Question

Calculate the percent transmittance of solutions having half the absorbance of the solutions in Problem 13-1.

Short answer

a) The percent transmittance for the absorbance of 0.021 is 95.3% .

b) The percent transmittance for the absorbance of 0.458 is 34.48 %.

c) The percent transmittance for the absorbance of 0.122 is 75.5 %.

d) The percent transmittance for the absorbance of 0.1895 is 64.6 %.

e) The percent transmittance for the absorbance of 0.2175 is 60.6 %.

f) The percent transmittance for the absorbance of 0.2565 is 55.4 %.

Step-by-step solution

Part (a) Step 1: Given information

Express the following absorbances in terms of percent transmittance:

(a) 0.042 (d) 0.379

(b) 0.917 (e) 0.435

(c) 0.245 (f) 0.513

The relation between absorbance and transmittance is related by Beer’s law.

The expression for the Beer’s law is:

A = -log T

Where,

• A is the absorbance of the solution.

• T is the transmittance of the solution.

Rearrange the above expression in order to obtain the percent transmittance

${10}^{-A}={10}^{(\log T\%/100)}$

Simplify the expression for percent transmittance.

$T\%=\left({10}^{-A}\right)100$..........(1)

Part (a) Step 2: Explanation

Substitute the value in equation 1.

$$\begin{gathered} T\%=\left({10}^{-A}\right)100 \\ =\left({10}^{-0.021}\right)100 \\ =(0.953)100 \\ =95.53\% \end{gathered}$$

The percent transmittance for the absorbance of 0.021 is 95.53 %.

Part (b) Step 1: Explanation

Substitute the value in equation 1.

$$\begin{gathered} T\%=\left({10}^{-A}\right)100 \\ =\left({10}^{-0.458}\right)100 \\ =(0.348)100 \\ =34.48\% \end{gathered}$$

The percent transmittance for the absorbance of 0.458 is 34.48 %.

Part (c)  Step 1: Explanation

Substitute the value in equation 1.

$$\begin{gathered} T\%=\left({10}^{-A}\right)100 \\ =\left({10}^{-0.122}\right)100 \\ =(0.755)100 \\ =75.5\% \end{gathered}$$

The percent transmittance for the absorbance of 0.122 is 75.5 %.

Part (d) Step 1: Explanation

Substitute the value in equation 1.

$$\begin{gathered} T\%=\left({10}^{-A}\right)100 \\ =\left({10}^{-0.1895}\right)100 \\ =(0.646)100 \\ =64.6\% \end{gathered}$$

The percent transmittance for the absorbance of 0.1895 is 64.6 %.

Part (e) Step 1: Explanation

Substitute the value in equation 1.

$$\begin{gathered} T\%=\left({10}^{-A}\right)100 \\ =\left({10}^{-0.2175}\right)100 \\ =(0.606)100 \\ =60.6\% \end{gathered}$$

The percent transmittance for the absorbance of 0.2175 is 60.6 %.

Part (f) Step 1: Explanation

Substitute the value in equation 1.

$$\begin{gathered} T\%=\left({10}^{-A}\right)100 \\ =\left({10}^{-0.2565}\right)100 \\ =(0.554)100 \\ =55.4\% \end{gathered}$$

The percent transmittance for the absorbance of 0.2565 is 55.4 %.