As discussed in lecture, atmospheric pressure decreases exponentially with altitude, and the vertical pressure profile can be described approximately using the formula P(z) = P0 exp(-z/H), with H = RT/gM = 7.9 km and P0 = 101 kPa. (a) Given ozone concentrations of 40 ppb and 2 ppm in the troposphere (0--15 km) and stratosphere (15--50 km), respectively, calculate the stratospheric fraction of the total ozone molecules present in a vertical column that extends from sea level to outer space. Neglect ozone above 50 km altitude due to the low value of P at high altitudes, and assume ozone mole fractions given above are constant within each atmospheric layer. (b) Satellite measurements of ozone give the "total ozone column amount" or the vertical integral of ozone concentrations in units of molecules per cm3 of air. The results are reported in Dobson Units (DU): 1 DU = 2.7 × 1016 molecules cm-2. Calculate the ozone column amount in DU, corresponding to the pressure profile and ozone concentrations given above. Recall Avogadro's number, NA = 6.0 × 1023 molecules per mole, from which one can calculate [O3]= yPNA / RT, with T=270 K