Units of rate constants

Unitary rate constants obey the dimensional relationship (molL-1) (n 1) s-1, where n is the order of the reaction. As shown in the worked example in Section 1.3.1, a unitary rate constant is denoted by a lowercase k with a subscripted integer that identifies the particular reaction in a system of reactions (e.g., k-1). The direction of a reaction is usually written with an arrow facing from left to right on the page with a positive sign (or no sign) on the subscripted number of the rate constant indicating that is applies to the forward reaction. The negative subscript refers to the reverse reaction that is indicated by the arrow drawn from right to left.

Q: What is the mathematical expression that describes the rate at which A is converted into P, in the following first-order reaction?

On the left-hand side of the differential rate-equation, Eqn [1.8], the units (or dimensions) are those of reaction rate, namely, mol L-1 s-1, and those on the right must match these, according to the basic tenet of dimensional analysis. The [A] term has units of molL-1 so k must have units of s-1. Thus, simple dimensional analysis leads directly to the general expression (see above) for the units of a rate constant.

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