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Chapter 11: Problem 48

A zero-order reaction \(\mathrm{A} \rightarrow \mathrm{B}\). At the end of \(1 \mathrm{~h}, \mathrm{~A}\) is \(75 \%\) reacted. How much of it will be left unreacted at the end of \(2 \mathrm{~h}\). (a) \(12.5 \%\) (b) \(6.25 \%\) (c) \(3.12 \%\) (d) \(0 \%\)

Short Answer

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Step by step solution

01

Understand Zero-Order Reaction Kinetics

In a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactant. The rate law for a zero-order reaction is expressed as rate = -k[A]^0 = -k, where k is the rate constant. The concentration of A decreases linearly over time.
02

Calculate Initial Concentration

Let's assume the initial concentration of A is 100% at time t = 0 hours. After 1 hour, 75% has reacted, leaving 25% unreacted.
03

Apply Zero-Order Kinetics

The concentration of A will continue to decrease at the same rate since it's a zero-order reaction. After 2 hours, which is twice the amount of time as 1 hour, another 25% would have reacted (since 75% reacted in the first hour), leaving 25% - 25% = 0% unreacted.
04

Choose the Correct Answer

At the end of 2 hours, none of A will be left unreacted. The correct answer is (d) 0%.

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Key Concepts

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

Chemical Kinetics
Chemical kinetics is the study of reaction rates, how reaction rates change under varying conditions and by which mechanism the reaction proceeds. An essential aspect of chemical kinetics is understanding rate laws, which indicate how the rate of a chemical reaction is affected by the concentration of reactants.

In the context of a zero-order reaction, such as \( \mathrm{A} \rightarrow \mathrm{B} \), this branch of chemistry lets us predict how fast the reactant A will be converted into product B regardless of A's concentration. This defies the intuitive notion that more reactants will lead to a faster reaction, which is typical for other reaction orders, such as first or second order.
Reaction Rate
The reaction rate is a measure of how quickly the concentration of a reactant or product changes over time in a chemical reaction. In the case of zero-order reactions, this rate is constant. This means that the decrease in concentration of reactant A over time happens at a steady, unchanged pace. This is shown by the linear relationship between the concentration of A and time.

To visualize this, imagine a graph where the x-axis is time and the y-axis is concentration of A. For a zero-order reaction, the graph would display a straight line descending to zero, indicating that the reactant is being used up at a steady rate until none is left.
Rate Constant
The rate constant, represented by k in kinetics, is a proportionality constant that relates the reaction rate to the concentrations of reactants for a given reaction at a specific temperature. In the mathematical expression for the rate law of zero-order reactions, \( \text{rate} = -k[\mathrm{A}]^0 = -k \), k is a measure of the inherent rate at which the reaction proceeds.

Since zero-order reactions have a rate that does not depend on reactant concentration, the rate constant k actually represents the reaction rate itself. It is unique to a particular reaction and can be affected by external conditions such as temperature, but within the context of our problem, knowing that k remains the same allows us to predict the concentration of A over time with great accuracy.
  • The larger the rate constant, the faster the product forms.
  • Since the reaction is zero-order, the constant gives the rate of reaction as a fixed value, which applies at all concentrations of the reactant until the reactant is depleted.

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Most popular questions from this chapter

For irreversible elementary reactions in parallel: \(\mathrm{A} \stackrel{K_{1}}{\longrightarrow} \mathrm{R}\) and \(\mathrm{A} \stackrel{K_{2}}{\longrightarrow} \mathrm{S}\), the rate of disappearance of reactant ' \(\mathrm{A}\) ' is (a) \(\left(k_{1}-k_{2}\right) C_{\mathrm{A}}\) (b) \(\left(k_{1}+k_{2}\right) C_{\mathrm{A}}\) (c) \(1 / 2\left(k_{1}+k_{2}\right) C_{\mathrm{A}}\) (d) \(k_{1} C_{\mathrm{A}}\)

Consider the chemical reaction: \(\mathrm{N}_{2}(\mathrm{~g})\) \(+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{~g})\). The rate of this reaction can be expressed in terms of time derivative of concentration of \(\mathrm{N}_{2}(\mathrm{~g})\), \(\mathrm{H}_{2}(\mathrm{~g})\) or \(\mathrm{NH}_{3}(\mathrm{~g})\). Identify the correct relationship amongst the rate expressions (a) rate \(\begin{aligned} \text { (b) rate } &=-\frac{\mathrm{d}\left[\mathrm{N}_{2}\right]}{\mathrm{d} t}=-\frac{1}{3} \frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{d} t} \\ &=+\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{NH}_{3}\right]}{\mathrm{d} t} \\ &=+2 \frac{\mathrm{d}\left[\mathrm{NH}_{2}\right]}{\mathrm{d} t}=-3 \frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{d} t} \\ \mathrm{~d} t \end{aligned}\) (c) rate \(\begin{aligned} &=-\frac{\mathrm{d}\left[\mathrm{N}_{2}\right]}{\mathrm{d} t}=\frac{1}{3} \frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{d} t} \\ &=+\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{NH}_{3}\right]}{\mathrm{d} t} \\ \text { (d) rate } &=-\frac{\mathrm{d}\left[\mathrm{N}_{2}\right]}{\mathrm{d} t}=-\frac{\mathrm{d}\left[\mathrm{H}_{2}\right]}{\mathrm{d} t} \\\ &=+\frac{\mathrm{d}\left[\mathrm{NH}_{3}\right]}{\mathrm{d} t} \end{aligned}\)

For a reaction of order \(n\), the integrated form of the rate equation is: \((n-1) \cdot K \cdot t\) \(=\left(C_{0}\right)^{1-n}-(C)^{1-n}\), where \(C_{0}\) and \(C\) are the values of the reactant concentration at the start and after time ' \(t\) '. What is the relationship between \(t_{3 / 4}\) and \(t_{1 / 2}\), where \(t_{3 / 4}\) is the time required for \(C\) to become \(C_{0} / 4\). (a) \(t_{3 / 4}=t_{1 / 2} \cdot\left[2^{n-1}+1\right]\) (b) \(t_{3 / 4}=t_{1 / 2}\left[2^{n-1}-1\right]\) (c) \(t_{3 / 4}=t_{1 / 2}\left[2^{n+1}-1\right]\) (d) \(t_{3 / 4}=t_{1 / 2} \cdot\left[2^{n+1}+1\right]\)

The time taken in \(75 \%\) completion of a zero-order reaction is \(10 \mathrm{~h}\). In what time, he reaction will be \(90 \%\) completed? a) \(12.0 \mathrm{~h}\) (b) \(16.6 \mathrm{~h}\) c) \(10.0 \mathrm{~h}\) (d) \(20.0 \mathrm{~h}\)

Which is wrong about the rate of a reaction among the following? (a) Rate of a reaction cannot be negative. (b) Rate of a reaction is change in concentration of the reactant per unit time per unit stoichiometric coefficient of that component. (c) Average rate and instantaneous rate are always different. (d) Rate may depend upon surface area of the reactants.
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