The reaction 2 NO 2 → 2 NO + O 2 has the rate constant k = 0.63 M -1 s -1 . (b) If the initial concentration of NO 2 is 0.100 M, how would you determine how long it would take for the concentration to decrease to 0.025 M?

Hey everyone today, we're given the rate constant for the decomposition of hydrogen iodide at 25°C. And we're being asked to find how long it would take for the concentration of hydrogen iodide to fall from 0.156 moller to 0. Mohler. So before doing anything, I'd like to take a look at the rate constant that's given and that's because it gives us a very crucial piece of information. Now, the units here says more clarity to the power of negative one time, second, to the power of -1. Which is another way of writing one over polarity times seconds, times time. So because we have these units, we can actually go ahead and say that we're dealing with a second order equation or a second order reaction as such. We can go ahead and use the integrated rate law for a second order reaction to go ahead and find how long it would take for the concentration to change. So let's go ahead and write out that integrated rate law recall. And this can this can be found in your textbook as well. But the rate law goes as such. One over the concentration of the the final concentration of the reactant is equal to the rate constant times the time it takes for the reaction to proceed plus one over the initial concentration. And we already have most of these values. We know that the initial concentration, 0.156 Mohler. The final concentration, a sub t 0.0956, smaller. And that K. Is equal to 1.6 times 10 to the negative three polarity times. To the power of negative one times seconds. The power of negative one. So, setting all of this in excuse me, we get that one over 0. morning is equal to 1.6 times 10 to the Native three. And I'll leave out the units for now, just for the sake of space and simplicity, times T. Which which we're trying to solve for plus one over the initial concentration. So simplifying and rearranging for tea. Now we'll eventually get that T. Is equal to 4.05 More to Power Native one divided by 1.6 times 10 to the negative three moller to the Native one times seconds to the negative one. Which gives us a final value of 2531 seconds. Therefore, the time it would take for the concentration of hydrogen iodide to decrease from 0.156 moller to 0.0956 Mohler is seconds. I hope this helps. And I look forward to seeing you all in the next one

Ch.14 - Chemical Kinetics

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Brown 14th Edition

Ch.14 - Chemical Kinetics

Problem 95b

Chapter 14, Problem 95b

The reaction 2 NO₂ → 2 NO + O₂ has the rate constant k = 0.63 M^-1s^-1.
(b) If the initial concentration of NO₂ is 0.100 M, how would you determine how long it would take for the concentration to decrease to 0.025 M?

Verified step by step guidance

Step 1: Identify the order of the reaction. In this case, the reaction is second order with respect to NO2, as indicated by the stoichiometric coefficient in front of NO2 in the balanced chemical equation.

Step 2: Write down the rate law for the reaction. For a second order reaction, the rate law is given by: \(\frac{1}{[A]_t} - \frac{1}{[A]_0} = kt\), where [A]_t is the concentration of the reactant at time t, [A]_0 is the initial concentration of the reactant, k is the rate constant, and t is the time.

Step 3: Substitute the given values into the rate law. In this case, [A]_0 is the initial concentration of NO2, which is 0.100 M, [A]_t is the final concentration of NO2, which is 0.025 M, and k is the rate constant, which is 0.63 M^-1s^-1.

Step 4: Solve the equation for t. This will give you the time it takes for the concentration of NO2 to decrease from 0.100 M to 0.025 M.

Step 5: Remember to check the units of your answer. The time should be in seconds, as the rate constant k is given in M^-1s^-1.

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Key Concepts

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

Rate Law and Reaction Order

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. For the reaction 2 NO2 → 2 NO + O2, the rate law can be determined based on the stoichiometry of the reaction, which indicates that it is second-order with respect to NO2. Understanding the reaction order is crucial for calculating how concentration changes over time.

Integrated Rate Laws

Integrated rate laws relate the concentration of reactants to time. For a second-order reaction, the integrated rate law is given by 1/[A] = kt + 1/[A0], where [A] is the concentration at time t, [A0] is the initial concentration, and k is the rate constant. This equation allows us to calculate the time required for the concentration of NO2 to decrease from 0.100 M to 0.025 M.

Units of the Rate Constant

The units of the rate constant (k) provide insight into the order of the reaction. For a second-order reaction, the units of k are M^-1s^-1, indicating that the rate depends on the square of the concentration of the reactant. Understanding these units is essential for correctly applying the integrated rate law and ensuring that calculations are dimensionally consistent.