Consider the following concentration–time data for the decomposition reaction AB → A + B. (c) What is the time (in minutes) when the AB concentration reaches a value of 0.0250 M?

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Identify the order of the reaction by analyzing the concentration-time data provided. This can be done by plotting the data and determining which plot (zero-order, first-order, or second-order) yields a straight line.

Once the order of the reaction is determined, use the appropriate integrated rate law equation. For a first-order reaction, the equation is: $\ln \left(C\right)=-\mathrm{kt}+\ln (C$₀), where $C$ is the concentration at time $t$, $C$₀ is the initial concentration, and $k$ is the rate constant.

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Determine the rate constant $k$ using the slope of the line from the plot corresponding to the reaction order. For a first-order reaction, the slope is $-k$.

Substitute the known values into the integrated rate law equation. Use the initial concentration $C$₀, the rate constant $k$, and the target concentration $0.0250M$ to solve for the time $t$.

Calculate the time $t$ using the rearranged equation: $t=\frac{\ln (\frac{C}{/}}{}$₀)-k. This will give you the time in minutes when the concentration of AB reaches $0.0250M$.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Reaction Kinetics

Reaction kinetics is the study of the rates of chemical processes. It involves understanding how different factors, such as concentration, temperature, and catalysts, affect the speed of a reaction. In this context, knowing the kinetics of the decomposition of AB into A and B is essential to determine how the concentration of AB changes over time.

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Concentration Units

Concentration is a measure of the amount of a substance in a given volume of solution, typically expressed in molarity (M), which is moles of solute per liter of solution. Understanding how to interpret and manipulate concentration values is crucial for solving problems related to chemical reactions, such as determining when the concentration of AB reaches a specific value.

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SI Units

Integrated Rate Laws

Integrated rate laws relate the concentration of reactants to time for a given reaction order. For a first-order reaction, for example, the integrated rate law can be used to calculate the concentration of a reactant at any time. In this case, applying the appropriate integrated rate law will allow us to find the time when the concentration of AB reaches 0.0250 M.

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Related Practice

Textbook Question

The decomposition of N2O5 is a first-order reaction. At 25 °C, it takes 5.2 h for the concentration to drop from 0.120 M to 0.060 M. How many hours does it take for the concentration to drop from 0.030 M to 0.015 M? From 0.480 M to 0.015 M?

Textbook Question

You wish to determine the reaction order and rate constant for the following thermal decomposition reaction: AB2 S 1>2 A2 + B2 (c) Describe how you would determine the value of the rate constant.

Textbook Question

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