## CHM 112 Section 1

Homework Assignment #4
##### Due February 1, 2006 by 8:05 a.m.

Practice (not to be turned in): Problems: 13.38, 13.40, 13.41

Consider the following questions:

0) Even in the gas phase, where kinetic-molecular theory works well, theoretical calculation of rate constants from first principals generally does not succeed. Explain this statement in terms of collision theory.

The difficulty in calculating rate constants theoretically is based on the orientation term. Finding the fraction of molecules that have collisions in the correct orientation is challenging and is not based upon simple principals.

1) A modest temperature rise, say 10 oC, increases the collision frequency by only a few per cent. However, this same temperature rise can increase the rate constant by a factor of two or more. Explain.

The frequency factor normally is not the controlling factor when the temperature rises. Most often, the activation energy term is most important, where a small rise in temperature is amplified by the exponential increase in the fraction of reacting molecules.

2) The activation energy for an endothermic reaction is always equal to or greater than the enthalpy change. Explain.

In an endothermic reaction the energy of the products is higher than the energy of the reactants. The activation energy also is an energy increase. The activation energy must be at least as high as the products energy or the reaction would never take place. Thus, the activation energy must be at least as large as the enthalpy in an endothermic reaction.

3) The relationship between the magnitudes of the activation energy and the enthalpy for exothermic reactions is random. Explain.

In an exothermic reaction, the energy of the products is lower than the energy of the reactants. In contrast, the activation energy measures the increase in energy the reactants are required to achieve to allow reaction. The amount of energy increase required to initiate reaction (the activation energy) is unrelated to the amount of energy ultimately released by the reaction (the enthalpy).

4) A mixture of hydrogen gas and oxygen gas in a vessel is stable at room temperature. However, if this mixture is exposed to a spark there is an immediate explosion that consumes all of the limiting reagent. Explain in terms of collision theory.

The spark provides the energy for some of the molecules to exceed the activation energy, which allows them to react. Since the reaction is exothermic, more heat is generated, which allows more molecules to react. All of this happens quickly, which leads to the explosion.

5) In the reaction between iodine atoms to form iodine molecules the orientation term in collision theory does not contribute. Explain.

Iodine atoms are spherical, so matter which direction a second atom approaches the first atom, the same reactivity is available.

6) Using the appropriate experimental techniques, gas phase molecules can be emitted from a nozzle into a vacuum such that all of the molecules have about the same direction and about the same speed. This molecular beam is said to be "cold" and is, therefore, unreactive. Explain why there is so little reactivity in these molecules that contain substantial kinetic energy.

If all the molecules are moving in the same direction and at the same speed, there are no collisions. No collisions means no reactions.

7) A mixture of gas phase fluorine atoms will react much faster to form fluorine molecules than a mixture of iodine atoms to form iodine atoms at the same temperature. Yet, the bond energies of F2 and I2 are about the same. Explain in terms of collision theory.

Orientation does not play a role because both reactants are spherical. It is possible that the activation energies are different for the two reactions, but that seems unlikely since both products are diatomic molecules containing only a single bond. Thus, the controlling factor must be the collision frequency, which, at constant temperature, is controlled by the mass of the reacting species. Since the mass of the F atoms is much less, the velocities of the atoms is higher, which leads to more collisions and faster reactivity.

8) In the context of collision theory, the rate constant k is a probability factor, not a true probability. Explain the difference between a probability and a probability factor.

A probability has values between 0 and 1 (a probability of 0 means the event never happens and a probability of 1 means the event always happens) and are unitless. Rate constants can have values from 0 to much larger than 1 and contain units. Rate constants are probability factors because they contain the probability of reaction in them, along with other factors that lead to the correct units associated with the order of reaction.

9) Many reactions are known that occur in the solid state, i.e., molecules in solids that react with themselves. Often, the orientation term is the most important factor for determining the rate constant. Explain why.

The collision frequency is unimportant because all of the molecules are always adjacent to each other in the solid state. If the molecules are lined up wrong, i.e. the wrong orientation, then there can be no reaction no matter what the temperature. In contrast, if the molecules align correctly, then reaction can be achieved even at modest temperatures.