We investigate the correlation of HCN 1-0 with gas mass in the central 300 pc of the Galaxy. We find that on the ~10 pc size scale of individual cloud cores, HCN 1-0 is well correlated with dense gas mass when plotted as a log-log relationship. There is ~0.75 dex of scatter in this relationship from clouds like Sgr B2, which has an integrated HCN 1-0 intensity of a cloud less than half its mass, and others that have HCN 1-0 enhanced by a factor of 2-3 relative to clouds of comparable mass. We identify the two primary sources of scatter to be self-absorption and variations in HCN abundance. We also find that the extended HCN 1-0 emission is more intense per unit mass than in individual cloud cores. In fact the majority (80%) of HCN 1-0 emission comes from extended gas with column densities below 7 x 1022 cm-2, accounting for 68% of the total mass. We find variations in the brightness of HCN 1-0 would only yield a ~10% error in the dense gas mass inferred from this line in the Galactic center. However, the observed order of magnitude HCN abundance variations, and the systematic nature of these variations, warn of potential biases in the use of HCN as dense gas mass tracer in more extreme environments such as an active galactic nucleus and shock-dominated regions. We also investigate other 3 mm tracers, finding that HNCO is better correlated with mass than HCN, and might be a better tracer of cloud mass in this environment.
