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Chapter 14: Problem 102

A first-order reaction, \(\mathrm{A} \longrightarrow\) products, has a halflife of \(75 \mathrm{s},\) from which we can draw two conclusions. Which of the following are those two (a) the reaction goes to completion in 150 s; (b) the quantity of \(A\) remaining after 150 s is half of what remains after 75 s; (c) the same quantity of A is consumed for every 75 s of the reaction; (d) one- quarter of the original quantity of A is consumed in the first 37.5 s of the reaction; (e) twice as much A is consumed in 75 s when the initial amount of \(\mathrm{A}\) is doubled; (f) the amount of \(\mathrm{A}\) consumed in 150 s is twice as much as is consumed in 75 s.

Short Answer

Expert verified
Based on the analysis of the statements, the two correct conclusions that we can draw from the information on the reaction's half-life are: (b) the quantity of \(A\) remaining after 150 seconds is half of what remains after 75 seconds and (e) twice as much \(A\) is consumed in 75 seconds when the initial amount of \(A\) is doubled.

Step by step solution

01

Analyze Statement (a)

Statement (a) suggests the reaction completes in 150 seconds, which is twice the half-life. This isn't correct for a first-order reaction. After one half-life (75 seconds), half of the original quantity of A remains. After another half-life (another 75 seconds), only half of that remaining amount is consumed, not the entire remaining amount. Therefore, statement (a) is incorrect.
02

Analyze Statement (b)

Statement (b) suggests that the quantity of A remaining after 150 seconds is half of what remains after 75 seconds. This is correct. After 75 seconds (one half-life), half of the original amount of A remains. After another half-life (another 75 seconds), only half of the remaining amount is left. Therefore, statement (b) is correct.
03

Analyze Statement (c)

Statement (c) suggests that the same quantity of A is consumed for every 75 seconds of the reaction. This is not correct. While it is true that the reaction rate is proportional to the amount of reactant, in a first-order reaction, the actual quantity of A consumed decreases with each successive half-life. Therefore, statement (c) is incorrect.
04

Analyze Statement (d)

Statement (d) is claiming that one quarter of A is consumed in the first 37.5 seconds. This isn’t true for a first-order reaction. The half-life is defined as the time it takes for half of the reactant to be consumed, not a quarter. Therefore, statement (d) is incorrect.
05

Analyze Statement (e)

Statement (e) is asserting that if the initial amount of A is doubled, twice as much A is consumed in 75 seconds. This is true for a first-order reaction. Since the reaction rate is proportional to the concentration of the reactant, if we start with twice as much reactant, we'll consume twice as much in the same amount of time. Hence, statement (e) is correct.
06

Analyze Statement (f)

Statement (f) suggests that the amount of A consumed in 150 seconds is twice as much as is consumed in 75 seconds. It's the case with the first-order reaction that half the reactant remains after one half-life (75 seconds in this case), and half of the remaining reactant is consumed after the next half-life. Actually, the amount consumed in the first 75 seconds is more than that consumed in the next 75 seconds, so statement (f) is incorrect.

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Most popular questions from this chapter

In the reaction \(A(g) \longrightarrow 2 B(g)+C(g),\) the total pressure increases while the partial pressure of \(\mathrm{A}(\mathrm{g})\) decreases. If the initial pressure of \(\mathrm{A}(\mathrm{g})\) in a vessel of constant volume is \(1.000 \times 10^{3} \mathrm{mmHg}\) (a) What will be the total pressure when the reaction has gone to completion? (b) What will be the total gas pressure when the partial pressure of \(\mathrm{A}(\mathrm{g})\) has fallen to \(8.00 \times 10^{2} \mathrm{mmHg} ?\)

A reaction is \(50 \%\) complete in 30.0 min. How long after its start will the reaction be \(75 \%\) complete if it is (a) first order; (b) zero order?

Explain the important distinctions between each pair of terms: (a) first-order and second-order reactions; (b) rate law and integrated rate law; (c) activation energy and enthalpy of reaction; (d) elementary process and overall reaction; (e) enzyme and substrate.

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 \(t=30 \mathrm{min}\).

The reaction \(2 \mathrm{NO}+\mathrm{Cl}_{2} \longrightarrow 2 \mathrm{NOCl}\) has the rate law: rate of reaction \(=k[\mathrm{NO}]^{2}\left[\mathrm{Cl}_{2}\right] .\) Propose a twostep mechanism for this reaction consisting of a fast reversible first step, followed by a slow step.
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