/(mol·cm).

Using the given signal-to-signal ratio for the standard mixture, we can write the following equation:

(Signal Ti unknown / Signal Co unknown) = (Signal Ti standard / Signal Co standard)

Substituting the given values:
0.128 / 0.218 = 2.65 / 1.00

Simplifying the equation:
0.128 * 1.00 = 0.218 * 2.65
0.128 = 0.5777

Now, we need to calculate the molar absorptivity of cobalt using the given concentration of cobalt in the standard mixture:

Concentration Co standard = 1.58 micrograms/mL = 1.58 * 10^-6 g/mL
Absorbance Co standard = 0.218

We can use the formula:

Absorbance = ε * concentration * path length

The path length is typically 1 cm in atomic absorption spectroscopy.

0.218 = ε * (1.58 * 10^-6) * 1
ε = 0.218 / (1.58 * 10^-6)
ε = 1.38 * 10^5 L/(mol·cm)

Now, we can calculate the concentration of titanium in the unknown solution:

Concentration Ti standard = 2.31 micrograms/mL = 2.31 * 10^-6 g/mL
Absorbance Ti unknown = 0.128

Using the same formula as before:

0.128 = ε * (concentration Ti unknown) * 1
0.128 = (1.38 * 10^5) * (concentration Ti unknown)
concentration Ti unknown = 0.128 / (1.38 * 10^5)
concentration Ti unknown = 9.28 * 10^-7 mol/L

Therefore, the concentration of titanium in the original unknown solution is 9.28 * 10^-7 mol/L.