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Lecture 4sf

# Lecture 4sf - Differential Rate Law Consider a general...

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Unformatted text preview: Differential Rate Law Consider a general chemical equation: A + B → products Some possible expressions for rate are:- or - where and are instantaneous rates. These rates depend on the concentrations of the reacting species. In general, we can write an equation, called the differential rate law , expressing how the rate depends on concentrations. Such an equation is generally of the form: Rate = k[A] n [B] m where n and m are called the “order” with respect to a given reactant concentration. n = order with respect to reactant A m = order with respect to reactant B n + m = the total order of the reaction. Most of the time, n and m are integers, usually 0, 1, 2. Occasionally, n and m can be fractions such as or . The value of n and m must be determined experimentally, from data on rates and concentrations. These values cannot be predicted from the stoichiometric coefficients of the reaction. The most common approach to finding the rate law (value of n, m in the rate equation), is to compare initial rates with initial concentrations. This is called the method of initial rates. Consider the reaction: NH 4 + (aq) + NO 2- (aq) → N 2 (g) + 2H 2 O( ) Rate = k[NH 4 + ] n [NO 2- ] m Expt [NH 4 + ] [NO 2- ] Initial Rate (M s-1 ) 1 0.100 0.0050 1.35 x 10-7 2 0.100 0.010 2.70 x 10-7 3 0.200 0.010 5.40 x 10-7 We compare concentration ratios and rate ratios, for different pairs of experiments. If possible, we pick a pair of experiments where all concentration remains the same except for one, and the rate then depends only on this single concentration. Compare Concentration ratio Rate Ratio Expt 1,2 = 2.0 ( for NO 2- ) 7 7 10 x 35 . 1 10 x 70 . 2-- = 2.00 Expt 2,3 = 2.00 (for NH 4 + ) 7 7 10 x 7 . 2 10 x 40 . 5-- = 2.00 Comparing experiments 1,2, [NH 4 + ] is constant, and the rate depends only on the change in [NO 2- ]. We see that when [NO 2- ] doubles, the rate also doubles. This is a first order reaction with respect to NO 2- (m = 1) Explicitly, we are comparing concentration ratios and rate ratios for experiments 1 and 2 where the concentration changes are for NO 2- . ( 1 2 c c ) m = 1 2 r r where c = concentration, r = rate 2.00 m = 2.00 m = 1 Comparing experiments 2,3 [NO 2- ] is constant, and the rate depends only on the change in [NH 4 + ]. We see that when [NH 4 + ] doubles, the rate also doubles. This is a first order reaction with respect to NH 4 + (n = 1) Explicitly, we are comparing concentration ratios and rate ratios for experiments 2 and 3 where the concentration changes are for NH 4 + . ( 2 3 c c ) n = 2 3 r r where c = concentration, r = rate 2.00 n = 2.00 n = 1 Therefore, the overall rate law is: Rate = k[NH 4 + ][NO 2- ] The reaction is first order in NH 4 + , first order in NO 2- , and second order overall (n + m = 2)....
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Lecture 4sf - Differential Rate Law Consider a general...

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