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Estimation of K_{l}a

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Simple mass balance considerations for the concentration of dissolved oxygen
give:

When the air is turned off, there is no supply term, and the equation
becomes:

Data taken immediately after aeration ceases should be ignored because
air bubbles entrained in the medium may provide some oxygen. Quickly, the
concentration of oxygen assumes a linear decline with a slope equal to
- RX. If there has been an independent measurement of cell mass, the specific
uptake coefficient can be calculated. Usually the goal is estimating K_{l}a,
so the value of R times X is sufficient. We do not have to know R or X
alone.

When aeration resumes, the supply term again becomes important. However,
all terms in the equation except K_{l}a are now known or easily
found. The saturation value of dissolved oxygen can be estimated from published
data or can be measured experimentally with broth free of organisms. The
value of dC/dt is equal to the slope of the curve of C versus t. Substitute
the numbers into the equation and solve.

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