Serum taken from a patient being treated with lithium for manic-depressive illness was analyzed for lithium concentration. A reading of 291 units was obtained for the intensity of the 671 nm red emission line. Then 1.00 mL of a 11.7 mM Lithium standard was added to 9.00 mL of serum, and this spiked serum gave an intensity reading of 729 units. What is the original concentration of Li in the serum?
To determine the original concentration of lithium in the serum, we need to use the method of standard addition.
Let's calculate the change in intensity caused by adding the standard solution:
Change in intensity = Intensity of spiked serum - Intensity of serum without standard
Change in intensity = 729 units - 291 units
Change in intensity = 438 units
Now, we can calculate the concentration of lithium in the spiked serum:
Concentration of lithium in spiked serum (Cspike) = (Change in intensity / Slope) + Intercept
To find the slope and intercept, we need to determine the relationship between concentration and intensity. For this, we need another standard of known concentration.
Assuming that a standard solution of lithium with a concentration of 11.7 mM also gives an intensity reading of 291 units under the same conditions, we can use this information to determine the slope and intercept.
Let's first calculate the change in intensity caused by the standard solution:
Change in intensity (standard) = Intensity of standard - Intensity of serum without standard
Change in intensity (standard) = 291 units - 291 units
Change in intensity (standard) = 0 units
Since the change in intensity caused by the standard solution is 0 units, the slope of the concentration-intensity relationship is:
Slope = (Change in intensity (standard) - Change in intensity) / (Concentration (standard) - Concentration (spike))
Slope = (0 units - 438 units) / (11.7 mM - 0 mM)
Slope = -438 units / 11.7 mM
Now, let's find the intercept. Since the intercept represents the intensity when the concentration is zero, we can use the intensity of the serum without standard:
Intercept = Intensity of serum without standard
Intercept = 291 units
Now that we have the slope and intercept, we can calculate the original concentration of lithium in the serum.
Original concentration of lithium in the serum = (Intensity of serum - Intercept) / Slope
Using the given intensity of the serum (291 units):
Original concentration of lithium in the serum = (291 units - 291 units) / (-438 units / 11.7 mM)
Original concentration of lithium in the serum = 0 mM
Therefore, the original concentration of lithium in the serum is 0 mM.
To determine the original concentration of lithium (Li) in the serum, we need to use the information provided about the intensity of the emission line before and after spiking the serum with a known lithium concentration.
Let's break down the steps to solve this problem:
Step 1: Calculate the dilution factor.
- In this case, 1.00 mL of a 11.7 mM lithium standard was added to 9.00 mL of serum.
- The total volume after spiking becomes 1.00 mL + 9.00 mL = 10.00 mL.
- The dilution factor is calculated as the total volume after spiking divided by the original volume of serum: 10.00 mL / 9.00 mL = 1.1111 (approximately).
Step 2: Calculate the corrected intensity of the spiked serum.
- The intensity reading after spiking the serum is given as 729 units.
- The corrected intensity is obtained by multiplying the intensity reading by the dilution factor: corrected intensity = 729 units × 1.1111 = 810 units (approximately).
Step 3: Calculate the concentration of lithium in the spiked serum.
- The concentration of lithium in the spiked serum can be determined using the Beer-Lambert law.
- Beer-Lambert law states that the concentration of an analyte is directly proportional to the absorbance or intensity of light.
- We have the intensity of the spiked serum (810 units) and the known concentration of lithium standard (11.7 mM).
- We can set up a proportion to solve for the concentration of lithium in the spiked serum:
(11.7 mM) / (810 units) = (x mM) / (291 units), where x is the concentration of lithium in the spiked serum.
- Solve the proportion for x:
x mM = (11.7 mM * 291 units) / 810 units ≈ 4.201 mM.
Step 4: Calculate the original concentration of lithium in the serum.
- The original lithium concentration in the spiked serum is 4.201 mM.
- We need to account for the dilution factor to calculate the original concentration in the serum.
- Divide the concentration found in step 3 by the dilution factor:
Original concentration = 4.201 mM / 1.1111 ≈ 3.781 mM.
Therefore, the original concentration of lithium in the serum is approximately 3.781 mM.