6) (a) Calculate the absorbance of the solution if its concentration is 0.0278 M and its molar extinction coefficient is 35.9 L/(mol cm). The depth of the cell is 5 mm. (b) What is the %T? (7) Calculate the absorbance of the solution if the transmitted light intensity is 70% of the initial light beam intensity

Answer:

6) (a) 0.499; (b) 31.7 %

7) 0.15

Explanation:

6) (a) Absorbance

Beer's Law is

[tex]A = \epsilon cl\\A = \text{35.9 L&\cdot$mol$^{-1}$cm$^{-1}$} $\times$ 0.0278 mol$\cdot$L$^{-1} \times $ 0.5 cm = \mathbf{0.499}[/tex]

(b) Percent transmission

[tex]A = \log {\left (\dfrac{1}{T}}\right)}\\\\\%T = 100T\\\\T = \dfrac{\%T}{100}\\\\\dfrac{1}{T} = \dfrac{100 }{\%T}\\\\A = \log \left(\dfrac{100 }{\%T} \right ) = 2 - \log \%T\\\\0.499 = 2 - \log \%T\\\\\log \%T = 2 - 0.499 = 1.501\\\\\%T = 10^{1.501} = \mathbf{31.7}[/tex]

7) Absorbance

[tex]A = \log \left (\dfrac{I_{0}}{I} \right ) = \log \left (\dfrac{I_{0}}{0.70I_{0}} \right ) = \log \left (\dfrac{1}{0.70} \right ) = -\log(0.70) = \mathbf{0.15}}[/tex]

The absorbance of the solution with the given molar extinction coefficient, concentration, and path length is approximately 0.5, and the percent transmittance is approximately 31.6%. When the transmitted light is 70% of the initial light beam intensity, the absorbance is approximately 0.523.

The subject matter is related to the concept of absorbance in Chemistry. In this specific case, you are required to know and apply the Beer-Lambert law, which states that the absorbance (A) of a solution is directly proportional to its concentration (c) and the path length (l). The formula used is A = εcl, where ε is the molar extinction coefficient.

For part (a), plug the given values into the above formula to get: A = 35.9 L/(mol cm) * 0.0278 mol/L * 0.5 cm = 0.4987. So, the absorbance of the solution is approximately 0.5.

Now, for part (b), the percent transmittance (%T) can be calculated using the relationship A = 2 - log(%T). Solving for %T gives: %T = 10^(2-A) = 10^(2-0.4987) = 31.6%. So the %T is approximately 31.6%.

For part (7), the decrease in the intensity of light by 70% means the transmitted light is 30% of the initial intensity. The absorbance in this case can be calculated directly from the formula A = -log(I/I0) where I/I0 = 0.30. Hence, A = -log(0.30) = 0.523. So the absorbance, when the transmitted light intensity is 70% of the initial light beam intensity, is approximately 0.523.

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