Given the following diagrams at 𝑡=0 min and 𝑡=30 min, b. After four half-life periods for a first-order reaction, what fraction of reactant remains? [Section 14.3]

Verified step by step guidance

Identify that the problem involves a first-order reaction and the concept of half-life.

Recall that for a first-order reaction, the half-life (t_{1/2}) is constant and does not depend on the initial concentration.

Understand that after each half-life period, the concentration of the reactant is reduced by half.

Calculate the fraction of reactant remaining after four half-life periods using the formula: (1/2)^n, where n is the number of half-lives.

Substitute n = 4 into the formula to determine the fraction of reactant remaining after four half-life periods.

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Key Concepts

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

First-Order Reactions

First-order reactions are chemical reactions where the rate is directly proportional to the concentration of one reactant. This means that as the concentration of the reactant decreases, the rate of the reaction also decreases. The mathematical representation of a first-order reaction is given by the equation: rate = k[A], where k is the rate constant and [A] is the concentration of the reactant.

Half-Life

The half-life of a reaction is the time required for the concentration of a reactant to decrease to half of its initial value. For first-order reactions, the half-life is constant and does not depend on the initial concentration. This property allows for straightforward calculations of remaining reactant after multiple half-lives, as each half-life reduces the amount by half.

Fraction of Reactant Remaining

To determine the fraction of reactant remaining after a certain number of half-lives, one can use the formula: (1/2)^n, where n is the number of half-lives that have passed. After four half-lives, the fraction of the original reactant remaining would be (1/2)^4, which equals 1/16. This concept is crucial for understanding how reactants diminish over time in first-order kinetics.

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Textbook Question

You study the rate of a reaction, measuring both the concentration of the reactant and the concentration of the product as a function of time, and obtain the following results:

Which chemical equation is consistent with these data: (i) A → B, (ii) B → A, (iii) A → 2 B, (iv) B → 2 A?

Textbook Question

Suppose that for the reaction K+L⟶M, you monitor the production of M over time, and then plot the following graph from your data: b. Is the reaction completed at 𝑡=15 min?

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Textbook Question

The following diagrams represent mixtures of NO(g) and O2(𝑔). These two substances react as follows:

2 NO(𝑔)+O2(𝑔)⟶2 NO2(𝑔)

It has been determined experimentally that the rate is second order in NO and first order in O2. Based on this fact, which of the following mixtures will have the fastest initial rate? [Section 14.2]

Textbook Question

Which of the following linear plots do you expect for a reaction A⟶products if the kinetics are a. zero order, [Section 14.3]

Textbook Question

The accompanying graph shows plots of ln k versus 1>T for two different reactions. The plots have been extrapolated to the y-intercepts. Which reaction (red or blue) has (a) the larger value for Ea,