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The thermal decomposition of $\mathrm{N}_{2} \mathrm{O}_{5}$ obeys first-order kinetics. At $45^{\circ} \mathrm{C},$ a plot of $\ln \left[\mathrm{N}_{2} \mathrm{O}_{5}\right]$ versus $t$ gives a slope of $-6.18 \times 10^{-4} \mathrm{min}^{-1} .$ What is the half-life of the reaction?

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$$1120 \mathrm{min}$$

Chemistry 102

Chapter 6

Chemical Kinetics

Kinetics

University of Central Florida

Drexel University

Lectures

22:42

In probability theory, the conditional probability of an event A given that another event B has occurred is defined as the probability of A given B, written as P(A|B). It is a function of the probability of B, the probability of A given B, and the probability of B.

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In chemistry, kinetics is the study of the rates of chemical reactions. The rate of a reaction is the change in concentration of a reactant over time. The rate of reaction is dependent on the concentration of the reactants, temperature, and the activation energy of the reaction.

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The first-order rate const…

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The rate equation for the …

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The decomposition of $\mat…

Hello. So today we're going to be looking at the first order to come position off dying nitrogen Penta oxide. And we see that since this is a first order reaction, we've plotted the natural log of the concentration of dinos gin Penta oxide over time. And it's a straight line with the slope given here. Well, if you remember, the equation for this line is the natural. Log off. A concentration of dinette Schumpeter oxide at some time is equal to negative, Katie, plus the natural log of the original concentration of the initial concentration. So we see that the it that in this equation the slope is negative, K. And since we know the slope, that means that the rate constant for this reaction a 6.18 times 10 to the negative four in verse minutes. So say we want to find the half life while the half life off a first order reaction is the natural log of to over the rate constant. So the natural too divided by 6.18 times 10 to the negative four do some math and we will see that are half life is 1120 minutes. So there we go. We've used really know about first order reactions and that this is learn your with this equation and using that information we've deduced.

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