The following data were collected for the desturction of O 3 by H (O 3 + H → O 2 + OH) at very low concentrations (b) Calculate the rate constant

everyone here has a specific reaction below. And we have the following data. We're gonna ask how about the rate constant. Over here we're gonna use our right law equation. And it's gonna be right. It was the rate constant. This concentration of a. The power of X. And X. Is in order with respect to A. That's construction of B. To the power of why and why is the order with respect to be. We need to first determine the order with respect to I minus and S. 208 to minus. In this case to find the right order for I minus. We're gonna use our 1st and 2nd experiments 7.23 1799. This sim Bhullar per second be equal to the rate constant concentration of I minus. It's gonna be 7.47 10 to 9- smaller the power of X. That was 1.28. I'm sentence to five molar concentration of S. 208 to minus the power of why. And then for the first reaction we have 2.41 Times 10 to the -9/s. Even though our rate constant, That's 2.49 Sentinel Meghan $5. The power of X. That was 1.28 10 10. Megan. five smaller the power of white. Now these are going to cancel out and the K cancels out Left up three Eagles through to the power of X. X. is equal to one. I'm minus his first order. And now to find the right order for S. 208 to minus. Gonna use our 3rd and 1st experiments. You have 9.64 times since the night of $9 per second. People to the right concept Times 2.49 Since Omega five Mahler. The power of That's 2.56. Um symptom Mega five smaller the power of Y. And then we have two points 11. I'm sensing a mate of mine dollar per second Equal to the great constant of 2.49. I'm sensing 195 more. The power of X. That's 1.28. I'm centenarian five baller. The power of Why? So now this is gonna cancel out and the K. Is gonna cancel out the front. Four equals two to the power of Y. And Y equals two S. 208 To minus the second order. For our rate, it's gonna be able to Okay. Construction of I minus construction of S. 208 to minus The power of two. So using our first experiment For the right we have 2.4, 1 time symptom leg of nine. Follow per second. You go to the right constant Times 2. 17 95 smaller 1.28 Constance and Meghan. five smaller square. We're gonna get 2.41 constant omega nine molar per second. It was okay. 4.08 since the 15th. What a cute. Okay We get 5.91 times 10 to the five Baller the negative. Two power, 2nd to the next one. Power. Thanks for watching my video. And I hope it was helpful.

Ch.18 - Chemistry of the Environment

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.18 - Chemistry of the Environment

Problem 87b

Chapter 18, Problem 87b

The following data were collected for the desturction of O₃ by H (O₃ + H → O₂ + OH) at very low concentrations (b) Calculate the rate constant

Verified step by step guidance

Identify the rate law for the reaction. Since the reaction is O_3 + H → O_2 + OH, the rate law can be expressed as rate = k[O_3][H], where k is the rate constant.

Use the experimental data provided to determine the rate of the reaction. This typically involves measuring the concentration of reactants over time.

Rearrange the rate law to solve for the rate constant k. This can be done by dividing the rate by the product of the concentrations of the reactants: k = rate / ([O_3][H]).

Substitute the measured rate and concentrations of O_3 and H into the rearranged rate law equation to calculate the value of the rate constant k.

Ensure that the units of the rate constant k are consistent with the order of the reaction. For a second-order reaction, the units of k are typically M^-1 s^-1.

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Key Concepts

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

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically formulated as rate = k[A]^m[B]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to each reactant. Understanding the rate law is essential for calculating the rate constant, especially in reactions involving low concentrations.

Order of Reaction

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. It indicates how the rate of reaction is affected by the concentration of that reactant. For example, a first-order reaction depends linearly on the concentration of one reactant, while a second-order reaction depends on the square of the concentration. Identifying the order is crucial for determining the rate constant from experimental data.

Arrhenius Equation

The Arrhenius equation relates the rate constant of a reaction to the temperature and activation energy. It is expressed as k = A * e^(-Ea/RT), where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. This equation helps in understanding how temperature influences the rate constant, which is particularly relevant when calculating k for reactions at varying temperatures.