From Method of Initial Rates to Integrated Rate Law Rates of Reaction From Method of Initial Rates to Integrated Rate Law

Method of Initial Rates The initial rates listed in the following table were determined for the reaction: 2NO(g) + Cl2(g)  2NOCl(g) What is the order of the reaction with respect to each reactant? What is the rate law? What is the value of the rate constant? Experiment Initial [NO] (M) Initial [Cl2] (M) Initial Rate of Consumption of Cl2 (M/s) 1 0.13 0.20 1.0 × 10-2 2 0.26 4.0 × 10-2 3 0.10 5.0 × 10-3 Complete as a quiz, then discuss/go over as a class while students correct their own work

Integrated Rate Laws N2O5 (g)  2NO2 (g) + ½ O2 (g) Time (s) [N2O5] (M) 0.1000 50 0.0707 100 0.0500 200 0.0250 400 0.00625 Integrated Rate Laws N2O5 (g)  2NO2 (g) + ½ O2 (g) Determine rate law for reaction from set of data consisting of concentration (or values of some function of concentration) versus time. What is the order of the reaction with respect to each reactant? What is the rate law? What is the value of the rate constant?

Integrated Rate Laws The Common Integrated Rate Laws: A  products First Order: rate = k[A] ln [A] = ln[A]o – kt Second Order: rate = k[A]2 (or rate = k[A][B]) 𝟏 [𝐀] = 𝟏 [𝐀] 𝒐 +𝐤𝐭 Uses of Integrated Rate Laws How long does it take? What concentration remains after a given time? What was the initial concentration? http://www.chem.purdue.edu/gchelp/howtosolveit/Kinetics/UsingIntegratedRateLaws.html

Integrated Rate Laws Rate = k Zero Order First Order Second Order http://www.chem.purdue.edu/gchelp/howtosolveit/Kinetics/IntegratedRateLaws.html Zero Order First Order Second Order The graph that is linear indicates the order of the reaction with respect to A.

Integrated Rate Laws Rate = k[A] Zero Order First Order Second Order http://www.chem.purdue.edu/gchelp/howtosolveit/Kinetics/IntegratedRateLaws.html Zero Order First Order Second Order The graph that is linear indicates the order of the reaction with respect to A.

Integrated Rate Laws Rate = k[A]2 Zero Order First Order Second Order http://www.chem.purdue.edu/gchelp/howtosolveit/Kinetics/IntegratedRateLaws.html Zero Order First Order Second Order The graph that is linear indicates the order of the reaction with respect to A.

Integrated Rate Law: Summary Table First Order Second Order Rate Law Concentration-Time Equation Linear Graph Graphical Determination of k Half-Life Equation

Integrated Rate Law: Summary Table First Order Second Order Rate Law Rate = −∆[R] ∆𝑡 = k[R]1 Rate = −∆[R] ∆𝑡 = k[R]2 Concentration-Time Equation ln[R]t = -kt + ln[R]o 1 [R] =𝑘𝑡+ 1 [R] o Linear Graph ln[R] vs. t 1 [R] vs. t Graphical Determination of k k = -slope k = slope Half-Life Equation 𝑡 1/2 = 0.693 𝑘 𝑡 1/2 = 1 𝑘 [R] o