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Account for the relationship between the rate of a reaction and its activation energy.

:How does an increase in temperature affect rate of reaction? Explain this effect in terms of the collision theory of the reaction rate

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掳C higher?

The rate constant at 325掳C for the decomposition reaction \({{\bf{C}}_{\bf{4}}}{{\bf{H}}_{\bf{8}}} \to {\bf{2}}{{\bf{C}}_{\bf{2}}}{{\bf{H}}_{\bf{4}}}\)is 6.1 脳 10^鈭�8 s^鈭�1, and the activation energy is 261 kJ per mole of\({{\bf{C}}_{\bf{4}}}{{\bf{H}}_{\bf{8}}}\). Determine the frequency factor for the reaction.

A study of the rate of the reaction represented as 2A鉄� B gave the following data:

1. Determine the average rate of disappearance of A between 0.0 s and 10.0 s, and between 10.0 s and 20.0 s.
2. Estimate the instantaneous rate of disappearance of A at 15.0 s from a graph of time versus (A). What are the units of this rate?
3. Use the rates found in parts (a) and (b) to determine the average rate of formation of B between 0.00 s and 10.0 s, and the instantaneous rate of formation of B at 15.0 s.

In terms of collision theory, to which of the following is the rate of a chemical reaction proportional?

(a) the change in free energy per second

(b) the change in temperature per second

(c) the number of collisions per second

(d) the number of product molecules

Hydrogen iodide, HI, decomposes in the gas phase to produce hydrogen, H₂, and iodine, I₂. The value of the rate constant, k, for the reaction was measured at several different temperatures, and the data are shown here:

What is the value of the activation energy (in kJ/mol) for this reaction?

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 掳C and \({\bf{8}}{\bf{.5 \times 1}}{{\bf{0}}^{{\bf{ - 11}}}}{{\bf{s}}^{{\bf{ - 1}}}}\) at 37 掳C. Determine the activation energy, the frequency factor, and the rate constant for this equation at 47 掳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 掳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)?

Use the PhET Reactions & Rates interactive simulation to simulate a system. On the 鈥淪ingle collision鈥� tab of the simulation applet, enable the 鈥淓nergy view鈥� by clicking the 鈥�+鈥� icon. Select the first A + BC鉄禔B + C reaction (A is yellow, B is purple, and C is navy blue). Using the 鈥渟traight shot鈥� default option, try launching the A atom with varying amounts of energy. What changes when the Total Energy line at launch is below the transition state of the Potential Energy line? Why? What happens when it is above the transition state? Why?

Use the PhET Reactions & Rates interactive simulation (http://openstaxcollege.org/l/ 16PHETreaction) to simulate a system. On the 鈥淪ingle collision鈥� tab of the simulation applet, enable the 鈥淓nergy view鈥� by clicking the 鈥�+鈥� icon. Select the first A + BC鉄禔B + C reaction (A is yellow, B is purple, and C is navy blue). Using the 鈥渁ngled shot鈥� option, try launching the A atom with varying angles, but with more Total energy than the transition state. Whathappenswhen the A atom hitstheBC molecule from different directions? Why?