Chapter 16: Problem 9
Give two reasons to measure initial rates in a kinetics study.
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Chapter 16: Problem 9
Give two reasons to measure initial rates in a kinetics study.
These are the key concepts you need to understand to accurately answer the question.
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The mathematics of the first-order rate law can be applied to any situation in which a quantity decreases by a constant fraction per unit of time (or unit of any other variable). (a) As light moves through a solution, its intensity decreases per unit distance traveled in the solution. Show that \(\ln \left(\frac{\text { intensity of light leaving the solution }}{\text { intensity of light entering the solution }}\right)\) \(=-\) fraction of light removed per unit of length \(\times\) distance traveled in solution (b) The value of your savings declines under conditions of constant inflation. Show that \(\ln \left(\frac{\text { value remaining }}{\text { initial value }}\right)\) \(=-\) fraction lost per unit of time \(\times\) savings time interval
Acetone is one of the most important solvents in organic chemistry, used to dissolve everything from fats and waxes to airplane glue and nail polish. At high temperatures, it decomposes in a first-order process to methane and ketene \(\left(\mathrm{CH}_{2}=\mathrm{C}=\mathrm{O}\right) .\) At \(600^{\circ} \mathrm{C},\) the rate constant is \(8.7 \times 10^{-3} \mathrm{~s}^{-1}\). (a) What is the half-life of the reaction? (b) How long does it take for \(40 . \%\) of a sample of acetone to decompose? (c) How long does it take for \(90 . \%\) of a sample of acetone to decompose?
16.89 A slightly bruised apple will rot extensively in about 4 days at room temperature \(\left(20^{\circ} \mathrm{C}\right)\). If it is kept in the refrigerator at \(0^{\circ} \mathrm{C}\), the same extent of rotting takes about 16 days. What is the activation energy for the rotting reaction?
For the reaction \(\mathrm{A}(g)+\mathrm{B}(g) \longrightarrow \mathrm{AB}(g),\) the rate is \(0.20 \mathrm{~mol} / \mathrm{L} \cdot \mathrm{s},\) when \([\mathrm{A}]_{0}=[\mathrm{B}]_{0}=1.0 \mathrm{~mol} / \mathrm{L}\). If the reaction is first order in \(\mathrm{B}\) and second order in \(\mathrm{A}\), what is the rate when \([\mathrm{A}]_{0}=\) \(2.0 \mathrm{~mol} / \mathrm{L}\) and \([\mathrm{B}]_{0}=3.0 \mathrm{~mol} / \mathrm{L} ?\)
In a classroom demonstration, hydrogen gas and oxygen gas are mixed in a balloon. The mixture is stable under normal conditions, but, if a spark is applied to it or some powdered metal is added, the mixture explodes. (a) Is the spark acting as a catalyst? Explain. (b) Is the metal acting as a catalyst? Explain.
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