To determine which equation is an expression of the rate law, let’s review what a rate law is. In chemistry, the rate law expresses the rate of a reaction as a function of the concentration of its reactants and a rate constant.
The given options are:
A. PV = nRT: This is the ideal gas law, which relates the pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T) of an ideal gas. It does not describe the rate of a reaction.
B. [tex]\[ k = Ae^{\frac{-E_a}{RT}} \][/tex]: This is the Arrhenius equation, which relates the rate constant (k) of a reaction to the temperature (T), the activation energy (Ea), and the frequency factor (A). While this equation is related to the rate constant of a reaction, it does not directly describe the rate of the reaction.
C. Rate = k[A][B]: This is the correct rate law expression. It states that the rate of the reaction depends on the concentration of reactants A and B and is proportional to the product of these concentrations multiplied by the rate constant (k).
D. [tex]\[ K_{eq} = \frac{[C][D]}{[A][B]} \][/tex]: This is the equilibrium constant expression, which relates the concentrations of the reactants and products at equilibrium. It does not describe the rate of a reaction.
Therefore, the correct equation that is an expression of the rate law is:
C. Rate = k[A][B]
