Respuesta :
Explanation:
a) Using Beer-Lambert's law :
Formula used :
[tex]A=\epsilon \times c\times l[/tex]
where,
A = absorbance of solution = 0.945
c = concentration of solution = ?
l = length of the cell = 1.20 cm
[tex]\epsilon[/tex] = molar absorptivity of this solution =[tex]5.56\times 10^4 M^{-1} cm^{-1}[/tex]
[tex]0.945=5.56\times 10^4 M^{-1} cm^{-1}\times 1.20 \times c[/tex]
[tex]c=1.4163\times 10^{-5} M=14.16 \mu M[/tex]
([tex]1\mu M=10^{-6} M[/tex])
14.16 μM is the molarity of the red dye solution at the optimal wavelength 519nm and absorbance value 0.945.
b) [tex]c=1.4163\times 10^{-5} mol/L[/tex]
1 L of solution contains [tex]1.4163\times 10^{-5} [/tex] moles of red dye.
Mass of [tex]1.4163\times 10^{-5} [/tex] moles of red dye:
[tex]1.4163\times 10^{-5}\times 879.86g/mol=0.01246 g[/tex]
[tex](w/v)\%=\frac{\text{Mass of solute (g)}}{\text{Volume of solvent (mL)}}\times 100[/tex]
[tex]red(w/v)\%=\frac{0.01246 g}{1000 mL}\times 100=0.001246\%[/tex]
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 = [tex]c=1.4163\times 10^{-5} M[/tex]
Concentration of red solution after dilution = c'
[tex]c=c'\times 5[/tex]
[tex]1.4163\times 10^{-5} M=c'\times 5[/tex]
[tex]c'=2.83\times 10^{-6} M[/tex]
The final concentration of the diluted solution is [tex]2.83\times 10^{-6} M[/tex]
