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For a chemical reaction aA + bB cC + dD the formula for rate is k[A]a[B]b, where k is the rate constant, [A] is the concentration of reactant A, and [B] is the concentration of reactant B. Each reaction has its own unique rate law and rate constant, so Table 15.1 is just generalizing for you what the rate law would be when given a reaction.
How would we take into account temperature and activation energy when calculating k? Also, I'm confused about all the meanings we have given K in this class. Is k here the rate or the equilibrium constant?
k is the rate constant, while K is the equilibrium constant generally. You don't need to factor the temperature or activation energy into an calculations of k, it is just a conceptual fact that you should know. There is no mathematical way to determine reaction rates besides experimenting.
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