If the atmospheric pressure is 598 torr, and the concentration of ozone is 290 ppm, what is the partial pressure of ozone?

Like percentages ppm has several forms usually w/w, w/v, or v/v. In this case probably v/v makes most sense. If we assume 1 L of gas, and as Roger shows the mol fraction of O3 is 0.00076, then the volume of O3 in that 1 L is 0.00076 L since volume is proportional to mol. Then to calculate ppm (v/v) ppm = (0.00076/1) x 10^6 ppm = 760 ppm