Question

(a) A $\mathbf{3}\mathbf{.}\mathbf{96}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}\mathbf{M}$solution of compound A exhibited an absorbance of 0.624 at 238nmin a 1.000 cmcuvet; a blank solution containing only solvent had an absorbance of 0.029at the same wavelength. Find the molar absorptivity of compound A.

(b) The absorbance of an unknown solution of compound A in the same solvent and cuvet was 0.375 at 238 nm. Find the concentration of A in the unknown.

(c) A concentrated solution of compound A in the same solvent was diluted from an initial volume ofto a final volume of 25.00mLand then had an absorbance of 0.733. What is the concentration of A in the concentrated solution?

Short answer

a) The molar absorptivity$1.50\times {10}^3{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1}$

b) The concentration of unknown A$2.31\times {10}^{-4}\mathrm{M}$

c) Concentration of compound A is$5.87\times {10}^{-3}\mathrm{M}$

Step-by-step solution

Define molar absorptivity

Molar absorptivity is a property of a substance which determines the fraction of light absorbed by it at a particular wavelength. Absorbance is the fraction of light absorbed.

$A=\epsilon cb$

Where,

$$\begin{gathered} \mathrm{\epsilon }=\mathrm{molarabsorptivitycoefficient} \\ \mathrm{b}=\mathrm{lengthofcuvet} \\ \mathrm{c}=\mathrm{concentrationofsolution} \\ \mathrm{A}=\mathrm{absorbance} \end{gathered}$$

The concentration of the absorbance

Theconcentration of the solution is$3.96\times {10}^{-4}\mathrm{M}$

Absorbance (A)$=0.624$

Wavelength$\left(\mathrm{\lambda }\right)=238\mathrm{nm}$

Length of cuvette$\left(\mathrm{b}\right)=1.00\mathrm{cm}$

Absorbance for blank solution is at$238\mathrm{nm}=0.029$

Therefore, the molar absorptivity is calculated below.

$$\begin{gathered} \mathrm{\epsilon }=\frac{\mathrm{A}}{\mathrm{bc}}=\frac{\begin{array}{c}\mathrm{A}=\mathrm{\epsilon cb}\\ 0.624-0.029\end{array}}{(196\times {10}^4{\mathrm{M}}^{-1}){\mathrm{cm}}^{-1}\left)\right(1.000\mathrm{cm})} \\ =1.50\times {10}^3{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1} \end{gathered}$$

The concentration of the unknown solution

Absorbance (A)$=0.375$

Wavelength $\left(\mathrm{\lambda }\right)=238\mathrm{nm}$

Length of cuvette$\left(\mathrm{b}\right)=1.00\mathrm{cm}$

Absorbance for blank solution is at $238nm=0.029$

Molar absorptivity of A$\left(\mathrm{\epsilon }\right)=1.50\times {10}^{-3}{\mathrm{M}}^{-}{\mathrm{cm}}^{-}$

Concentration of unknown compound A is calculated below.

$$\begin{gathered} \mathrm{c}=\frac{\mathrm{A}}{\mathrm{\epsilon b}}=\frac{0.375-10.029}{1.50\times {10}^3{\mathrm{M}}^{-1}{\mathrm{cm}}^{-1}\left(1000\mathrm{cm}\right)} \\ =2.31\times {10}^{-4}\mathrm{M} \end{gathered}$$

The concentration of A solution

Initial volume$=2.00\mathrm{mL}$

Final volume = 25.00ml

Absorbance (A) =0.743

Wavelength$\left(\mathrm{\lambda }\right)=238\mathrm{nm}$

Length of cuvette$\left(\mathrm{b}\right)=1.00\mathrm{cm}$

Absorbance for blank solution is at$238\mathrm{nm}=0.029$

Molar absorptivity of A $\left(\mathrm{\epsilon }\right)=1.50\times {10}^{-3}{\mathrm{M}}^{-}{\mathrm{cm}}^{-}$

The concentration of A is given below.

$$\begin{gathered} \mathrm{c}=(\mathrm{dilution}\mathrm{factor})\frac{\mathrm{A}}{\mathrm{\epsilon b}} \\ \mathrm{c}=\left(\frac{25.00\mathrm{ml}}{200\mathrm{ml}}\right)\frac{0.733-0.009}{\left(1.50\times {10}^3{\mathrm{M}}^{-1}{\mathrm{tm}}^{-1}\right)\left(1.000\mathrm{m}\right)} \\ =5.87\times {10}^{-3}\mathrm{M}. \end{gathered}$$