115. The previous exercise shows how the first-order integrated rate law is derived from the first-order differential rate law. Begin with the second-order differential rate law and derive the sec ond-order integrated rate law.

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Elin HesselLv2

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114. The A — first-order integrated rate law for the reaction products is derived from the rate law using calculus: Rate = k[A] (first-order rate law) d[A] Ratedt [A] =- [A] The equation just given is a first-order, separable differential equation that can be solved by separating the variables and inte- grating: d[A] = -kdt TAJ PINA[A] - kat JA), [A] kat In the integral just given, [A]o is the initial concentration of A. We then evaluate the integral: [In[A]] A) = -k[t]6 In[A] - In[A]o = -kt In[A] = -kt + In[A]o (integrated rate law) a. Use a procedure similar to the one just shown to derive an in- tegrated rate law for a reaction A — products, which is one- half order in the concentration of A (that is, Rate = k[A]"). b. Use the result from part a to derive an expression for the half- life of a one-half-order reaction.