Question

A photometer with a linear response to radiation gave a reading of $529$mV with the solvent in the light path and $272$mV when the solvent was replaced by an absorbing solution. The photometer was set to zero with no light striking the detector. Calculate

(a) the percent transmittance and absorbance of the absorbing solution.

(b) the expected transmittance if the concentration of absorber is one half that of the original solution.

(c) the transmittance to be expected if the light path through the original solution is doubled.

Short answer

Part (a) Percent transmittance is $51.4\%$and absorbance is $0.289$

Part (b) The transmittance is $0.714$

Part (c) The transmittance is$0.264$

Step-by-step solution

Part (a) Step 1. Given information

The transmittance (T) is the ratio of transmitted radiation intensity to incident radiation intensity. It shows how much radiation the sample has absorbed. As a result, transmittance (T) is calculated as follows:

$T=\frac{P_{\text{solution}}}{P_{\text{solvent}}}$and

$\%T=\frac{P}{P_{\circ }}\times 100\%$

The relationship between transmittance and absorbance is $A=-{\log }_{10}\left(T\right)$

$$\begin{gathered} P_{\text{solution=}}272\text{mV} \\ {P}_{\text{solvent=}}529\text{mV} \end{gathered}$$

Part (a) Step 2. Percent transmittance and absorbance

Use the formula of percent transmittance for the given values in the question as,

$$\begin{gathered} \%T=\left(\frac{272\mathrm{mV}}{529\mathrm{mV}}\right)(100\%) \\ =51.4\% \end{gathered}$$

For absorbance u the formula provided in the theory part as,

$$\begin{gathered} A=-{\log }_{10}\left(\frac{51.4}{100}\right) \\ =0.289 \end{gathered}$$

Part (b) Step 1. expected transmittance

Use the formula of absorbance as,

$A=\frac{0.289}{2}=0.144$

Now apply relationship between absorbance and transmittance as,

$T={10}^{(-0.144)}=0.714$

Part (c) Step 1. expected transmittance

Use formula for absorbance as,

$A=(0.289)\left(2\right)=0.578$

Now apply relationship between absorbance and transmittance as,

$T={10}^{(-0.578)}=0.264$