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In an experiment, a sample of NaClO3 was 90% decomposed in 48 min. Approximately how long would this decomposition have taken if the sample had been heated 20°C higher?

Short Answer

Expert verified

The time required for the decomposition is 12 minutes.

Step by step solution

01

Assumption and analysis

Assuming the reaction rate doubles for \(10^\circ C\)rise in temperature. The rate becomes \({{\bf{2}}^{\bf{2}}}{\bf{ = 4}}\,\,{\bf{times}}\) at \(20^\circ C\) higher, the time decreases by \({{\bf{2}}^{\bf{2}}}{\bf{ = 4}}\,\,{\bf{times}}\).

02

Calculation

Therefore, time required is \(\frac{{{\bf{48}}}}{{\bf{4}}}{\bf{ = 12}}\)min

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Most popular questions from this chapter

The annual production of \({\bf{HN}}{{\bf{O}}_{\bf{3}}}\) in 2013 was 60 million metric tons Most of that was prepared by the following sequence of reactions, each run in a separate reaction vessel.

\(\begin{align}\left( a \right){\bf{ }}4N{H_3}{\bf{ }}\left( g \right){\bf{ }} + {\bf{ }}5{O_2}{\bf{ }}(g) \to 4NO\left( g \right){\bf{ }} + {\bf{ }}6{H_2}O\left( g \right)\\\left( b \right){\bf{ }}2NO\left( g \right){\bf{ }} + {\bf{ }}{O_{2{\bf{ }}}}(g) \to 2N{O_{2{\bf{ }}}}\left( g \right)\\\left( c \right){\bf{ }}3N{O_2}{\bf{ }}\left( g \right){\bf{ }} + {\bf{ }}{H_2}O(l) \to 2HN{O_3}(aq) + NO(g)\end{align}\)

The first reaction is run by burning ammonia in air over a platinum catalyst. This reaction is fast. The reaction in equation (c) is also fast. The second reaction limits the rate at which nitric acid can be prepared from ammonia. If equation (b) is second order in NO and first order in \({{\bf{O}}_{\bf{2}}}\), what is the rate of formation of \({\bf{N}}{{\bf{O}}_{\bf{2}}}\) when the oxygen concentration is 0.50 M and the nitric oxide concentration is 0.75 M? The rate constant for the reaction is \({\bf{5}}{\bf{.8 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}{\bf{ L}}{{\bf{ }}^{\bf{2}}}{\bf{ mo}}{{\bf{l}}^{{\bf{ - 2}}}}{\bf{ s}}{{\bf{ }}^{{\bf{ - 1}}}}\).

Why are elementary reactions involving three or more reactants very uncommon?

Hydrogen reacts with nitrogen monoxide to form dinitrogen monoxide (laughing gas) according to the equation:\({{\bf{H}}_{\bf{2}}}{\bf{(g) + 2NO(g)}} \to {{\bf{N}}_{\bf{2}}}{\bf{O(g) + }}{{\bf{H}}_{\bf{2}}}{\bf{O}}\).Determine the rate law, the rate constant, and the orders with respect to each reactant from the following data:

The hydrolysis of the sugar sucrose to the sugars glucose and fructose, \({{\bf{C}}_{{\bf{12}}}}{{\bf{H}}_{{\bf{22}}}}{{\bf{O}}_{{\bf{11}}}}{\bf{ + }}{{\bf{H}}_{\bf{2}}}{\bf{O}} \to {{\bf{C}}_{\bf{6}}}{{\bf{H}}_{{\bf{12}}}}{{\bf{O}}_{\bf{6}}}{\bf{ + }}{{\bf{C}}_{\bf{6}}}{{\bf{H}}_{{\bf{12}}}}{{\bf{O}}_{\bf{6}}}\) follows a first-order rate equation for the disappearance of sucrose: \({\bf{Rate = k}}\left( {{{\bf{C}}_{{\bf{12}}}}{{\bf{H}}_{{\bf{22}}}}{{\bf{O}}_{{\bf{11}}}}} \right)\) (The products of the reaction, glucose and fructose, have the same molecular formulas but differ in the arrangement of the atoms in their molecules.)

  1. In neutral solution, \({\bf{k = 2}}{\bf{.1 \times 1}}{{\bf{0}}^{{\bf{ - 11}}}}{{\bf{s}}^{{\bf{ - 1}}}}\) at 27 °C and \({\bf{8}}{\bf{.5 \times 1}}{{\bf{0}}^{{\bf{ - 11}}}}{{\bf{s}}^{{\bf{ - 1}}}}\) at 37 °C. Determine the activation energy, the frequency factor, and the rate constant for this equation at 47 °C (assuming the kinetics remain consistent with the Arrhenius equation at this temperature).
  2. When a solution of sucrose with an initial concentration of 0.150 M reaches equilibrium, the concentration of sucrose is\({\bf{1}}{\bf{.65 \times 1}}{{\bf{0}}^{{\bf{ - 7}}}}{\bf{ M}}\). How long will it take the solution to reach equilibrium at 27 °C in the absence of a catalyst? Because the concentration of sucrose at equilibrium is so low, assume that the reaction is irreversible.
  3. Why does assuming that the reaction is irreversible simplify the calculation in part (b)?

Account for the increase in reaction rate brought about by a catalyst.

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