Problem 29 - Analytical Chemistry

Question

Kawakami and Igarashi developed a spectrophotometric method for nitrite based on its reaction with 5,10,15,20 -tetrakis( 4 -aminophenyl) porphrine (TAPP). As part of their study they investigated the stoichiometry of the reaction between TAPP and \(\mathrm{NO}_{2}^{-}\). The following data are derived from a figure in their paper. \({ }^{29}\) $$ \begin{array}{ccc} {[\mathrm{TAPP}](\mathrm{M})} & {\left[\mathrm{NO}_{2}^{-}\right](\mathrm{M})} & \text { absorbance } \\ \hline 8.0 \times 10^{-7} & 0 & 0.227 \\ 8.0 \times 10^{-7} & 4.0 \times 10^{-8} & 0.223 \\ 8.0 \times 10^{-7} & 8.0 \times 10^{-8} & 0.211 \\ 8.0 \times 10^{-7} & 1.6 \times 10^{-7} & 0.191 \\ 8.0 \times 10^{-7} & 3.2 \times 10^{-7} & 0.152 \\ 8.0 \times 10^{-7} & 4.8 \times 10^{-7} & 0.127 \\ 8.0 \times 10^{-7} & 6.4 \times 10^{-7} & 0.107 \\ 8.0 \times 10^{-7} & 8.0 \times 10^{-7} & 0.092 \\ 8.0 \times 10^{-7} & 1.6 \times 10^{-6} & 0.058 \\ 8.0 \times 10^{-7} & 2.4 \times 10^{-6} & 0.045 \\ 8.0 \times 10^{-7} & 3.2 \times 10^{-6} & 0.037 \\ 8.0 \times 10^{-7} & 4.0 \times 10^{-6} & 0.034 \end{array} $$ What is the stoichiometry of the reaction?

Step-by-Step Solution

Answer

The stoichiometry of the reaction is 1:1.

Step 1: Analyze Initial Data

The data shows a fixed concentration of TAPP at \(8.0 \times 10^{-7}\, \text{M}\) while the concentration of \(\mathrm{NO}_{2}^{-}\) varies. Observe how absorbance decreases as the \(\mathrm{NO}_{2}^{-}\) concentration increases. This indicates that \(\mathrm{NO}_{2}^{-}\) is reacting with TAPP, causing a change in absorbance.

Step 2: Calculate the Change in Absorbance

Determine the change in absorbance from the initial amount without \(\mathrm{NO}_{2}^{-}\) present (0.227) to the different concentrations of \(\mathrm{NO}_{2}^{-}\). This change helps understand the reaction's progress.

Step 3: Finding Equivalence Point

To determine stoichiometry, identify the point where adding more \(\mathrm{NO}_{2}^{-}\) doesn't significantly change the absorbance. This indicates completion of the reaction. Notably, this occurs between \(8.0 \times 10^{-7}\,\text{M}\) and \(1.6 \times 10^{-6}\,\text{M}\) of \(\mathrm{NO}_{2}^{-}\).

Step 4: Determine Stoichiometric Ratio

Notice that when \(\left[\mathrm{NO}_{2}^{-}\right] = 8.0 \times 10^{-7}\,\text{M}\) and \(\left[\mathrm{TAPP}\right] = 8.0 \times 10^{-7}\,\text{M}\), the absorbance is still decreasing. By the time \([\mathrm{NO}_{2}^{-}]\) reaches \(1.6 \times 10^{-6}\,\text{M}\), the absorbance is close to stabilized at a value of 0.058 showing most TAPP has reacted. This implies a \(1:1\) stoichiometric ratio of TAPP to \(\mathrm{NO}_{2}^{-}\).

Key Concepts

Reaction Stoichiometry

Reaction stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction. In this specific exercise, we analyzed the stoichiometry between TAPP and \( \mathrm{NO}_2^{-} \). The goal was to determine how these two reactants combine in a specific ratio to form the reaction product.

To find the stoichiometry, we observed changes in absorbance as the concentration of \( \mathrm{NO}_2^{-} \) increased while keeping TAPP constant. Initially, as \( \mathrm{NO}_2^{-} \) was added, the absorbance gradually decreased, suggesting \( \mathrm{NO}_2^{-} \)'s consumption in the reaction.

As the experiment proceeded, equilibrium was approached when \([\mathrm{NO}_2^{-}] \) equaled \([\mathrm{TAPP}] \). This equivalence point is crucial for identifying stoichiometric balance, ultimately indicating a \(1:1\) stoichiometric ratio. In essence, equal amounts of TAPP and \( \mathrm{NO}_2^{-} \) are required to completely react, marking the stoichiometric endpoint of this reaction.

Absorbance Measurement

Absorbance measurement is a key aspect of spectrophotometry and involves evaluating how much light a solution absorbs. Here, we used absorbance to track the reaction between TAPP and \( \mathrm{NO}_2^{-} \).

The principle behind measuring absorbance relates to the Beer-Lambert law, which states that absorbance is directly proportional to concentration. This means as the concentration of the reactant changes, so does the absorbance, allowing for a quantitative analysis of reaction progress.

In this exercise, the absorbance was measured at various concentrations of \( \mathrm{NO}_2^{-} \), keeping TAPP concentration constant at \(8.0 \times 10^{-7} \, \text{M}\). A clear decrease in absorbance was observed with increasing \( \mathrm{NO}_2^{-} \) concentrations. This understanding provided insight into how much \( \mathrm{NO}_2^{-} \) reacted with TAPP until the solution reached equilibrium. Detecting these trends in absorbance is vital for determining reaction points and supports broader chemical analysis.

Chemical Equilibrium

Chemical equilibrium refers to the state of a reaction where the forward and reverse reaction rates are equal. At equilibrium, the concentration of reactants and products remains constant. In our study of TAPP and \( \mathrm{NO}_2^{-} \), we focused on reaching this state to understand the stoichiometric balance.

As \( \mathrm{NO}_2^{-} \) was added to the solution, the absorbance changed until it eventually reached a stable point where adding more \( \mathrm{NO}_2^{-} \) did not significantly alter the absorbance. This plateau indicated that the reaction had reached equilibrium.

Typically, achieving equilibrium involves a dynamic balance between reactant consumption and product formation. Identifying when equilibrium is reached in this context helped verify our findings of the \( 1:1 \) stoichiometric ratio, as no significant change in absorbance suggested that most of the TAPP had reacted with \( \mathrm{NO}_2^{-} \). Understanding equilibrium is crucial for predicting the extent of chemical reactions and optimizing them in practical applications.