Question

If the molar absorptivity constant for the red dye solution is 5.56×104 M-1cm-1, calculate the molarity of the red dye solution at the optimal wavelength 519nm and absorbance value 0.945

You may assume L = 1.20cm. Hint: A=εLC

b. Convert the molarity in part a to w/v%. Show your work. Molar mass of FD&C red #3 = 879.86g/mol Refer to examples on next page

c. If you want to dilute the red dye solution in part a by 5 times in a single dilution step, explain in two sentences on how one should proceed with the dilution. In addition, calculate the final concentration of the diluted solution. Show your work for the numerical part of this question.

Answer 1

Step-by-step explanation:

a) Using Beer-Lambert's law :

Formula used :

`A=\epsilon * c* l`

where,

A = absorbance of solution = 0.945

c = concentration of solution = ?

l = length of the cell = 1.20 cm

`\epsilon` = molar absorptivity of this solution =
`5.56* 10^4 M^(-1) cm^(-1)`

`0.945=5.56* 10^4 M^(-1) cm^(-1)* 1.20 * c`

`c=1.4163* 10^(-5) M=14.16 \mu M`

(
`1\mu M=10^(-6) M`)

14.16 μM is the molarity of the red dye solution at the optimal wavelength 519nm and absorbance value 0.945.

b)
`c=1.4163* 10^(-5) mol/L`

1 L of solution contains
`1.4163* 10^(-5)` moles of red dye.

Mass of
`1.4163* 10^(-5)` moles of red dye:

`1.4163* 10^(-5)* 879.86g/mol=0.01246 g`

`(w/v)\%=\frac{\text{Mass of solute (g)}}{\text{Volume of solvent (mL)}}* 100`

`red(w/v)\%=(0.01246 g)/(1000 mL)* 100=0.001246\%`

c) In order to dilute red dye solution by 5 times, we will need to add 1 L of water to solution of given concentration.

Concentration of red dye solution =
`c=1.4163* 10^(-5) M`

Concentration of red solution after dilution = c'

`c=c'* 5`

`1.4163* 10^(-5) M=c'* 5`

`c'=2.83* 10^(-6) M`

The final concentration of the diluted solution is
`2.83* 10^(-6) M`