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Chapter 12: Problem 25

What are the units for each of the following if the concentrations are expressed in moles per liter and the time in seconds? a. rate of a chemical reaction b. rate constant for a zero-order rate law c. rate constant for a first-order rate law d. rate constant for a second-order rate law e. rate constant for a third-order rate law

Short Answer

Expert verified
a. The units for the rate of a chemical reaction are mol/Ls. b. The units for the rate constant of a zero-order rate law are mol/Ls. c. The units for the rate constant of a first-order rate law are s⁻¹. d. The units for the rate constant of a second-order rate law are L/mol·s. e. The units for the rate constant of a third-order rate law are L²/mol²·s.

Step by step solution

01

a. Units for the rate of a chemical reaction

The rate of a chemical reaction (represented as 'r') is usually expressed as the change in concentration (∆[A]) of the reacting species A over the change in time (∆t). Thus: \(r = \frac{-\Delta{[A]}}{\Delta{t}}\) The units for the change in concentration are moles per liter (mol/L) and time in seconds (s). Therefore, the unit for the rate of a chemical reaction will be in mol/Ls.
02

b. Units for the rate constant of a zero-order rate law

In a zero-order rate law, the rate of the reaction (r) is directly proportional to the concentration of the reactant [A]^0: \(r = k [A]^0\) Since [A]^0 = 1, the rate constant k has the same units as the rate of reaction. Thus, the units for a zero-order rate constant k are mol/Ls.
03

c. Units for the rate constant of a first-order rate law

In a first-order rate law, the rate of the reaction (r) is directly proportional to the concentration of the reactant [A]: \(r = k [A]\) To find the units of the rate constant k, we rearrange the equation: \(k = \frac{r}{[A]}\) Since the units of the rate are mol/Ls and the units of the concentration are mol/L, the units for the rate constant k in a first-order rate law are s⁻¹.
04

d. Units for the rate constant of a second-order rate law

In a second-order rate law, the rate of the reaction (r) is directly proportional to the square of the concentration of the reactant [A]^2: \(r = k [A]^2\) To find the units of the rate constant k, we rearrange the equation: \(k = \frac{r}{[A]^2}\) Since the units of the rate are mol/Ls and the units of the concentration squared are (mol/L)^2, the units for the rate constant k in a second-order rate law are L/mol·s.
05

e. Units for the rate constant of a third-order rate law

In a third-order rate law, the rate of the reaction (r) is directly proportional to the cube of the concentration of the reactant [A]^3: \(r = k [A]^3\) To find the units of the rate constant k, we rearrange the equation: \(k = \frac{r}{[A]^3}\) Since the units of the rate are mol/Ls and the units of the concentration cubed are (mol/L)^3, the units for the rate constant k in a third-order rate law are L²/mol²·s.

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Most popular questions from this chapter

A first-order reaction is \(75.0 \%\) complete in \(320 . \mathrm{s}\). a. What are the first and second half-lives for this reaction? b. How long does it take for \(90.0 \%\) completion?

Consider two reaction vessels, one containing \(\mathrm{A}\) and the other containing \(\mathrm{B}\), with equal concentrations at \(t=0 .\) If both substances decompose by first-order kinetics, where $$ \begin{array}{l} k_{\mathrm{A}}=4.50 \times 10^{-4} \mathrm{~s}^{-1} \\ k_{\mathrm{B}}=3.70 \times 10^{-3} \mathrm{~s}^{-1} \end{array} $$ how much time must pass to reach a condition such that \([\mathrm{A}]=\) \(4.00[\mathrm{~B}] ?\)

A certain reaction has an activation energy of \(54.0 \mathrm{~kJ} / \mathrm{mol}\). As the temperature is increased from \(22^{\circ} \mathrm{C}\) to a higher temperature, the rate constant increases by a factor of \(7.00 .\) Calculate the higher temperature.

Upon dissolving \(\operatorname{InCl}(s)\) in \(\mathrm{HCl}, \mathrm{In}^{+}(a q)\) undergoes a disproportionation reaction according to the following unbalanced equation: $$ \mathrm{In}^{+}(a q) \longrightarrow \operatorname{In}(s)+\mathrm{In}^{3+}(a q) $$ This disproportionation follows first-order kinetics with a halflife of \(667 \mathrm{~s}\). What is the concentration of \(\mathrm{In}^{+}(a q)\) after \(1.25 \mathrm{~h}\) if the initial solution of \(\mathrm{In}^{+}(a q)\) was prepared by dissolving \(2.38 \mathrm{~g} \operatorname{InCl}(s)\) in \(5.00 \times 10^{2} \mathrm{~mL}\) dilute HCl? What mass of \(\operatorname{In}(s)\) is formed after \(1.25 \mathrm{~h}\) ?

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