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The thiosulfate ion \(\left(\mathrm{S}_{2} \mathrm{O}_{3}^{2-}\right)\) is oxidized by iodine as follows: $$ 2 \mathrm{S}_{2} \mathrm{O}_{3}^{2-}(a q)+\mathrm{I}_{2}(a q) \longrightarrow \mathrm{S}_{4} \mathrm{O}_{6}^{2-}(a q)+2 \mathrm{I}^{-}(a q) $$ In a certain experiment, \(7.05 \times 10^{-3}\) mol/L of \(\mathrm{S}_{2} \mathrm{O}_{3}^{2-}\) is consumed in the first 11.0 seconds of the reaction. Calculate the rate of consumption of \(\mathrm{S}_{2} \mathrm{O}_{3}^{2-}\) . Calculate the rate of production of iodide ion.

Short Answer

Expert verified
The rate of consumption of the thiosulfate ion (S鈧侽鈧兟测伝) in the reaction is \(6.41 \times 10^{-4} \frac{mol}{L \cdot s}\), and the rate of production of iodide ion (I鈦) is also \(6.41 \times 10^{-4} \frac{mol}{L \cdot s}\), since they have a 1:1 stoichiometric relationship.

Step by step solution

01

Calculate the rate of consumption of S鈧侽鈧兟测伝

To calculate the rate of consumption of S鈧侽鈧兟测伝, we will use the formula: Rate of consumption = (Change in concentration) / (Change in time) We are given that the change in concentration of S鈧侽鈧兟测伝 is 7.05 脳 10鈦宦 mol/L, and the change in time is 11.0 seconds. Therefore, we can plug in these values into our formula: Rate of consumption of S鈧侽鈧兟测伝 = (7.05 脳 10鈦宦 mol/L) / (11.0 s)
02

Perform the calculation

Now we can perform the calculation to find the rate of consumption of S鈧侽鈧兟测伝: Rate of consumption of S鈧侽鈧兟测伝 = \( \frac{7.05 \times 10^{-3} \, mol/L} {11.0 \, s} \) = \(6.41 \times 10^{-4} \frac{mol}{L \cdot s}\)
03

Calculate the rate of production of I鈦

To calculate the rate of production of I鈦, we will use the stoichiometric relationship between S鈧侽鈧兟测伝 and I鈦 from the balanced chemical equation: 2 S鈧侽鈧兟测伝 + I鈧 鈫 S鈧凮鈧喡测伝 + 2 I鈦 From the balanced equation, we can see that for every 2 moles of S鈧侽鈧兟测伝 consumed, 2 moles of I鈦 are produced. Therefore, we have a 1:1 molar ratio between the consumption of S鈧侽鈧兟测伝 and the production of I鈦. This means that the rate of production of I鈦 will be equal to the rate of consumption of S鈧侽鈧兟测伝, which we calculated in Step 2. Rate of production of I鈦 = Rate of consumption of S鈧侽鈧兟测伝 = \(6.41 \times 10^{-4} \frac{mol}{L \cdot s}\)
04

Finalize the answer

The rate of consumption of the thiosulfate ion (S鈧侽鈧兟测伝) in the reaction is \(6.41 \times 10^{-4} \frac{mol}{L \cdot s}\), and the rate of production of iodide ion (I鈦) is also \(6.41 \times 10^{-4} \frac{mol}{L \cdot s}\), since they have a 1:1 stoichiometric relationship.

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Key Concepts

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

Thiosulfate Ion
The thiosulfate ion, \(\mathrm{S}_{2}\mathrm{O}_{3}^{2-}\), is a fascinating part of many chemical reactions due to its reducing properties. In this particular case, it acts as a reducing agent that gets oxidized by iodine. Thiosulfate ion has a tetrahedral molecular geometry, embodying two sulfur atoms and three oxygen atoms. Of these, one sulfur forms a double bond with one of the oxygen atoms while the other sulfur retains a lone pair, lending the ion its charge and reactivity.
This ion is commonly encountered in iodometry, a method of volumetric chemical analysis, where it represents a vital titrant. Its role is to react with iodine to revert it to iodide ions, allowing quantification of oxidizing agents or their reaction rates. Its practicality lies in helping to determine concentrations of other substances by reacting in predictable ways.
Iodide Ion
In chemical reactions, the iodide ion, \(\mathrm{I}^-\), functions as a product when iodine \(\mathrm{I}_2\) is reduced. This occurs in the outlined reaction where iodine reacts with thiosulfate ions to produce iodide ions. Here, the iodine molecule splits into two iodide ions, each effectively being a reduction reaction.
Iodide ions are vital in various chemical processes, often employed to track reactions involving iodine due to their straightforward formation and stable nature. Since iodide ions carry a negative charge, they can easily form ionic compounds with positively charged ions, diversifying their role in chemical processes.

