Question

to determine the moles of fe³⁺(aq) in a 100. ml sample of an unknown solution, excess kscn(s) is added to convert all the fe³⁺(aq) into the dark red species fescn²⁺(aq), as represented by the equation above. the absorbance of fescn²⁺(aq) at different concentrations is shown in the graph below. if the absorbance of the mixture is 0.20 at 453 nm, how many moles of fe³⁺(aq) were present in the 100. ml sample? (assume that any volume change due to adding the kscn(s) is negligible.)

Explanation:

Step1: Determine the concentration of \(FeSCN^{2 +}\)

From the graph, when the absorbance \(A = 0.20\), the concentration of \(FeSCN^{2+}\), \(C\) can be read.
By observing the linear - relationship in the graph (Beer's law \(A=\epsilon lC\), where \(A\) is absorbance, \(\epsilon\) is molar absorptivity, \(l\) is path - length, and \(C\) is concentration), when \(A = 0.20\), \(C=4\times10^{-5}\space M\)

Step2: Calculate the moles of \(FeSCN^{2+}\)

Use the formula \(n = C\times V\).
Given \(V=100\space mL=0.100\space L\) and \(C = 4\times10^{-5}\space M\) (moles per liter).
\(n=4\times 10^{-5}\space mol/L\times0.100\space L\)

Step3: Relate moles of \(FeSCN^{2+}\) to moles of \(Fe^{3+}\)

The reaction is \(Fe^{3+}(aq)+SCN^{-}(aq)
ightleftharpoons FeSCN^{2 +}(aq)\).
Since \(Fe^{3+}\) and \(FeSCN^{2+}\) have a \(1:1\) mole ratio (from the balanced chemical equation), the moles of \(Fe^{3+}\) is equal to the moles of \(FeSCN^{2+}\)

Answer:

\(n = 4\times10^{-6}\space mol\), so the answer is C.