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What is the effect of changing the concentration of one reactant on the rate of a first or zero order reaction, and how can this effect be determined experimentally using different techniques such as the initial rate method and integrated rate laws?

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In a chemical reaction, the rate at which the reaction occurs can be influenced by various factors, including the concentration of the reactants. The effect of changing the concentration of one reactant on the rate of a first or zero order reaction can be understood by examining the rate laws for these reactions.1. Zero-order reaction:For a zero-order reaction, the rate law is given by:Rate = kwhere k is the rate constant. In this case, the rate of the reaction is independent of the concentration of the reactants. Therefore, changing the concentration of one reactant will have no effect on the rate of a zero-order reaction.2. First-order reaction:For a first-order reaction, the rate law is given by:Rate = k[A]where k is the rate constant and [A] is the concentration of reactant A. In this case, the rate of the reaction is directly proportional to the concentration of the reactant. Therefore, increasing the concentration of one reactant will increase the rate of a first-order reaction, while decreasing the concentration will decrease the rate.To determine the effect of changing the concentration of one reactant on the rate of a reaction experimentally, different techniques can be employed, such as the initial rate method and integrated rate laws.1. Initial rate method:In this method, the initial rate of the reaction is measured at different initial concentrations of the reactants. By comparing the initial rates and the corresponding concentrations, the order of the reaction with respect to each reactant can be determined. For example, if doubling the concentration of a reactant doubles the initial rate, the reaction is first-order with respect to that reactant. If the initial rate remains constant when the concentration is changed, the reaction is zero-order with respect to that reactant.2. Integrated rate laws:Integrated rate laws relate the concentration of reactants to time and can be used to determine the order of a reaction. For zero-order and first-order reactions, the integrated rate laws are as follows:Zero-order: [A]t = [A]0 - ktFirst-order: ln[A]t = ln[A]0 - ktwhere [A]t is the concentration of reactant A at time t, [A]0 is the initial concentration of A, k is the rate constant, and t is the time.By monitoring the concentration of the reactants over time and plotting the data according to the integrated rate laws, the order of the reaction can be determined. For a zero-order reaction, a plot of [A]t versus t will yield a straight line with a slope of -k. For a first-order reaction, a plot of ln[A]t versus t will yield a straight line with a slope of -k.In summary, changing the concentration of one reactant will have no effect on the rate of a zero-order reaction, while it will directly affect the rate of a first-order reaction. The initial rate method and integrated rate laws can be used experimentally to determine the effect of changing the concentration of one reactant on the rate of a reaction and to establish the reaction order.
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