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.
Step 1: Calculate the change in intensity caused by the addition of the standard solution.
The change in intensity is given by the difference between the intensity of the spiked serum and the intensity of the serum alone:
Change in intensity = Intensity of spiked serum - Intensity of serum alone
Change in intensity = 729 units - 291 units
Change in intensity = 438 units
Step 2: Calculate the concentration of lithium in the spiked serum solution.
The concentration of lithium in the spiked serum solution can be calculated using the formula for molarity (M):
Molarity (M) = moles of solute / volume of solution in liters
Since we know the volume and concentration of the lithium standard solution, we can calculate the moles of lithium added to the serum.
Moles of lithium = Molarity of standard solution × Volume of standard solution (in liters)
Moles of lithium = 11.7 mM × 1.00 mL × (1 L / 1000 mL)
Moles of lithium = 0.0117 mol
Now, we need to calculate the concentration of lithium in the spiked serum solution:
Concentration of lithium in spiked serum = Moles of lithium / Volume of spiked serum solution (in liters)
Concentration of lithium in spiked serum = 0.0117 mol / 0.01 L
Concentration of lithium in spiked serum = 1.17 mol/L
Step 3: Calculate the original concentration of lithium in the serum alone.
To find the original concentration of lithium in the serum, we subtract the concentration of lithium in the spiked serum from the concentration of lithium in the serum alone.
Original concentration of lithium in serum = Concentration of lithium in spiked serum - Concentration of lithium in serum alone
Original concentration of lithium in serum = 1.17 mol/L - 0 mol/L
Original concentration of lithium in serum = 1.17 mol/L
Therefore, the original concentration of lithium in the serum is 1.17 mol/L.
To determine the original concentration of lithium (Li) in the serum, we will use the method of standard addition.
The principle behind standard addition is that we add a known amount of standard solution (with a known concentration) to the sample, and then compare the measured response to the response of the sample alone.
Given information:
- Reading from the patient's serum: 291 units
- Reading from spiked serum (sample + 1.00 mL standard): 729 units
- Concentration of the standard solution: 11.7 mM
- Volume of the standard solution added: 1.00 mL
- Volume of the spiked serum: 9.00 mL
First, let's calculate the change in intensity caused by the addition of the standard solution. We will subtract the initial reading (291 units) from the spiked serum reading (729 units):
Change in intensity = Reading of spiked serum - Reading of patient's serum
Change in intensity = 729 units - 291 units
Change in intensity = 438 units
Now, we can use this change in intensity to determine the concentration of lithium in the patient's serum.
The change in intensity is proportional to the change in concentration. So, we can set up a proportion with the change in concentration of the standard solution and the change in intensity:
(change in concentration of standard solution) / (change in intensity) = (original concentration of serum) / (initial intensity of serum)
Let's calculate the change in concentration of the standard solution:
Change in concentration of standard solution = (change in intensity) * (original concentration of serum) / (initial intensity of serum)
Substituting the known values:
Change in concentration of standard solution = 438 * (original concentration of serum) / 291
Now, we can solve for the original concentration of lithium in the serum. To do this, we divide both sides of the equation by the change in concentration of standard solution:
original concentration of serum = (change in concentration of standard solution) * (initial intensity of serum) / (change in intensity)
Substituting the known values:
original concentration of serum = (438 * original concentration of serum / 291) * 291 / 438
Simplifying the equation:
original concentration of serum = original concentration of serum
After simplification, we find that the original concentration of lithium in the serum is equal to the concentration of the standard solution, which is 11.7 mM.