Serum taken from a patient being treated with lithium for manic-depressive illness was analyzed for lithium concentration. A reading of 3.00xE2 units was obtained for the intensity of the 671 nM red emission line. Then 1.00 mL of a 11.8 mM Lithium standard was added to 9.00 mL of serum, and this spiked serum gave an intensity reading of 748 units. What is the original concentration of Li in the serum?
To find the original concentration of lithium in the serum, we can use the method of standard addition. This involves adding a known amount of a standard solution to the sample and comparing the change in measured intensity to determine the concentration of the substance in the original sample.
Let's break down the problem step by step:
1. We are given the intensity reading of the red emission line for the serum as 3.00 x 10^2 units.
2. We are also given that 1.00 mL of a 11.8 mM lithium standard was added to 9.00 mL of serum, and the resulting spiked serum had an intensity reading of 748 units.
To start, we need to calculate the change in intensity caused by adding the standard solution to the serum.
Change in intensity = Intensity of spiked serum - Intensity of serum
Change in intensity = 748 units - 300 units
Change in intensity = 448 units
Now, we can use this change in intensity to calculate the concentration of lithium in the serum.
Change in concentration = Change in intensity * (Concentration of standard / Intensity of standard)
Change in concentration = 448 units * (11.8 mM / 748 units)
Simplifying the units, we get:
Change in concentration = 0.0711 mM
Finally, we can calculate the original concentration of lithium in the serum:
Original concentration = Concentration of spiked serum - Change in concentration
Original concentration = 11.8 mM - 0.0711 mM
Original concentration ≈ 11.729 mM
Therefore, the original concentration of lithium in the serum is approximately 11.729 mM.