All Exams Test series for 1 year @ ₹349 only
Question

The percent transmittance of $8 \times 10^{-5}$ M solution of $KMnO_4$ is 39.8 when measured at 510 nm in a cell of path length of 1 cm. The absorbance and the molar extinction coefficient (in $M^{-1} cm^{-1}$) of this solution are, respectively,

The correct answer is
0.4 and 5000

To solve this problem, we will use Beer-Lambert's Law, which states that the absorbance (\(A\)) of a solution is related to its percent transmittance (%T) by the formula:

\(A = -\log_{10}(T)\)

where \(T\) is the transmittance in decimal form. Since percent transmittance is given, we first convert this to a decimal by dividing by 100:

\(T = \frac{39.8}{100} = 0.398\)

Now, we can calculate the absorbance:

\(A = -\log_{10}(0.398)\)

Calculating the above gives:

\(A \approx 0.4\)

Next, we need to find the molar extinction coefficient (\\(\epsilon\)), using the Beer-Lambert Law formula:

\(A = \epsilon \cdot c \cdot l\)

where \(c\) is the concentration (given as \(8 \times 10^{-5} \, \text{M}\)) and \(l\) is the path length (given as 1 cm). Substituting the known values:

\(0.4 = \epsilon \cdot (8 \times 10^{-5}) \cdot 1\)

Solving for \(\epsilon\) gives:

\(\epsilon = \frac{0.4}{8 \times 10^{-5}} = 5000 \, \text{M}^{-1} \, \text{cm}^{-1}\)

Thus, the absorbance is 0.4 and the molar extinction coefficient is 5000 \(\text{M}^{-1} \, \text{cm}^{-1}\).

The correct answer is therefore:

0.4 and 5000

Was this answer helpful?

Important Questions from UV Vis Spectroscopy

  1. A 0.005 M solution of compound X transmits 80% of the incident light of wavelength ($\lambda$) 500 nm. The absorbance of 0.01 M solution of X is ______ (rounded off to three decimal places).
    (Given: path length = 1.0 cm)
Need Expert Advice?

Start Your Preparation with Prepp Mobile App

Download the app from Google Play & App Store
Download the app from Google Play & App Store
Prepp Mobile App