The on-line estimation of non-measurable substances and key process variables is relevant for the real-time monitoring of the bioprocesses. This paper deals with the on-line estimation of microbial growth rate and biomass concentration based on measures of the product concentration. The algorithm does not require a model of the growth rate and it can be applied to batch, fed-batch and continuous processes. The proposed observer, which is based on second-order sliding mode ideas, provides smooth estimates with reduced-order error dynamics. It is also shown that in case of error in the product formation parameters, convergence to an error bound can be achieved. Numerical simulations under different operating conditions are provided and the estimates obtained for lactic acid production are contrasted with documented experimental data.