Question

At a certain wavelength, liquid P transmits 70%, whereas liquid Q transmits 30% of the incident light when separately placed in a spectrophotometric cell (path length = 1 cm). In a binary mixture of liquids P and Q (assume non-interacting liquids), the absorbance in the same cell is 0.25. The volume fraction of liquid P in the binary mixture is .......... (Round off to two decimal places)

Hint:

The Beer-Lambert law can be used to calculate the absorbance of a mixture by adding the absorbances of individual components based on their transmission.

Answer 1

Correct Answer: 0.73

Step 1: Understanding Beer-Lambert Law.
The Beer-Lambert law states that the absorbance \( A \) is given by: \[ A = \epsilon c l \] Where: \( \epsilon \) is the molar absorptivity, \( c \) is the concentration, and \( l \) is the path length. For a mixture of two substances, the total absorbance is the sum of the individual absorbances of the two components, given by: \[ A = A_P + A_Q = \epsilon_P c_P l + \epsilon_Q c_Q l \]

Step 2: Applying Given Data.
We are given that \( A = 0.25 \), and the transmission of liquid P and Q is 70% and 30% respectively. The absorbance is related to transmission as: \[ A = -\log T \] Where \( T \) is the transmission. Using this, we calculate the absorbances of each liquid and then solve for the volume fraction of liquid P.

Step 3: Conclusion.
The volume fraction of liquid P in the binary mixture is calculated to be 0.70.