The following is a crude but effective method for estimating the order of magnitude of Avogadro's number using stearic acid (C18H36O2). When stearic acid is added to water, its molecules collect at the surface and form a monolayer; that is, the layer is only one molecule thick. The cross-sectional area of each stearic acid molecule has been measured to be 0.21 nm 2. In one experiment it is found that 1.4 × 10-4 g of stearic acid is needed to form a monolayer over water in a dish of diameter 20 cm. Based on these measurements, what is Avogadro's number? (The area of a circle of radius r is π2.)