GATE BT 2022 | Question: 50

Question

Liquid-phase mass transfer coefficient $(k_{L})$ is measured in a stirred tank vessel using steady-state method by sparging air. Oxygen uptake by the microorganism is measured. The bulk concentration of $\text{O}_{2}$ is $10^{-4} \text{mol L}^{-1}.$ Solubility of $\text{O}_{2}$ in water at $25^{\circ}\text{C}$ is $10^{-3} \text{mol L}^{-1}.$

If the oxygen consumption rate is $9\times 10^{-4} \text{mol L}^{-1} \; \text{s}^{-1},$ and interfacial area is $100\; \text{m}^{2}/\text{m}^{3},$ the value of $k_{L}$ is ___________ $\text{cm s}^{-1}.$