# Plotting the data using Beer-Lambert law [closed]

For the spectroscopy lab we had a stock dye ($$\pu{1.00E-4 M}$$ Erioglaucine Blue) that we had to dilute. We had to dilute $$\pu{1 mL},$$ $$\pu{3 mL},$$ $$\pu{5 mL},$$ $$\pu{8 mL},$$ and $$\pu{10 mL}$$ in $$\pu{100 mL}$$ of water and measure their absorbance $$A.$$ I obtained the following data:

$$\begin{array}{ccc} \hline V/\pu{mL} & A & λ/\pu{nm} \\ \hline 1 & 0.127 & 629.0 \\ 3 & 0.342 & 626.2 \\ 5 & 0.550 & 627.6 \\ 8 & 0.850 & 628.3 \\ 10 & 1.064 & 626.9 \\ \hline \end{array}$$

How do I get the concentration in $$\pu{mol L^-1}$$ in order to make the graph? If I could get one example from this data set I should be able to calculate the rest for myself. I just need a head start.

• I corrected a few typos, terminology ("concentration in Moles" is meaningless) and tried to make the data somewhat more readable, but I'm still not sure what graph you are talking about. Do you mean a calibration curve? Also, what about getting the molar absorptivity for your dye? – andselisk Sep 20 at 14:56
• @ Jasmine. You must absolutely measure your absorbances at the same wavelength. If you change the wavelength for each sample, you cannot use your measurements for any graph or calculations whatsoever. The only hope is to admit that the absorbances at $626.2$ nm and $629.0$ nm are not significantly different. Is it the case ? – Maurice Sep 20 at 20:57
• Jasmine, wert @Maurice's comment: did you record the apsorption spectrum at one of the concentrations? What difference does it show in the wavelength range your measurements cover? Also, what is the spectral resolution of your instrument? Do you really have 4 significant digits in your data? Why did the wavelengths change between measurements? – cbeleites unhappy with SX Sep 21 at 7:32

You need to be aware of the dilution formula in order to plot concentration on the x-axis and absorbance on the y-axis:

$$C_iV_i = C_fV_f$$

So your initial concentration is your stock concentration and your initial volume is listed in the table. Your final volume is $$\pu{100 mL}$$. Can you determine $$C_f$$? With that you would be able to calculate all 5 different concentrations.

Keep in mind, that you need to fix the wavelength of measurement. Since the spectrum is very broad, $$\pu{1 nm}$$ will not make a huge difference. You may not have perfect linearity.

• @Jasmine: I just want to make a point for M. Farooq's answer (kind of icing on the cake). You want the concentration in $\pu{mol L−1}$. Since the concentration of your original stock solution is already given in $\pu{mol L−1}$, you do not have to convert units of $V_i$ and $V_f$ during the calculations. Just make sure both in same units so they will be cancelled out from either side of the equation. – Mathew Mahindaratne Sep 20 at 21:49