For a zero order reaction, half life is independent of initial concentration of reactant.
Let the rate law for the reaction be $$r = k[\ce{A}]^n[\ce{B}]^m$$ Show
What are the results? Is it the rate? or is it the half life? Finding the value of $\mathbf{m}$ 1. If it is the rate, then It is obvious that $m$ should be zero. 2. If it is the half life, then For this to happen, $m$ should be equal to $1$$^*$, because only for a first order or a pseudo first order reaction, half life is independent of initial concentration of reactant. *This is correct only if A is in excess Half LifeThe half-life of a reaction is defined as the time required for the initial concentration of a reactant to be decreased by 50%. This is not the time for half of the reaction to occur! Half-life is denoted by t½ The half-life is related to the rate constant; thus, if we know the half-life we can also find the rate constant. The half-life also depends upon the order of the reaction. Zero Order Reaction
First Order Reaction
Second Order Reaction
Effect of Temperature on Reaction RatesThe orders of reaction are independent of temperature - orders change only when the reaction changes. Thus, the entire temperature dependence of a reaction, as expressed in a rate law, is found in the rate constant, k. Think about a typical rate law: Rate = –k[A]m The rate depends on how much is there (the concentration term, [A] m) and how effectively what is there can react, k. In this interpretation, k is a probability factor! Collision TheoryIn Collision Theory, three things must happen for a reaction to occur:
Each of these events has a probability associated with it. The rate constant is found from the product of each individual probability. Number of Collisions:Z = collision frequency From the kinetic theory of gases the collision frequency is found to be proportional to the square root of absolute temperature: Z T½Orientation of collisions:The structure of molecules influences the outcome of reactions. The correct parts of molecules must "touch" during a collision so the correct bonds can be broken and remade into the new molecule. Consider the example: Cl(g) + O3(g) → ClO(g) + O2(g) This reaction is important in the upper atmosphere. The rate of reaction depends upon the orientation of the collision between the chlorine atoms and the ozone: If the orientation is wrong, no reaction occurs. With the correct orientation, reaction can proceed. There is no temperature dependence of the orientation of collisions. Energy:For reaction to occur, collisions must have enough energy present. Not all collisions meet this criterion, so not all collisions lead to reaction. The temperature dependence of the energy term is found to be proportional to an exponential factor: where Ea is called the activation energy, R is the gas constant (in energy units), and T is the absolute temperature. Ea defines the amount of energy required in a collision to "activate" the reaction The total probability of a reaction is given by: k Zfpwhere
This leads to the temperature dependence of the rate constant: Transition State TheoryTransition State Theory extends Collision Theory by ascribing structural details to collisions. When molecules collide, a new "molecule" is formed, at least temporarily. This new molecule is called an activated complex. The activated complex is a high-energy molecule and this energy can be redistributed within the molecule. Breaking bonds, changing bond angles, and making new bonds accomplishes the energy redistribution. When the activated complex falls apart, it may return to the same geometry as reactants or it may fall apart into a new geometry: the products. Graphically, this can be shown using a potential energy diagram: In this example, the enthalpy of reaction is positive (i.e., the reaction is endothermic). The activation energy is always positive. Catalysts work by becoming part of the activated complex and lowering Ea. This speeds the reaction up. Does the halfNotice that, for zero-order reactions, the half-life depends on the initial concentration of reactant and the rate constant.
Is rate of zero order reaction is independent of initial concentration of reactant?A zero-order reaction, unlike the other orders of reaction, has a rate that is independent of the reactant concentration (s).
For which reaction halfThe half-life of a reaction is the time required for a reactant to reach one-half its initial concentration or pressure. For a first-order reaction, the half-life is independent of concentration and constant over time. Created by Jay.
For which order halfSolution : For a first order reaction, half-life period is independent of initial concentration of the reacting species and is calculated from the rate constant or vice versa.
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