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Chapter 14: Problem 112

If the plot of the reactant concentration versus time is nonlinear, but the concentration drops by \(50 \%\) every 10 seconds, then the order of the reaction is (a) zero order; (b) first order; (c) second order; (d) third order.

Short Answer

Expert verified
The order of reaction is first (option b).

Step by step solution

01

Understand What the Problem is Asking

The problem specifies that the plot of reactant concentration versus time is nonlinear, and the concentration drops by \(50 \%\) every 10 seconds. So, it can be deduced that this problem involves half-lives.
02

Identify What a Half-Life is in Regards to Kinetics

A half-life refers to the amount of time required for the concentration of a reactant to decrease by 50%. The key point here is that for a first-order reaction, the half-life is independent of the initial concentration. This means that it takes the same amount of time for the concentration to decrease by \(50 \%\) regardless of its initial concentration.
03

Compare with Given Information

Given that the concentration of the reactant drops by \(50 \%\) every 10 seconds, this behavior is a unique characteristic of a first-order reaction. Therefore, the reaction order is first.
04

Verify with Kinetics Theory

In kinetics, zero order means that the rate of reaction is independent of the concentration of reactants, which is not applicable in this case. Second order would mean that the rate doubles for every halving of concentration, and that does not apply either. Third order is when the rate changes based on changes to the concentration to the third power, which also does not apply here. Hence, the first order reaction is confirmed as it aligns with the given condition.

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Key Concepts

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

Reaction Kinetics
In the world of chemistry, reaction kinetics refers to the study of the rates at which chemical processes occur and the factors affecting them. This field helps us understand how fast or slow a reaction takes place and what controls the speed of reactions.
There are several factors that can influence reaction kinetics, such as the concentration of reactants, temperature, and presence of catalysts. These elements can speed up or slow down the rate of a chemical reaction.
To mathematically describe these rates, we use rate laws, which are equations that relate the reaction rate to the concentration of the reactants. Rate laws also incorporate rate constants and reaction order, providing comprehensive insights into the reaction dynamics. Understanding these aspects helps scientists and students predict how changing one component in the reaction will impact the overall progress of the chemical transform.
Half-Life
The concept of half-life is essential in understanding how reactant concentrations diminish over time in a reaction. A half-life is defined as the amount of time it takes for half of the reactant to be consumed or converted to product.
For first-order reactions, the half-life is a unique property because it remains constant throughout the reaction. This means the time required for the concentration of a reactant to fall to half of its initial value does not change, no matter what the starting concentration is. This is unlike reactions of other orders where the half-life may vary depending on concentration variations.
Knowing about half-life helps in determining the speed of a reaction. It provides an easy way to compare how quickly reactants are consumed in first-order reactions versus other types of reactions. This understanding is particularly useful in fields like pharmacology and environmental science, where reaction speed is crucial for applications like drug metabolism and pollutant degradation.
Reaction Order Determination
Determining the order of a reaction is a critical step in understanding how a reactant’s concentration affects the rate of a chemical reaction. Reaction order is typically deciphered by examining how changes in reactant concentrations alter the reaction rate, often depicted in plots or graphs.
A reaction can be first-order, second-order, or even zero-order, with each having distinct characteristics. In first-order reactions, the rate of reaction is directly proportional to the concentration of one reactant. This leads to an exponential decrease in concentration over time, observed as a consistent half-life.
  • First-order: Half-life is constant.
  • Second-order: Rate changes with the square of the concentration.
  • Zero-order: Rate is independent of concentration.
To identify the reaction order, one can experiment by measuring the concentration of reactants over time and observing the pattern of decrease. By plotting these values and recognizing specific patterns, one can determine whether the reaction fits the characteristics of a first-order or another order, as demonstrated in the original exercise. This is a fundamental technique in obtaining deeper insights into chemical reactions and their kinetics.

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Most popular questions from this chapter

The reaction \(A+B \longrightarrow\) products is first order in \(A\) first order in \(\mathrm{B},\) and second order overall. Consider that the starting concentrations of the reactants are \([\mathrm{A}]_{0}\) and [ \(\mathrm{B}]_{0},\) and that \(x\) represents the decrease in these concentrations at the time \(t .\) That is, \([\mathrm{A}]_{t}=[\mathrm{A}]_{0}-x\) and \([\mathrm{B}]_{t}=[\mathrm{B}]_{0}-x .\) Show that the integrated rate law for this reaction can be expressed as shown below. $$\ln \frac{[\mathrm{A}]_{0} \times[\mathrm{B}]_{t}}{[\mathrm{B}]_{0} \times[\mathrm{A}]_{t}}=\left([\mathrm{B}]_{0}-[\mathrm{A}]_{0}\right) \times k t$$

If the plot of the reactant concentration versus time is linear, then the order of the reaction is (a) zero order; (b) first order; (c) second order; (d) third order.

The mechanism proposed for the reaction of \(\mathrm{H}_{2}(\mathrm{g})\) and \(\mathrm{I}_{2}(\mathrm{g})\) to form \(\mathrm{HI}(\mathrm{g})\) consists of a fast reversible first step involving \(\mathrm{I}_{2}(\mathrm{g})\) and \(\mathrm{I}(\mathrm{g}),\) followed by a slow step. Propose a two-step mechanism for the reaction \(\mathrm{H}_{2}(\mathrm{g})+\mathrm{I}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{HI}(\mathrm{g}),\) which is known to be first order in \(\mathrm{H}_{2}\) and first order in \(\mathrm{I}_{2}.\)

For the reaction \(A \longrightarrow 2 B+C\), the following data are obtained for \([\mathrm{A}]\) as a function of time: \(t=0 \mathrm{min}\) \([\mathrm{A}]=0.80 \mathrm{M} ; 8 \mathrm{min}, 0.60 \mathrm{M} ; 24 \mathrm{min}, 0.35 \mathrm{M} ; 40 \mathrm{min}\) \(0.20 \mathrm{M}\) (a) By suitable means, establish the order of the reaction. (b) What is the value of the rate constant, \(k ?\) (c) Calculate the rate of formation of \(\mathrm{B}\) at \(t=30 \mathrm{min}\).

We have used the terms order of a reaction and molecularity of an elementary process (that is, unimolecular, bimolecular). What is the relationship, if any, between these two terms?
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