The Environmental Protection Agency (EPA) has established air quality standards. For ozone \(\left(\mathrm{O}_{3}\right),\) the 8 -hour average concentration permitted under the standards is 0.085 parts per million (ppm). (a) Calculate the partial pressure of ozone at 0.085 ppm if the atmospheric pressure is \(100 \mathrm{kPa}\). (b) How many ozone molecules are in $1.0 \mathrm{~L}\( of air? Assume \)T=25^{\circ} \mathrm{C}$.

To calculate the partial pressure of ozone at 0.085 ppm, we need to find the concentration of ozone in parts per million and convert it to partial pressure by the assumption that ozone in air behaves as an ideal gas. 1. Convert the concentration of ozone in parts per million to a fraction: \[0.085 \, \text{ppm} = \frac{0.085}{10^6}\] 2. Multiply the atmospheric pressure by the fraction of ozone concentration to find the partial pressure of ozone: \[P_\text{O3} = (100 \, \text{kPa}) \times \frac{0.085}{10^6}\]

Calculate the partial pressure of ozone (O3): \[P_\text{O3} =(100 \, \text{kPa}) \times \frac{0.085}{10^6} = 8.5 \times 10^{-6} \, \text{kPa}\]

To find the number of ozone molecules in 1.0 L of air, we will first find the number of moles of O3 using the ideal gas law, then convert moles of O3 to molecules using Avogadro's number. 1. Convert the partial pressure of ozone to pascals: \[P_\text{O3} = (8.5 \times 10^{-6} \, \text{kPa})\times (10^3 \, \text{Pa/kPa}) = 8.5 \times 10^{-3} \, \text{Pa}\] 2. Convert the volume of air to cubic meters: \[V = 1.0\, \text{L} \times \left( \frac{1 \, \text{m}^3}{10^3\, \text{L}}\right) = 1.0 \times 10^{-3} \, \text{m}^3\] 3. Convert the temperature to Kelvin: \[T = 25 \, \text{°C} + 273.15 = 298.15 \, \text{K}\] 4. Use the ideal gas law to find the number of moles of ozone: \[PV=nRT \Rightarrow n=\frac{PV}{RT}\] 5. Substitute the known values to find the number of moles of ozone: \[n=\frac{(8.5\times10^{-3}\, \text{Pa})(1.0\times10^{-3}\, \text{m}^3)}{(8.314\, \text{J/mol K})(298.15\, \text{K})}\] 6. Convert the number of moles of ozone to molecules using Avogadro's number: \[N_\text{ozone} = n\left(6.022\times10^{23}\, \text{molecules/mol}\right)\]

Calculate the number of ozone molecules in 1.0 L of air: \[N_\text{ozone} = \frac{(8.5\times10^{-3}\, \text{Pa})(1.0\times10^{-3}\, \text{m}^3)}{(8.314\, \text{J/mol K})(298.15\, \text{K})}(6.022\times10^{23}\, \text{molecules/mol}) \approx 2.05 \times 10^{15} \, \text{ozone molecules}\]