Respuesta :
Solution :
Given :
The spectrophotometer reading is (A) = 0.18
Absorbdance Vs Concentration follows a straight line relation passing throght the origin.
Let the relation be of the form A = mC -------(1)
where, A = absorbdance
C = concentration (μg/L)
For a given point, A = 0.9
C = 3 μg/L
From equation (1), we have
0.9 = m x 3
m = 0.3
Therefore the complete equation of the spectrophometer calibration curve becomes A = 0.3C
Now we have the relation relating the concenrtation of the traces and the absorbdance. Let us now calculate the concentration of the traces in sample for which A = 0.18.
[tex]$C = \frac{0.18}{0.3}$[/tex]
= 0.6
Traces concentration = 0.6 μg/L
Now in order to calculate the volume of the blood in a grown man we must know how much dye(mass) was injected into his blood.
For that it is given that the trace solution of 0.6 [tex]$cm^3$[/tex] and 5 μg/L was injected.
∴ Mass of the dye in solution injected [tex]$=\frac{5 \times 10^{-3} \times 10^6 \ \mu g\times 0.6 \ cm^3}{10^3 \ cm^3}$[/tex]
= 3 μg
This much of mass is diluted throughout the blood volume.
Thus if V(L) is total blood volume, then 0.6 μg/L x V = 3 μg
This means that the total mass of dye in the body is what we injected initially i.e. 3 μg and must be holding by V(L) of blood.
∴ [tex]$V=\frac{3\ \mu g}{0.6 \ \mu g/L}$[/tex]
= 5 L