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Chapter 10: Problem 29

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?

Short Answer

Expert verified
The stoichiometry of the reaction is 1:1.

Step by step solution

01

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.
02

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.
03

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 \(\mathrm{NO}_{2}^{-}\).
04

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 \(\mathrm{NO}_{2}^{-}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

The concentration of \(\mathrm{Na}\) in plant materials are determined by flame atomic emission. The material to be analyzed is prepared by grinding, homogenizing, and drying at \(103^{\circ} \mathrm{C}\). A sample of approximately \(4 \mathrm{~g}\) is transferred to a quartz crucible and heated on a hot plate to char the organic material. The sample is heated in a muffle furnace at \(550^{\circ} \mathrm{C}\) for several hours. After cooling to room temperature the residue is dissolved by adding \(2 \mathrm{~mL}\) of \(1: 1 \mathrm{HNO}_{3}\) and evaporated to dryness. The residue is redissolved in \(10 \mathrm{~mL}\) of \(1: 9 \mathrm{HNO}_{3},\) filtered and diluted to \(50 \mathrm{~mL}\) in a volumetric flask. The following data are obtained during a typical analysis for the concentration of \(\mathrm{Na}\) in a \(4.0264-\mathrm{g}\) sample of oat bran. $$ \begin{array}{lcc} {\text { sample }} & \mathrm{mg} \mathrm{Na} / \mathrm{L} & \text { emission (arbitrary units) } \\ \hline \text { blank } & 0.00 & 0.0 \\ \text { standard 1 } & 2.00 & 90.3 \\ \text { standard } 2 & 4.00 & 181 \\ \text { standard } 3 & 6.00 & 272 \\ \text { standard } 4 & 8.00 & 363 \\ \text { standard } 5 & 10.00 & 448 \\ \text { sample } & & 238 \end{array} $$ Report the concentration of sodium in the sample of oat bran as \mug Na/g sample.

A chemical deviation to Beer's law may occur if the concentration of an absorbing species is affected by the position of an equilibrium reaction. Consider a weak acid, HA, for which \(K_{\mathrm{a}}\) is \(2 \times 10^{-5}\). Construct Beer's law calibration curves of absorbance versus the total concentration of weak acid \(\left(C_{\text {total }}=[\mathrm{HA}]+\left[\mathrm{A}^{-}\right]\right),\) using values for \(C_{\text {total }}\) of \(1.0 \times 10^{-5}, 3.0 \times 10^{-5}, 5.0 \times 10^{-5}, 7.0 \times 10^{-5}, 9.0 \times 10^{-5}, 11 \times 10^{-5}\), and \(13 \times 10^{-5} \mathrm{M}\) for the following sets of conditions and comment on your results: (a) \(\varepsilon_{\mathrm{HA}}=\varepsilon_{\mathrm{A}^{-}}=2000 \mathrm{M}^{-1} \mathrm{~cm}^{-1} ;\) unbuffered solution. (b) \(\varepsilon_{\mathrm{HA}}=2000 \mathrm{M}^{-1} \mathrm{~cm}^{-1} ; \varepsilon_{\mathrm{A}^{-}}=500 \mathrm{M}^{-1} \mathrm{~cm}^{-1} ;\) unbuffered solution. (c) \(\varepsilon_{\mathrm{HA}}=2000 \mathrm{M}^{-1} \mathrm{~cm}^{-1} ; \varepsilon_{\mathrm{A}^{-}}=500 \mathrm{M}^{-1} \mathrm{~cm}^{-1} ;\) solution buffered to a \(\mathrm{pH}\) of 4.5 Assume a constant pathlength of \(1.00 \mathrm{~cm}\) for all samples.

Saito describes a quantitative spectrophotometric procedure for iron based on a solid-phase extraction using bathophenanthroline in a poly(vinyl chloride) membrane. \({ }^{22}\) In the absence of \(\mathrm{Fe}^{2+}\) the membrane is colorless, but when immersed in a solution of \(\mathrm{Fe}^{2+}\) and \(\mathrm{I}^{-},\) the membrane develops a red color as a result of the formation of an \(\mathrm{Fe}^{2+}\) -bathophenanthroline complex. A calibration curve determined using a set of external standards with known concentrations of \(\mathrm{Fe}^{2+}\) gave a standardization relationship of $$ A=\left(8.60 \times 10^{3} \mathrm{M}^{-1}\right) \times\left[\mathrm{Fe}^{2+}\right] $$ What is the concentration of iron, in \(\mathrm{mg} \mathrm{Fe} / \mathrm{L},\) for a sample with an absorbance of 0.100 ?

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The concentration of phenol in a water sample is determined by using steam distillation to separate the phenol from non-volatile impurities, followed by reacting the phenol in the distillate with 4 -aminoantipyrine and \(\mathrm{K}_{3} \mathrm{Fe}(\mathrm{CN})_{6}\) at \(\mathrm{pH} 7.9\) to form a colored antipyrine dye. A phenol standard with a concentration of 4.00 ppm has an absorbance of 0.424 at a wavelength of \(460 \mathrm{nm}\) using a \(1.00 \mathrm{~cm}\) cell. A water sample is steam distilled and a \(50.00-\mathrm{mL}\) aliquot of the distillate is placed in a 100 -mL volumetric flask and diluted to volume with distilled water. The absorbance of this solution is 0.394 . What is the concentration of phenol (in parts per million) in the water sample?
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