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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?
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At a certain wavelength, liquid P transmits 70%, whereas liquid Q tran...
Answer:

Introduction:

The problem gives the percentage of incident light transmitted by liquid P and Q when separately placed in a spectrophotometric cell. It also gives the absorbance of a binary mixture of liquids P and Q in the same cell. We need to determine the volume fraction of liquid P in the binary mixture.

Explanation:

Step 1: Calculation of Transmittance and Absorbance

The transmittance of liquid P (T_P) is given as 70%, which means it absorbs 30% of the incident light. Similarly, the transmittance of liquid Q (T_Q) is given as 30%, which means it absorbs 70% of the incident light. The absorbance of the binary mixture (A_mix) is given as 0.25.

Using the relation between transmittance and absorbance, we can calculate the absorbance of each liquid in the binary mixture.

A_P = log(1/T_P) = log(1/0.7) = 0.155

A_Q = log(1/T_Q) = log(1/0.3) = 0.477

A_mix = A_P * f_P + A_Q * f_Q

where f_P and f_Q are the volume fractions of liquids P and Q in the binary mixture, respectively.

Step 2: Calculation of Volume Fraction of Liquid P

Substituting the values of A_P, A_Q, and A_mix in the above equation, we get:

0.25 = 0.155 * f_P + 0.477 * (1 - f_P)

Solving for f_P, we get:

f_P = (0.25 - 0.477)/(0.155 - 0.477) = 0.743

Therefore, the volume fraction of liquid P in the binary mixture is 0.743, which means that the remaining volume fraction is 1 - 0.743 = 0.257 for liquid Q.

Conclusion:

In conclusion, the volume fraction of liquid P in the binary mixture is 0.743, which means that the remaining volume fraction is 0.257 for liquid Q.
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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?
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