Answer : The equilibrium concentration of
in the trial solution is ![4.58\times 10^{-8}M](https://tex.z-dn.net/?f=4.58%5Ctimes%2010%5E%7B-8%7DM)
Explanation :
First we have to calculate the initial moles of
and
.
![\text{Moles of }Fe^{3+}=0.20M\times 9.0mL=1.8mmol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20%7DFe%5E%7B3%2B%7D%3D0.20M%5Ctimes%209.0mL%3D1.8mmol)
and,
![\text{Moles of }SCN^-=0.0020M\times 1.0mL=0.0020mmol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20%7DSCN%5E-%3D0.0020M%5Ctimes%201.0mL%3D0.0020mmol)
The given balanced chemical reaction is,
![Fe^{3+}(aq)+SCN^-(aq)\rightleftharpoons FeSCN^{2+}(aq)](https://tex.z-dn.net/?f=Fe%5E%7B3%2B%7D%28aq%29%2BSCN%5E-%28aq%29%5Crightleftharpoons%20FeSCN%5E%7B2%2B%7D%28aq%29)
Since 1 mole of
reacts with 1 mole of
to give 1 mole of ![FeSCN^{2+}](https://tex.z-dn.net/?f=FeSCN%5E%7B2%2B%7D)
The limiting reagent is, ![SCN^-](https://tex.z-dn.net/?f=SCN%5E-)
So, the number of moles of
= 0.0020 mmole
Now we have to calculate the concentration of
.
![\text{Concentration of }FeSCN^{2+}=\frac{0.0020mmol}{9.0mL+1.0mL}=0.00020M](https://tex.z-dn.net/?f=%5Ctext%7BConcentration%20of%20%7DFeSCN%5E%7B2%2B%7D%3D%5Cfrac%7B0.0020mmol%7D%7B9.0mL%2B1.0mL%7D%3D0.00020M)
Using Beer-Lambert's law :
where,
A = absorbance of solution
C = concentration of solution
l = path length
= molar absorptivity coefficient
and l are same for stock solution and dilute solution. So,
![\epsilon l=\frac{A}{C}=\frac{0.480}{0.00020M}=2400M^{-1}](https://tex.z-dn.net/?f=%5Cepsilon%20l%3D%5Cfrac%7BA%7D%7BC%7D%3D%5Cfrac%7B0.480%7D%7B0.00020M%7D%3D2400M%5E%7B-1%7D)
For trial solution:
The equilibrium concentration of
is,
![[SCN^-]_{eqm}=[SCN^-]_{initial}-[FeSCN^{2+}]](https://tex.z-dn.net/?f=%5BSCN%5E-%5D_%7Beqm%7D%3D%5BSCN%5E-%5D_%7Binitial%7D-%5BFeSCN%5E%7B2%2B%7D%5D)
= 0.00050 M
Now calculate the
.
![C=\frac{A}{\epsilon l}=\frac{0.220}{2400M^{-1}}=9.17\times 10^{-5}M](https://tex.z-dn.net/?f=C%3D%5Cfrac%7BA%7D%7B%5Cepsilon%20l%7D%3D%5Cfrac%7B0.220%7D%7B2400M%5E%7B-1%7D%7D%3D9.17%5Ctimes%2010%5E%7B-5%7DM)
Now calculate the concentration of
.
![[SCN^-]_{eqm}=[SCN^-]_{initial}-[FeSCN^{2+}]](https://tex.z-dn.net/?f=%5BSCN%5E-%5D_%7Beqm%7D%3D%5BSCN%5E-%5D_%7Binitial%7D-%5BFeSCN%5E%7B2%2B%7D%5D)
![[SCN^-]_{eqm}=(0.00050M)-(9.17\times 10^{-5}M)](https://tex.z-dn.net/?f=%5BSCN%5E-%5D_%7Beqm%7D%3D%280.00050M%29-%289.17%5Ctimes%2010%5E%7B-5%7DM%29)
![[SCN^-]_{eqm}=4.58\times 10^{-8}M](https://tex.z-dn.net/?f=%5BSCN%5E-%5D_%7Beqm%7D%3D4.58%5Ctimes%2010%5E%7B-8%7DM)
Therefore, the equilibrium concentration of
in the trial solution is ![4.58\times 10^{-8}M](https://tex.z-dn.net/?f=4.58%5Ctimes%2010%5E%7B-8%7DM)