A spatially smoothed jump condition is developed for the process of diffusion and reaction at a catalytic surface where a first-order, irreversible reaction takes place at isolated regions on the fluid-solid interface. The point jump condition for this process is given by -n(gamma kappa).D gamma delc(A gamma) = kc(A gamma) at the gamma-kappa interface, in which the rate coefficient k undergoes abrupt changes with position on the fluid-solid interface. The averaging procedure leads to a spatially smoothed jump condition that takes the form -n(gamma kappa).D(gamma)del [c(A gamma)](gamma) = k(eff)[c(A gamma)](gamma) at the gamma-kappa interface, in which the effective reaction rate coefficient is determined by the solution of a closure problem. It is this effective reaction rate coefficient, times the interfacial area per unit volume, that is measured in a typical experimental study of diffusion and reaction in a porous catalyst. The solution of the closure problem allows one to relate the intrinsic properties of the catalytic surface to k(eff), and the results are presented in terms of a surface effectiveness factor as a function of a Thiele modulus.