Chemistry: Reactant Concentration's Impact on Reaction Rates, Summaries of Law

Download Chemistry: Reactant Concentration's Impact on Reaction Rates and more Summaries Law in PDF only on Docsity! The Rate Laws We are interested to know how the rate of reaction depends on the concentrations of reactants. When chemical reaction takes place, the concentrations of reactants and products change continuously during the course of the life-span of the reaction. Hence, it becomes difficult to measure the change in concentration accurately. This further complicates if the reverse reaction occurs some point in time. Therefore, it is desirable to measure the initial reaction rate based on the initial (starting) concentrations. It happens that the rate is directly proportional to some power of initial concentrations of reactants. Based on this, we can write the rate law for a general type of reaction: aA + bB cD + dD The rate law for the above equation is rate α [A]x[B]y The symbol α is the proportionality sign. This sign is not suitable for any kind of calculations and hence it must be removed. When we remove that we introduce a constant and the equation is written with an equal sign as follows. rate = k [A]x[B]y (1) where k is known as rate constant is the proportionality constant between the reaction rate and reactant concentrations. The above equation is known as rate law or rate equation. If we know initial concentrations of A and B as well as k, x, and y, we can calculate the rate of reaction using the above equation. The values of k, x, and y are usually determined experimentally. The order of reaction is judged by the numerical values of x and y. Say for example, x =1 and y=2. Then we say the reaction is first- order with respect A, second-order with respect B, and overall it is third-order (3 = 1+2). If x=0 or y=0 or x=y=0, then we say the reaction is zero-order with respect A or zero-order with respect B or zero-order with respect to A and B. As you know anything to the power zero is one. That means the reaction rate is independent of the initial concentrations. By knowing the x and y, we can better understand how the reaction rate depends on the initial concentrations. Suppose, for example, a particular reaction has yielded x = 2 and y =1. The rate law for the reaction according to Equation (1) is rate = k [A]2 [B]1 = k [A]2 [B] Note that if either x =1 or y=1 or x = y= 1, the number one is omitted from the rate law expression because [ ] 1 is the same as [ ]. This reaction is second-order with respect A, first-order with respect B, and overall it is third-order. This rate law tells us that if we double the concentration of A, the reaction rate will increase by a factor of 4 because of 1 power 2 in the expression. Let us verify this statement assuming initially [A] = 1.0 M and [B] =1.0 and doubling [A] from 1.0 M to 2.0 M: for [A] = 1.0 M rate1 = k (1.0 M)2 (1.0 M) = k (1.0 M3) (initial) for [A] =2.0 M rate2 = k (2.0 M)2 (1.0 M) = 4 x k(1.0 M3) (doubling A) Thus you can see rate2 = 4 x rate1 Now if we double the concentration of B keeping the concentration of A constant, the reaction rate will double. Let test this statement setting [A]=1.0 M and [B] =1.0 M and doubling [B] from 1.0 M to 2.0 M: for [B] = 1.0 M rate3 = k (1.0 M)2 (1.0 M) = k (1.0 M3) (initial) for [B] = 2.0 M rate4 = k (1.0 M)2 (2.0 M) = 2 x k (1.0 M3) (doubling B) Hence rate4 = 2 x rate3 This simple analysis illustrates how the change in concentrations of reactants alters the reaction rate. In general, • if the power of the reactant is 1, then the rate increases 2-fold times(doubles) when the concentration of the reactant is doubled (because 21) • if the power of the reactant is 2, then the rate increases 4-fold times(quadruples) when the concentration of the reactant is doubled (because 22) • if the power of the reactant is 3, then the rate increases 8-fold times when the concentration of the reactant is doubled ( because 23) Experimental Determination of Order of Reaction To determine the rate law applicable to a particular chemical reaction, one needs to establish the exact values for x, y, and k that depends on whether one reactant or more than one reactant are involved. One reactant: If a chemical reaction involves one reactant, it is a simple matter to determine the order of reaction by measuring the rate of reaction as a function of concentration of the reactant. If the rate doubles when the concentration of reactant is doubled, the reaction is the first-order. If the rate becomes 4-fold times (quadruples) when the concentration of the reactant is doubled, the reaction is the second-order and similarly, the third, the fourth, and the higher orders. 2