1 ml of whole blood is collected and centrifuged to obtain a plasma sample. The volume of the plasma sample is 600 microlitres. A 1 in 4 dilution of the plasma is made and analysed using a cholesterol assay like the one you performed in the laboratory. 10 microlitres of both the diluted plasma sample and a cholesterol standard are assayed using 1mL of cholesterol reagent. Following incubation at 37 degrees Celcius, the samples are measured spectrophotometrically at 500nm.

If the absorbance of the plasma sample assay was 0.5, the absorbance of the cholesterol standard assay was 0.3, and the concentration of cholesterol in the original whole blood sample was 4.5mM, what was the concentration of the cholesterol standard (in mM)?
(assume all of the cholesterol in the whole blood sample was recovered in the plasma)

Any help is greatly appreciated

2.5

It isn't clear from your post if the standard was diluted in a manner similar to that of the sample. I will assume it was; if not you will need to make a adjustment for the dilution.

If the sample is 4.5 mM and gave A = 0.5, it must be a higher concn than the standard at A = 0.3. So the standard sample must be 4.5 mM s 0.3/0.5 = ?

To find the concentration of the cholesterol standard, we can use the Beer-Lambert Law, which states that absorbance is directly proportional to concentration.

First, let's calculate the dilution factor for the plasma sample:

Dilution factor = (volume of initial sample) / (volume of final sample)
Dilution factor = (1 ml) / (600 µl)
Dilution factor = 1.67

Next, let's calculate the concentration of the diluted plasma sample:

Concentration of diluted plasma sample = (concentration of original plasma sample) / (dilution factor)
Concentration of diluted plasma sample = (4.5 mM) / (1.67)
Concentration of diluted plasma sample ≈ 2.69 mM

Now, let's calculate the concentration of the cholesterol standard using the absorbance values:

Absorbance of the cholesterol standard = (concentration of the cholesterol standard) × (absorptivity)
Absorptivity is a constant specific to the assay reagents and wavelength used.

Absorbance of the cholesterol standard = 0.3

Therefore, we can rearrange the equation to solve for the concentration of the cholesterol standard:

Concentration of the cholesterol standard = (absorbance of the cholesterol standard) / (absorptivity)

Given that the absorbance of the cholesterol standard is 0.3, you need to know the specific absorptivity value for the assay reagents and wavelength used to calculate the concentration of the cholesterol standard accurately.

To solve this problem, we need to use the principles of dilution and the Beer-Lambert law. Let's break down the steps to find the concentration of the cholesterol standard.

Step 1: Calculate the dilution factor
In this case, a 1 in 4 dilution of the plasma sample was made to perform the cholesterol assay. This means that the diluted plasma sample used in the assay is one-fourth the concentration of the original plasma sample. Therefore, the dilution factor is 1/4.

Step 2: Calculate the concentration of cholesterol in the diluted plasma sample
We know that the volume of the plasma sample is 600 microlitres. Since a 1 in 4 dilution was made, the concentration of cholesterol in the diluted plasma sample is four times that of the original plasma sample.
So, the concentration of cholesterol in the diluted plasma sample is (4.5 mM) * (4) = 18 mM.

Step 3: Calculate the concentration of cholesterol in the cholesterol standard
We can use the Beer-Lambert law to relate the absorbance of the cholesterol standard to its concentration.
The Beer-Lambert law equation is:

A = εlc

Where:
- A is the absorbance
- ε is the molar absorptivity constant (a constant for a given compound)
- l is the path length (in this case, 1 cm, as common in spectrophotometry)
- c is the concentration of the compound in solution

We can rearrange the formula to solve for the concentration (c):

c = A / (ε * l)

Given that the absorbance of the cholesterol standard is 0.3 and assuming the molar absorptivity constant and path length are constant, we can calculate the concentration of cholesterol in the cholesterol standard.
Let's denote the concentration of the cholesterol standard as X mM.

X = 0.3 / (ε * 1)

Step 4: Calculate the molar absorptivity constant (ε)
Since we are assuming all other factors (like path length) are constant, we can consider the absorbance ratio between the cholesterol standard and diluted plasma sample to calculate ε.

ε = (Concentration of cholesterol in diluted plasma sample) / (Concentration of cholesterol standard)

ε = 18 mM / X

Step 5: Calculate the concentration of the cholesterol standard
Now that we have ε, we can substitute it back into Step 3's equation:

X = 0.3 / ((18 mM / X) * 1)

Simplifying the equation:

X * 18 mM = 0.3

X = 0.3 / (18 mM)

X ≈ 0.0167 mM

Therefore, the concentration of the cholesterol standard (in mM) is approximately 0.0167 mM.