We have used three-wavelength UV-spectrophotometry to study the reaction of the alkaline fading of phenolphthalein in the critical solution of 2-butoxyethanol + water. It was found that when the temperature was far away from the critical point, the values of the natural logarithm of the rate constant k and the natural logarithm of the chemical equilibrium K determined in our experiments had good linear relationships with the reciprocal of temperature, which served as the backgrounds and were used for correcting k and K in the critical region. The critical slowing down of the reaction and the critical anomaly of the chemical equilibrium were detected near the critical point. The value of the critical exponent characterizing the slowing down effect of the reaction rate was obtained to be 0.156, which was close to the value 0.11 associated with the heat capacity divergence and agreed with the theoretical prediction. The experimental result also confirmed the theoretical prediction of 0.11 for the critical exponent characterizing the weak divergence of the singularity of the chemical equilibrium.