A stock solution of inulin has a concentration of 500mg/ml. From this stock 0.05ml is diluted with 0.05ml of sterile saline. After 30 min blood is sampled and produces a result of 50ug/ml. What is total extravascular volume?
I just need to find what the diluted part is so I can use it in an equation.
To find the concentration of the diluted solution, you need to calculate the amount of inulin in the diluted part of the solution.
First, let's determine the amount of inulin in the original stock solution that was transferred into the dilution:
Amount of inulin in the 0.05 ml stock solution = 500 mg/ml × 0.05 ml
Amount of inulin in the 0.05 ml stock solution = 25 mg
Next, we know that the 0.05 ml of stock solution was diluted with an equal volume of sterile saline (0.05 ml), resulting in a total volume of 0.1 ml.
Now, we can calculate the concentration of inulin in the diluted solution after the dilution:
Concentration of inulin in the diluted solution = (Amount of inulin in diluted solution) / (Volume of diluted solution)
Since we have 25 mg of inulin in 0.05 ml of stock solution, we can use this information to calculate the concentration:
Concentration of inulin in the diluted solution = (25 mg) / (0.1 ml)
Now, we need to convert the concentration to units of ug/ml to match the given blood result:
Concentration of inulin in the diluted solution = (25 mg) / (0.1 ml) × (1000 ug/mg)
Concentration of inulin in the diluted solution = 250000 ug / 0.1 ml
Concentration of inulin in the diluted solution = 2,500,000 ug/ml
Given the blood result of 50 ug/ml, we can set up an equation to find the total extravascular volume:
(Concentration of inulin in the diluted solution) × (Volume of blood) = (Concentration of inulin in the extravascular volume) × (Total extravascular volume)
Substituting the known values:
(2,500,000 ug/ml) × (Volume of blood) = (50 ug/ml) × (Total extravascular volume)
Now, you can rearrange the equation to solve for the total extravascular volume:
Total extravascular volume = [(2,500,000 ug/ml) × (Volume of blood)] / (50 ug/ml)
Plug in the volume of the blood sampled, which is given in the problem, and solve for the total extravascular volume.