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Write a general rate law for the reaction $$\mathrm{H}_{2} \mathrm{O}_{2}(a q)+3 \mathrm{I}^{-}(a q)+2 \mathrm{H}^{+}(a q) \rightarrow \mathrm{I}_{3}^{-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ using \(x, y, z\) as orders.

Short Answer

Expert verified
The general rate law for the given reaction is: \[Rate = k[H_2O_2]^x[I^-]^y[H^+]^z \]

Step by step solution

01

Identify reactants

In the given reaction, we have three reactants: Hydrogen peroxide (\(H_2O_2\)), iodide ion (\(I^-\)), and hydrogen ion (\(H^+\)). The products of this reaction are Triiodide ion (\(I_3^-\)) and water (\(H_2O\)). Step 2: Write the rate law with variables x, y, and z as orders
02

Write general rate law

The general rate law of a reaction is given by the equation: \[Rate = k[Reactant_1]^x[Reactant_2]^y[Reactant_3]^z \] where k is the rate constant, and x, y, and z are the orders of the reaction with respect to the respective reactants. In our case: Rate = \[k[H_2O_2]^x[I^-]^y[H^+]^z \] Step 3: Final rate law
03

Final rate law

The general rate law for the given reaction is: \[Rate = k[H_2O_2]^x[I^-]^y[H^+]^z \]

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Key Concepts

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

Reaction Kinetics
Understanding reaction kinetics is pivotal in studying how chemical reactions occur and develop over time. It involves measuring the rate of a chemical reaction and determining the sequence of steps, known as the reaction mechanism, through which reactants transform into products.

For the provided exercise, which explores the reaction of hydrogen peroxide with iodide ions and hydrogen ions, reaction kinetics helps us to understand how these substances react together. More specifically, we are interested in how the concentration of each reactant influences the rate of reaction.

In practical settings, we observe this by monitoring concentrations of reactants over time and describing these changes mathematically. This hands-on approach yields valuable insights into the system's behavior, guides predictions, and informs the development of new products and processes in industries such as pharmaceuticals, materials science, and environmental engineering.
Rate Constant
The rate constant in reaction kinetics, designated as 'k,' is a proportionality factor that connects the concentrations of reactants to the rate of the reaction. It is specific to each chemical reaction and varies with temperature. In our exercise, the rate constant helps us quantify the speed of the reaction.

We can conceptualize the rate constant as the reaction's 'pace setter.' A larger rate constant indicates a faster reaction under the same conditions, which is significant in industrial processes that rely on efficient chemical synthesis.

Since the rate constant can be sensitive to environmental changes, it becomes a critical parameter to control in both laboratory experimentation and industrial chemical production. An example of practical importance would be in the pharmaceutical industry, where the rate constant must be carefully managed to ensure the quality and safety of drug manufacturing.
Order of Reaction
The order of reaction provides insight into the relationship between the concentration of reactants and the rate of the chemical reaction. It is defined by the exponents 'x,' 'y,' and 'z' in our rate law expression, where these exponents represent how the rate is affected by changes in reactant concentrations.

An order of one implies a directly proportional relationship; as reactant concentration doubles, so does the reaction rate. An order of zero means the concentration has no effect on the rate, while fractional or negative orders indicate more complex relationships.

Determining the order of reaction can assist in unraveling the reaction mechanism and is fundamental in the design and analysis of chemical processes. As such, chemists and engineers use this information to optimize conditions to achieve desirable reaction speeds and yields, which is tantamount in processes ranging from the synthesis of fine chemicals to the treatment of waste products.

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Most popular questions from this chapter

Suppose a postulated mechanism does generate the experimental rate law, and when the elementary steps are added together, the balanced equation for the overall reaction is generated. What can you say about the postulated mechanism?

Given the general form of the rate law, Rate \(=k[\operatorname{Reactant} 1]^{x}[\text { Reactant } 2]^{y}\) answer the following questions: (a) Which part of the rate law reflects the inherent factors of the reaction? (b) What is the general name for the exponents \(x\) and \(y ?\) (c) How do we calculate the overall order of a chemical reaction? (d) Suppose the reaction is second-order with respect to reactant 1 and first- order with respect to reactant \(2 .\) What are the values of \(x\) and \(y\), and what is the overall order of a reaction with only these two reactants? (e) Suppose reactant 1 does not appear in the rate law. What does this say about the value of its order? What is the meaning of the value of its order?

The reaction \(\mathrm{A}+2 \mathrm{~B}+\mathrm{C} \rightarrow \mathrm{AB}_{2} \mathrm{C}\) has a rate that does not change when more \(C\) is added to the reaction flask. Suppose the overall reaction order is 2, and the reaction is first-order with respect to \(\mathrm{A}\). (a) Write the rate law for this reaction, (b) What is the order for reactant \(C ?\)

The reaction \(\mathrm{N}_{2}+3 \mathrm{H}_{2} \rightarrow 2 \mathrm{NH}_{3}\) is exothermic. Draw a reaction-energy profile for the reaction. Label the gap that represents \(\Delta E_{\mathrm{rxn}} .\)

The following is a two-step mechanism for how chlorine atoms in the upper atmosphere react with and decompose ozone. \(\mathrm{Cl}+\mathrm{O}_{3} \rightarrow \mathrm{ClO}+\mathrm{O}_{2}\) \(\mathrm{O}+\mathrm{ClO} \rightarrow \mathrm{Cl}+\mathrm{O}_{2}\) According to the mechanism, which is the intermediate and which is the catalyst? Justify your choices. (Hint: Write the overall reaction.)

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