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Chapter 13: Problem 5

Write the reaction rate expressions for the following reactions in terms of the disappearance of the reactants and the appearance of products: (a) \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \longrightarrow 2 \mathrm{HI}(g)\) (b) \(5 \mathrm{Br}^{-}(a q)+\mathrm{BrO}_{3}^{-}(a q)+6 \mathrm{H}^{+}(a q) \longrightarrow\) $$ 3 \mathrm{Br}_{2}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) $$

Short Answer

Expert verified
The rate of reaction (a) in terms of the disappearance of H2 and I2 or the appearance of HI is given as \( -\frac{1}{2}\frac{d[\mathrm{H}_{2}]}{dt} = -\frac{1}{2}\frac{d[\mathrm{I}_{2}]}{dt} = \frac{d[\mathrm{HI}]}{dt} \) and the rate of reaction (b) in terms of disappearance of the reactants Br-, BrO3- and H+ and formation of the products Br2 and H2O is given as \(-\frac{1}{5}\frac{d[\mathrm{Br}^-]}{dt} = -\frac{d[\mathrm{BrO}_{3}^-]}{dt} = -\frac{1}{6}\frac{d[\mathrm{H}^+]}{dt} = \frac{1}{3}\frac{d[\mathrm{Br}_2]}{dt} = \frac{1}{3}\frac{d[\mathrm{H}_2\mathrm{O}]}{dt}\)

Step by step solution

01

Write the rate expression for reaction (a)

In reaction (a) we have to divide the change in concentration of a reactant or product by the stoichiometric coefficient. In this case, the rate of reaction can be written in terms of the disappearance of H2 and I2 or the appearance of HI. If the reaction is proceeding in the direction as written, the rate can be expressed as follows: \( -\frac{1}{2}\frac{d[\mathrm{H}_{2}]}{dt} = -\frac{1}{2}\frac{d[\mathrm{I}_{2}]}{dt} = \frac{d[\mathrm{HI}]}{dt} \)
02

Write the rate expression for reaction (b)

Similarly, for reaction (b), we divide the change in concentration of each reactant or product by its stoichiometric coefficient. The rate can be expressed in terms of disappearance of the reactants Br-, BrO3- and H+ or the appearance of the products Br2 and H2O. If the reaction is proceeding in the direction as written, the rate can be expressed as follows: \(-\frac{1}{5}\frac{d[\mathrm{Br}^-]}{dt} = -\frac{d[\mathrm{BrO}_{3}^-]}{dt} = -\frac{1}{6}\frac{d[\mathrm{H}^+]}{dt} = \frac{1}{3}\frac{d[\mathrm{Br}_2]}{dt} = \frac{1}{3}\frac{d[\mathrm{H}_2\mathrm{O}]}{dt}\)

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Most popular questions from this chapter

The reaction \(\mathrm{H}+\mathrm{H}_{2} \longrightarrow \mathrm{H}_{2}+\mathrm{H}\) has been studied for many years. Sketch a potential energy versus reaction progress diagram for this reaction.

A protein molecule, \(\mathrm{P}\), of molar mass \(\mathscr{A}\) dimerizes when it is allowed to stand in solution at room temperature. A plausible mechanism is that the protein molecule is first denatured (that is, loses its activity due to a change in overall structure) before it dimerizes: $$ \begin{array}{rlr} \mathrm{P} & \stackrel{k}{\longrightarrow} \mathrm{P}^{*}(\text { denatured }) & \text { slow } \\ 2 \mathrm{P}^{*} \longrightarrow \mathrm{P}_{2} & \text { fast } \end{array} $$ where the asterisk denotes a denatured protein molecule. Derive an expression for the average molar mass (of \(\mathrm{P}\) and \(\mathrm{P}_{2}\) ), \(, \overline{\mathscr{M}}\), in terms of the initial protein concentration \([\mathrm{P}]_{0}\) and the concentration at time \(t,\) \([\mathrm{P}]_{,}\) and \(\mathscr{A} .\) Describe how you would determine \(k\) from molar mass measurements.

The rate law for the decomposition of ozone to molecular oxygen \(2 \mathrm{O}_{3}(g) \longrightarrow 3 \mathrm{O}_{2}(g)\) is rate \(=k \frac{\left[\mathrm{O}_{3}\right]^{2}}{\left[\mathrm{O}_{2}\right]}\) The mechanism proposed for this process is \(\mathrm{O}_{3} \stackrel{k_{1}}{k_{-1}} \mathrm{O}+\mathrm{O}_{2}\) \(\mathrm{O}+\mathrm{O}_{3} \stackrel{k_{2}}{\longrightarrow} 2 \mathrm{O}_{2}\) Derive the rate law from these elementary steps. Clearly state the assumptions you use in the derivation. Explain why the rate decreases with increasing \(\mathrm{O}_{2}\) concentration.

The rate constant of a first-order reaction is \(4.60 \times\) \(10^{-4} \mathrm{~s}^{-1}\) at \(350^{\circ} \mathrm{C} .\) If the activation energy is \(104 \mathrm{~kJ} /\) mol, calculate the temperature at which its rate constant is \(8.80 \times 10^{-4} \mathrm{~s}^{-1}\)

On which of the following properties does the rate constant of a reaction depend: (a) reactant concentrations, (b) nature of reactants, or (c) temperature?
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