In a process called quorum sensing, bacteria monitor their population density via extracellular signaling molecules and modulate gene expression accordingly. In this paper, a one-dimensional model of a growing Pseudomonas aeruginosa biofilm is examined. Quorum sensing has been included in the model through equations describing the production, degradation, and diffusion of the signaling molecules, acyl-homoserine lactones, in the biofilm. From this model, we are able to make some important observations about quorum sensing. First, in order for quorum sensing to initiate near the substratum, in accordance with experimental observations, the model suggests that cells in oxygen-deficient regions of the biofilm must still be synthesizing the signal compound. Second, the induction of quorum sensing is related to a critical biofilm depth; once the biofilm grows to the critical depth, quorum sensing is induced. Third, the critical biofilm depth varies with the pH of the surrounding fluid. Of particular interest is the prediction of a critical pH threshold, above which quorum sensing is not possible at any depth. These results highlight the importance of careful study of the relationship among metabolic activity of the bacterium, signal synthesis, and the chemistry of the surrounding environment.