First Order Rate Constant in Chemical Kinetics

First-Order Reactions

• A first-order reaction rate is dependent on the concentration of a single reactant (A).
• The rate of change in the concentration of Z (dx/dt) is equal to kA (a0 - x), where kA is the first-order rate constant.
• Integration of the rate equation yields -ln(a0 - x) = kAt - I, where I is the constant of integration.
• The rate constant (kA) has units of s^-1.
• A plot of ln[A] versus t is linear with a slope of -kA.

Second-Order Reactions

• A second-order reaction rate is dependent on the product of the concentrations of two reactants (A and B).
• The rate equation is r = kA (a0 - x)(b0 - x), where a0 and b0 are the initial concentrations of A and B.
• Integration of the rate equation yields ln[b0(a0 - x)/a0(b0 - x)] = kAt.
• A plot of 1/[A] versus time yields a straight line for a second-order reaction.

Zero-Order Reactions

• A zero-order reaction rate is independent of the concentration of reactants.
• The rate equation is r = kA, where kA is the zero-order rate constant.
• Integration of the rate equation yields x = kAt.
• A plot of the product concentration versus time yields a straight line with a slope equal to the apparent zero-order rate constant.

nth-Order Reactions

• Higher-order reactions are uncommon due to the low probability of simultaneous multiple body collisions.
• Many rate laws incorporate multiple elementary reactions, resulting in a composite rate law with order >2.