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Ch.14 - Chemical Kinetics
Brown - Chemistry: The Central Science 15th Edition
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Non è quello che usi tu?Cambia libro di testo
Capitolo 14, Problema 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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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.
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Average Rate of 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.
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Rate Law Fundamentals

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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Equilibrium Constant K