Atmospheric scientists often use mixing ratios to express the concentrations of trace compounds in air. Mixing ratios are often expressed as ppmv (parts per million volume): $${\text {ppmv of}} \ X=\frac{\text { vol of } X \text { at STP }}{\text { total vol of air at STP }} \times 10^{6}$$ On a certain November day, the concentration of carbon monoxide in the air in downtown Denver, Colorado, reached \(3.0 \times 10^{2}\) ppmv. The atmospheric pressure at that time was 628 torr and the temperature was $0^{\circ} \mathrm{C}$ . a. What was the partial pressure of CO? b. What was the concentration of CO in molecules per cubic meter? c. What was the concentration of CO in molecules per cubic centimeter?

To find the partial pressure of CO, we first need to calculate the total moles of the gas at the given pressure and temperature using the Ideal Gas Law. The Ideal Gas Law is given as: \(PV = nRT\) where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. Here, T is given in Celsius. To change it to Kelvin, we just add 273 to the Celsius temperature: T = \( 0 + 273 = 273K \) We also need to convert the pressure from torr to atm: Pressure in atm = Pressure in torr / 760 Pressure in atm = \(628 / 760 \approx 0.8263 \) Now, rewrite the Ideal Gas Law equation for the number of moles and rearrange as follows: Moles (n) = \(P_{air}V / RT\) We are given mixing ratio in ppmv, which we can rewrite using the given formula, ppmv of CO = \( (n_{CO}) / (n_{total}) × 10^6 \) So we can rearrange this formula to find moles (n) of CO: Moles (n_{CO}) = \( ppmv_{CO} × n_{total} / 10^6 \) Now, to find the partial pressure of CO (P_{CO}), use the Ideal Gas Law again by rearranging the equation for pressure: Partial Pressure of CO (P_{CO}) = \( n_{CO}RT / V \) Plug in the values we found for the moles of CO and the total pressure: Partial Pressure of CO = \(3.0 × 10^2 \times 0.8263 \times (0.08206 \times 273) / 10^6\) Partial Pressure of CO = \(0.00616 \space atm\)

To convert concentration to molecules per cubic meter, we will first find the number of moles of CO in 1 m^3 using the Ideal Gas Law: Moles of CO in 1 m^3 (n_{CO}) = \( (P_{CO} × 10^3) / RT \) Now, to convert moles to molecules, we can use Avogadro's number (6.022 × 10^23 molecules per mole): Molecules of CO in 1 m^3 = \( n_{CO} × (6.022 × 10^23) \) Plug in the values we found: Molecules of CO in 1 m^3 = \(((0.00616 \times 10^3) / (0.08206 \times 273)) × (6.022 × 10^23)\) Molecules of CO in 1 m^3 = \(8.63 × 10^{19} \)

To convert concentration from molecules per cubic meter to molecules per cubic centimeter, we can use the conversion factor \( (1 m^3 = 10^6 cm^3) \) by dividing the molecules per cubic meter by the conversion factor: Molecules of CO per cm^3 = Molecules of CO per m^3 / 10^6 Plug in the value we found: Molecules of CO per cm^3 = \( 8.63 × 10^{19} / 10^{6} \) Molecules of CO per cm^3 = \( 8.63 × 10^{13} \) So the results are: a. The partial pressure of CO is \(0.00616 \space atm\). b. The concentration of CO in molecules per cubic meter is \(8.63 × 10^{19}\). c. The concentration of CO in molecules per cubic centimeter is \(8.63 × 10^{13}\).