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lecture+5sf

# lecture+5sf - Effect of Temperature on Rate aA bB products...

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Effect of Temperature on Rate aA + bB → products 1 Rate = k[A] n [B] m This equation shows how rate depends on concentration. Temperature is not included in this equation. However, rates are definitely temperature dependent. In general, a higher temperature means a faster reaction. Although temperature is not explicitly in the rate equation, the rate constant k is temperature dependent. So, as temperature increases, k increases, and thus the rate will also increase. Collision Theory Reactants A and B cannot react if they are in different parts of the world. If reactants A and B react, they must have an encounter—a collision . A collision is a necessary but not a sufficient condition for a reaction of two different species. If there is a reaction, there must have been a collision. But the converse is not necessarily true. Every collision does not produce a reaction. A higher temperature means molecules are moving faster. This will increase collision frequency, but this increased collision frequency is not the main explanation for the temperature dependence of rate. Let’s analyze what happens if the temperature is increased slightly, from room temperature, 298 K, to 10K above that, 308 K. The average velocity of molecule is given by: v = M RT 3 where T is the temperature and M is the molar mass Compare two identical gases (same molar mass) at temperatures T 2 and T 1 . v 2 = M RT 3 2 v 1 = M RT 3 1 Comparing by ratio: 1 2 v v = 1 2 T T

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If T 2 = 308 K and T 1 = 298 K, then 1 2 T T = 298 308 = 1.017 This means that at 308 K, the molecules move about 1.7% faster than the molecules move at 298 K, meaning a relatively small increase in collision frequency Generally, we find rates are much more temperature dependent than can be predicted by just an increase in collision frequency. A rough guideline states: a 10 K increase in temperature doubles the rate of a slow reaction. This is not an exact rule, but just a “ballpark” figure. Some reaction rates may increase by less than double, some more than double, for a 10 K temperature increase. But the velocity increase of 1.7% is much less than a doubling. The increase in rate must be explained by something more than just an increased collision frequency. The equation v = M RT 3 represents the average velocity. But most collisions do not result in a reaction. Only collisions with enough energy (called the activation energy) result in a chemical reaction. In most cases, this means only a small percentage of the collisions actually result in a reaction. Thus, an analysis of changes in the average velocity is irrelevant, since these “average” molecules are not reacting. The important effect of temperature is to change the energy distribution, making it more likely that the collision will have sufficient energy.
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lecture+5sf - Effect of Temperature on Rate aA bB products...

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