This characteristic also makes them useful in various applications, from nutrition to medicine, showcasing the permanent demand and utility of iodide across multiple disciplines.
Stoichiometry
Stoichiometry is the study of the quantitative relationships between the reactants and products in a chemical reaction. In the given reaction between thiosulfate ions and iodine, stoichiometry plays a crucial role in determining how much of each reactant is required, and how much product is produced. The balanced equation:
  • \(2 \, \mathrm{S}_{2}\mathrm{O}_{3}^{2-} + \mathrm{I}_2 \rightarrow \mathrm{S}_{4}\mathrm{O}_{6}^{2-} + 2 \, \mathrm{I}^-\)
indicates a 2:1 stoichiometric ratio between the thiosulfate ions consumed and iodine used, and a 1:1 ratio between thiosulfate ions and iodide ions produced.
This stoichiometric information lets us calculate the rate of iodide ion production if we know the rate of thiosulfate ion consumption, and vice versa. Understanding these ratios is key in many chemical calculations, ensuring reactants are mixed in correct proportions for desired results.
Chemical Kinetics
Chemical kinetics is the branch of chemistry dealing with the rates of reactions and how they change under varying conditions. It assesses the speed at which reactants convert to products, unveiling reaction mechanisms and dynamics. In the provided reaction, chemical kinetics is applied to measure how swiftly the thiosulfate ions are consumed and how quickly iodide ions are produced over time.
By making use of the formula:
  • Rate = (Change in concentration) / (Change in time)
we understand how varying concentrations impact the speed of reactions. The calculated rate of \(6.41 \times 10^{-4} \, \text{mol/L/s}\) for both consumption and production in this reaction demonstrates the effect of a stoichiometric 1:1 ratio.
Kinetics unveils crucial reaction controls, painting a picture of speed, ensuring processes are efficient, and establishing how catalysts, temperature, and concentrations affect reaction rates.

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Most popular questions from this chapter

A certain reaction has the form $$ \mathrm{aA} \longrightarrow $$ At a particular temperature, concentration versus time data were collected. A plot of 1\(/[\mathrm{A}]\) versus time (in seconds) gave a straight line with a slope of \(6.90 \times 10^{-2} .\) What is the differential rate law for this reaction? What is the integrated rate law for this reaction? What is the value of the rate constant for this reaction? If \([\mathrm{A}]_{0}\) for this reaction is \(0.100 M,\) what is the first half-life (in seconds)? If the original concentration (at \(t=0 )\) is \(0.100 M,\) what is the second half-life (in seconds)?

The mechanism for the gas-phase reaction of nitrogen dioxide with carbon monoxide to form nitric oxide and carbon dioxide is thought to be $$ \begin{array}{c}{\mathrm{NO}_{2}+\mathrm{NO}_{2} \longrightarrow \mathrm{NO}_{3}+\mathrm{NO}} \\ {\mathrm{NO}_{3}+\mathrm{CO} \longrightarrow \mathrm{NO}_{2}+\mathrm{CO}_{2}}\end{array} $$ Write the rate law expected for this mechanism. What is the overall balanced equation for the reaction?

Provide a conceptual rationale for the differences in the halflives of zero-, first-, and second-order reactions.

Consider the following initial rate data for the decomposition of compound AB to give A and B: Determine the half-life for the decomposition reaction initially having 1.00\(M \mathrm{AB}\) present.

The decomposition of iodoethane in the gas phase proceeds according to the following equation: $$ \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{I}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}(g) $$ At \(660 . \mathrm{K}, k=7.2 \times 10^{-4} \mathrm{s}^{-1} ;\) at \(720 . \mathrm{K}, k=1.7 \times 10^{-2} \mathrm{s}^{-1}\) What is the value of the rate constant for this first-order decomposition at \(325^{\circ} \mathrm{C} ?\) If the initial pressure of iodoethane is 894 torr at \(245^{\circ} \mathrm{C},\) what is the pressure of iodoethane after three half-lives?

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