Lactase is an enzyme that breaks down the milk sugar “lactose” into glucose and galactose. This enzyme is produced in the small intestine of humans and other mammals, and has an optimum pH of 6.5. Lacking lactase, a person consuming dairy products may experience the symptoms of lactose intolerance.

Lactase can be purchased as a food supplement, or can be added to milk to produce "lactose-free" milk products. Industrial production of lactase can be achieved by fermentation of soybean with Aspergillus oryzae.

A fermented soybean medium containing 30 mg per litre of lactase and 105 cells per litre of Aspergillus oryzae needs to be sterilised at 121 °C before subsequent separation and purification processes. While the sterilisation is a crucial step to kill the Aspergillus oryzae cells, this unavoidable thermal treatment also denatures some of the enzyme molecules.

The values of the Arrhenius constant and Ed for the Aspergillus oryzae cells are:

A (cells) = 1×1036 min-1 Ed (cells) = 65 kcal mol-1

The values of the Arrhenius constant and Ed for the lactase are:

A (lactase) = 1×104 min-1 Ed (lactase) = 10 kcal mol-1

Calculate the amount of active lactase in the sterilised medium when using a 10,000 litre fermenter, if the sterility assurance level (SAL) should be 10-3. Ignore the effects of the heat-up and cool-down periods.