A bleaching apparatus comprises a measurement chamber has a first substance, the amount of the first substance in the measurement chamber being known. A dosing unit inputs a second substance to the measurement chamber for causing a chemical reaction between the first substance and the second substance, one of the first substance and the second substance being chlorine dioxide and another of the first substance and the second substance being filtered sample from pulp slurry of a pulp process. At least one sensor performs detection of a property known to depend on the chemical reaction between the first substance and the second substance as a function of time. A data processing unit determines chemical demand of chlorine dioxide for washing loss in a bleaching sub-process on the basis of at least one value in the detected property within a known period of time after the input of the second substance.