A student records a transmittance of 40 percent for a particular solution. What
ID: 992748 • Letter: A
Question
A student records a transmittance of 40 percent for a particular solution. What would the transmittance be if the solution concentration were doubled? A metal cation M^n+ reacts with a ligand L to form the complex aM^n+ + bL rightarrow [M_aL_b]^n+ Using a 0.005 M solution of M^n+ (A) and a 0.005 M solution of L (B), a series of solutions was prepared as shown below. Each solution was diluted to 50 mL and the absorbance was measured. Calculate the mole fractions of the metal cation and the ligand for each solution. Show your calculations. Make a plot of absorbance (y axis) versus mole fraction of the metal cation and the mole fraction of the ligand (x axis). Attach the graph to this report. Determine the composition of the complex.Explanation / Answer
A1)
This problem is based on Beer-Lambert’s law.
Mathematical expression for Beer-Lambert’s law is,
A = bC
Where,
A = absorbance of solution
= Molar absorptivity
b = path length
C = concentration of the solution.
Molar absorptivity () is constant for given analyte and if path length kept constant throughout the experiment,
Absorbance is directly proportional to the concentration (C)
A C
i.e. A/C = constant
We can write,
A1/C1 = A2/C2
A2/A1 = C2/C1 ……………… (1)
Absorbance (A) related with transmittance (T) as,
A = - log T
For % transmittance (%T) we have
A = -log(T/100)
A = -[log(T) – log100)]
A = -[log(T) – 2]
A = 2 – log(T) ……………….. (2)
For given condition T = 40 %
Let us calculate Absorbance (say A1) at concentration (C1) for 40% transmittance,
A1 = 2 – log(40)
A1 = 2 – 1.6021
A1 = 0.3979
Let at concentration C2 absorbance be A2
As per given condition now concentration is doubled,
C2 = 2 x C1
C2/C1 = 2
Let us put this value of C2/C1 and A1 in eq.(1) and solve it for A2,
A2/A1 = C2/C1
A2/(0.3979) = 2
A2 = 2x 0.3979
A2 = 0.7958
Then, using eq.(2) we can calculate %T as,
0.7958 = 2 – log(T)
log(T) = 2 – 0.7958
log(T) = 1.2042
T = 101.2042
T = 16%
On doubling concentration transmittance become 16%.
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