Potassium thiocyanate, \(\mathrm{KSCN},\) is often used to detect the presence of \(\mathrm{Fe}^{3+}\) ions in solution through the formation of the red \(\mathrm{FeSCN}^{2+}\left(K_{\mathrm{f}}=8.9 \times 10^{2}\right) .\) What is \(\left[\mathrm{Fe}^{3+}\right]\) when \(0.50 \mathrm{~L}\) each of \(0.0015 M \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}\) and \(0.20 M \mathrm{KSCN}\) are mixed?

In any chemical reaction, the limiting reagent is the reactant that is completely consumed first. It limits the amount of product formed because once it is used up, no further reaction can occur. Understanding which reagent is limiting is crucial, as it determines the maximum yield of the reaction.

Let's break it down with our example of \(\mathrm{Fe}^{3}+\) and \(\mathrm{SCN}^{-}\).

• We start with 0.00075 moles of \(\mathrm{Fe}^{3}+\) and 0.10 moles of \(\mathrm{SCN}^{-}\).
• Since the chemical reaction is in a 1:1 ratio, the \(\mathrm{Fe}^{3}+\) will be the limiting reagent because it has fewer moles compared to \(\mathrm{SCN}^{-}\).

This means that only 0.00075 moles of \(\mathrm{FeSCN}^{2+}\) will form, as the reaction will stop once all \(\mathrm{Fe}^{3}+\) is consumed.

Equilibrium concentration refers to the concentration of reactants and products in a chemical reaction when it has reached a state where the rates of the forward and reverse reactions are equal. This means there’s no net change in the concentration of any species over time.

To find equilibrium concentrations, follow the steps from our example:

• Calculate the moles of each species after the reaction goes to completion with the limiting reagent.
• Determine the entire volume of the solution after mixing; in this case, it's 1.00 L.
• Convert the moles of each species to molarity (moles per liter).

For instance, the equilibrium concentrations were: \(\left[\mathrm{FeSCN}^{2+}\right] = 0.00075 \space M\textrm{ and } \left[\mathrm{SCN}^{-}\right] = 0.09925 \space M.\)

A chemical reaction involves the conversion of reactants into products, which occurs through breaking and forming chemical bonds. Each reaction can be described by a balanced chemical equation that represents the conservation of mass and charge.

In our example, the balanced chemical equation is: <\[\mathrm{Fe}^{3}+ + \mathrm{SCN}^{-} \leftrightarrow \mathrm{FeSCN}^{2+}\].
This equation indicates that one mole of \(\mathrm{Fe}^{3}+\) reacts with one mole of \(\mathrm{SCN}^{-}\) to form one mole of \mathrm{FeSCN}^{2+}\.
Understanding this balanced equation is crucial because it provides the stoichiometric relationships needed to understand the proportions and calculations in the reaction.
The equilibrium constant \(K_{f}\) for this reaction is given by:
<\[K_{f} = \frac{[\mathrm{FeSCN}^{2+}]}{[\mathrm{Fe}^{3}+][\mathrm{SCN}^{-}]}\]\