Potassium thiocyanate, KSCN , is often used to detect the presence of Fe^3+ ions in solution thr

Potassium thiocyanate, KSCN , is often used to detect the...

Potassium thiocyanate, $\mathrm{KSCN}$ , is often used to detect the presence of $\mathrm{Fe}^{3+}$ ions in solution through the formation of the red $\mathrm{Fe}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{SCN}^{2+}$ (or, more simply, FeSCN $^{2+} ; K_{\mathrm{f}}=8.9 \times 10^{2} )$ What is $\left[\mathrm{Fe}^{3+}\right]$ when 0.50 $\mathrm{L}$ each of 0.0015 $\mathrm{M} \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{3}$ and 0.20$M \mathrm{KSCN}$ are mixed?

Key Concepts

Chemical Equilibrium

Chemical equilibrium is the state in a reversible reaction where the rate of the forward reaction equals the rate of the backward reaction, resulting in constant concentrations of reactants and products over time. This concept allows us to set up expressions that relate the concentrations of all species in the reaction through the equilibrium constant, which is critical for solving problems that require computing unknown concentrations when the system has reached equilibrium.

Formation Constant (Kf)

The formation constant, or stability constant, quantifies the strength of the complex ion formed in a reaction. It is defined as the ratio of the concentration of the complex ion to the product of the concentrations of the individual ions, each raised to the power of their stoichiometric coefficients, at equilibrium. This constant helps determine how far a reaction proceeds in the formation of a complex, indicating whether the complex ion is highly favored or not.

Reaction Stoichiometry and Limiting Reactant

Reaction stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. When mixing solutions, determining the initial moles and concentrations of each reactant is crucial, as one reactant may be completely consumed (limiting reactant), thereby controlling the extent of the reaction. This concept is essential for setting up the equilibrium expressions accurately, especially when one of the reactants is present in much smaller amounts compared to the other.

Equilibrium Approximations

In many equilibrium problems, especially when one reactant is used in a much smaller amount than another and when the equilibrium constant is moderately large or small, approximations can simplify the calculations. By assuming that the change in concentration of a species is negligible compared to its initial concentration, one can avoid solving complex algebraic equations. However, these assumptions must be checked for validity after the calculation.

Transcript

00:01 Question number 100 is a complex ion formation question that involves a limiting reactant calculation.

00:12 We have 0 .5 liters of an iron 3 plus containing solution and 0 .5 liters of a thiosyanate containing solution.

00:26 And when we mix them together, the iron 3 plus should combine with the sulfur or the thiosyanate in order to make the iron thiosionate complex.

00:41 The kf value for the formation of this complex ion will simply be equal to the concentration of the product divided by the concentrations of the reactants, and its value is given to us at 8 .9 times 10 to the 2.

00:58 So the first thing we need to do is to determine what the limiting reactant is.

01:03 We have a certain amount of iron 3 plus and a certain amount of thiosynate, and we can calculate the amount of product that can be produced with each amount of reactant.

01:13 The reactant that produces the least amount of product will be the limiting reactant, and the amount of product that limiting reactant makes will be the maximum amount of product possible.

01:25 So we start with 0 .5 liters of a .0015 molar solution of iron 3 plus, its iron 3 nitrate that completely dissociates.

01:46 So this will give us moles of iron 3 plus.

01:50 In the reaction, 1 mole iron 3 plus forms 1 mole of the complex ion.

01:54 So this allows us to calculate 0 .075 moles of product that can be made from the amount of iron 3 plus that we have.

02:06 We'll do the same thing with the amount of thiosynate that we have.

02:10 We have a 0 .5 liter solution at a 0 .2 molar concentration.

02:17 The product of the volume and the molarity will give us the moles of thiosyonate that we have...

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