Rate Law p

You have qualitatively observed factors affecting reaction rate but… There is a mathematical relationship between reaction rate and factors affecting it! Must be determined empirically (experimentally)

The Rate Law For a reaction: aX + bY  products Rate is proportional to the product of the initial concentrations of the reactants raised to some exponent r  [X] m [Y] n r = k [X] m [Y] n Where k is the rate constant for a specific reaction at a specific temperature. Note: Exponents do NOT have to equal molar coefficients

The balanced chemical equation is the first step We know reaction rate depends on [R] Recall: rate = ∆[R]/∆t But does [NH 4 + ] have a greater effect than [NO 2 - ]? Example

Compare Experiments 1 and 2: when [NH 4 + ] doubles, the initial rate doubles. To determine the rate law we measure the rate at different starting conditions.

Compare Experiments 5 and 6: when [NO 2 - ] doubles, the initial rate doubles. r = k[NH 4 + ] 1 [NO 2 - ] 1 or r = k[NH 4 + ][NO 2 - ] I.e. reaction rate depends equally on the initial concentrations of each reactant

Order of Reaction The exponents in the rate law describe the dependence of rate on initial concentration Overall order of reaction is the sum of each of the individual orders of reaction. r = k[NH 4 + ][NO 2 - ] Order of reaction wrt NH 4 + is 1 Order of reaction wrt NO 2 - is 1 Overall order of reaction is 2 (1+1)

For the reaction: 2 X + 2 Y + 3 Z  products Experimentally the rate law has been determined as: r = k[X] 1 [Y] 2 [Z] 0 Because r  [X] 1 If initial [X] doubles, rate will double too 2 1 If initial [X] triples, rate will triple too 3 1

r = k[X] 1 [Y] 2 [Z] 0 Because r  [Y] 2 If initial [Y] doubles, rate will multiply by 4 (2 2 ) If initial [Y] triples, rate will multiply by 9 (3 2 ) Because r  [Z] 0 If initial [Z] doubles, rate will multiply by 1 (2 0 ), the rate will remain unchanged If initial [Z] triples, rate will multiply by 1 (3 0 ), the rate will remain unchanged I.e. [Z] does NOT affect reaction rate r = k[X] 1 [Y] 2

Determining the Rate Constant (k) Using the experimental data below calculate the rate constant, k A + B  Products Trial[A] (mol/L)[B] (mol/L)Rate (mol/L·s)

Practice P. 377 #1-6 P. 381 #1,2,5