A reaction A + B → C obeys the following rate law: Rate = k[B] 2 . (c) What are the units of the rate constant?

Hello in this problem, we are told if the order of the reaction of nitric oxide and ozone reacting for nitrogen dioxide and oxygen is second in nitric oxide and first in ozone. What is the rate law? And what are the units for the reaction rate constant? So recall that the general form of the rate law we have, the rate is equal to the reaction rate constant, sums are concentrations of our reactant to some order X and Y. It's okay again, is our reaction rate constant? And be our our reactant and X and Y are orders of the reaction. And they have to be determined experimentally. So in this problem then we start off with our rate again is equal to some reaction rate constant. We have our reactant nitric oxide and ozone. We're told that it is second order in nitric oxide. And it is first order in ozone. So the ones are not explicitly written, the ones are understood. So we don't put a superscript one um around the ozone. So this is our rate law expression or the reaction of nitric oxide and ozone where it's second order in nitric oxide. And first order in ozone. Now we are asked to find the reaction rate constant units. So we are going to solve for a reaction rate constant. It's okay then we'll be equal to the rate divided by the concentration of nitric oxide squared by by the concentration of ozone. And so these are our units recall that rate is always going to have some change in concentration over a period of time. So we have a concentration over a period of time. Those are always going to be our units for the rate and then we follow our units for the concentrations and then raise them to the powers indicated by the reaction rate law. So we have the concentration of nitric oxide is squared and that is then times the concentration of ozone which is to the one power. And now we can simplify this so we can cancel out one of the concentration units. And what we are left with then is one over the concentration squared and seconds. We can rewrite this And put the units in the numerator there in the denominator. Then the power is now minus. We bring it up to the numerator. So concentration to the -2 Seconds to the -1. And so our units for the reaction rate constant Are again concentration to the -2 seconds to the -1. Keep in mind that we know what the units for the rate has to be. There always have to be some concentration per unit time. And then we have concentrations which have units of polarity and then we pay attention to the order of the reaction to determine whether they are squared as in this example or first order is also shown in this example. Thanks for watching. Hope this help

Ch.14 - Chemical Kinetics

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Brown 14th Edition

Ch.14 - Chemical Kinetics

Problem 27c

Chapter 14, Problem 27c

A reaction A + B → C obeys the following rate law: Rate = k[B]². (c) What are the units of the rate constant?

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Identify the rate law given in the problem: Rate = k[B]^2. This indicates that the rate of the reaction depends on the concentration of B squared.

Recall that the rate of a reaction is typically expressed in units of concentration per unit time, such as mol/L/s.

The concentration of B is expressed in mol/L. Since the rate law is Rate = k[B]^2, the concentration term [B]^2 will have units of (mol/L)^2 or mol^2/L^2.

To find the units of the rate constant k, rearrange the rate law to solve for k: k = Rate / [B]^2.

Substitute the units into the rearranged equation: k = (mol/L/s) / (mol^2/L^2). Simplify this expression to determine the units of k.

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Key Concepts

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

Rate of Reaction

The rate of a chemical reaction quantifies how quickly reactants are converted into products. It is typically expressed in terms of concentration change over time, such as moles per liter per second (mol/L/s). Understanding the rate is crucial for determining how the concentration of reactants affects the speed of the reaction.

Rate Law

A rate law is an equation that relates the rate of a reaction to the concentration of its reactants, each raised to a power corresponding to their reaction order. In the given rate law, Rate = k[B]<sup>2</sup>, the reaction is second-order with respect to B, indicating that the rate is proportional to the square of the concentration of B. This relationship is essential for calculating the units of the rate constant.

Units of the Rate Constant (k)

The units of the rate constant (k) depend on the overall order of the reaction. For a second-order reaction, like the one described, the units of k are derived from the rate equation. Since the rate has units of mol/L/s and the concentration of B is in mol/L, the units of k must be L/(mol·s) to ensure that the equation is dimensionally consistent.

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Textbook Question

A reaction A + B → C obeys the following rate law: Rate = k[B]². (a) If [A] is doubled, how will the rate change? Will the rate constant change?

Textbook Question

A reaction A + B → C obeys the following rate law: Rate = k[B]². (b) What are the reaction orders for A and B? What is the overall reaction order?

Textbook Question

Consider a hypothetical reaction between A, B, and C that is first order in A, zero order in B, and second order in C. (a) Write the rate law for the reaction.

Textbook Question

Consider a hypothetical reaction between A, B, and C that is first order in A, zero order in B, and second order in C. (b) How does the rate change when [A] is doubled and the other reactant concentrations are held constant? (c) How does the rate change when [B] is tripled and the other reactant concentrations are held constant? (d) How does the rate change when [C] is tripled and the other reactant concentrations are held constant? (f) By what factor does the rate change when the concentrations of all three reactants are cut in half?

Textbook Question

Consider a hypothetical reaction between A, B, and C that is first order in A, zero order in B, and second order in C. (e) By what factor does the rate change when the concentrations of all three reactants are tripled?

A reaction A + B → C obeys the following rate law: Rate = k[B]2. (c) What are the units of the rate constant?

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Key Concepts

Rate of Reaction

Rate Law

Units of the Rate Constant (k)

A reaction A + B → C obeys the following rate law: Rate = k[B]². (c) What are the units of the rate constant?