Employing the scaling arguments, we show that the temperature dependence of the chemical diffusion coefficient near the points corresponding to continuous phase transitions has power-law or inverse logarithmic singularities, D-c proportional to \Delta T\(alpha/(1 - alpha)) for alpha > 0, proportional to \Delta T\(-alpha) for alpha < 0, or proportional to 1/\1n\Delta T parallel to for alpha = 0, where alpha is the specific heat exponent. Monte Carlo simulations, executed with the parameters corresponding to the O/W(110) system, indicate that these singularities, occurring in a very narrow temperature interval, can be reproduced only if the lattice size is large (L > 500). Outside the critical region, the temperature dependence of D-c is regular and the deviations from the ideal Arrhenius behavior are relatively weak. In particular, at appreciable coverages, the variations of the activation energy for chemical diffusion are about 10 kJ/mol (this value amounts to approximate to 10% of the activation energy).