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): 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 \(\mathrm{CO}\) ? b. What was the concentration of \(\mathrm{CO}\) in molecules per cubic meter? c. What was the concentration of \(\mathrm{CO}\) in molecules per cubic centimeter?

Step by step solution

01

Calculate the total pressure in atm

First, we need to convert the total atmospheric pressure given in torr to atmospheres (atm). To do this, we use the conversion factor 1 atm = 760 torr: Total Pressure (atm) = \(\frac{628\,\text{torr}}{760\,\text{torr/atm}} = 0.826\,\text{atm}\)

02

Calculate the partial pressure of CO

We now use the mixing ratio to find the partial pressure of CO: Partial Pressure of CO = Total Pressure × Mixing Ratio(ppmv) × \(\frac{1}{10^6}\) Partial Pressure of CO = \(0.826\,\text{atm} × 3.0 × 10^{2}\, \text{ppmv} × \frac{1}{10^6} = 2.478 × 10^{-4}\, \text{atm}\) b. Find the concentration of CO in molecules per cubic meter

03

Use the Ideal Gas Equation

Now, we will use the Ideal Gas Equation and Avogadro's number to find the concentration of CO in the air: \(PV = nRT\) \(n = \frac{PV}{RT}\) Here, P is the partial pressure of CO, V is the volume, n is the number of moles, R is the universal gas constant and T is the temperature in Kelvin. The temperature in Kelvin is 273 K (0°C + 273).

04

Convert pressure to Pascal

First, we need to convert the partial pressure of CO from atm to Pascal (Pa) by using the conversion factor 1 atm = 101325 Pa: Partial Pressure of CO (Pa) = \(2.478 × 10^{-4}\, \text{atm} × 101325\, \text{Pa/atm} = 25.10\, \text{Pa}\)

05

Calculate the number of moles of CO per cubic meter

Now, we can calculate the number of moles of CO per cubic meter using the Ideal Gas Equation. We assume a volume of 1 cubic meter (m³) for convenience: \(n = \frac{PV}{RT} = \frac{(25.10\, \text{Pa})(1\, \text{m}^3)}{(8.314\, \text{J/mol·K})(273\, \text{K})} = 0.0111\, \text{mol/m}^3\)

06

Calculate the concentration of CO in molecules per cubic meter

Now, we will multiply the moles of CO per cubic meter by Avogadro's number (6.022 x 10²³ molecules/mol) to find the concentration of CO in molecules per cubic meter: Concentration of CO (molecules/m³) = \(0.0111\, \text{mol/m}^3 × 6.022 × 10^{23}\, \text{molecules/mol} = 6.68 × 10^{21}\, \text{molecules/m}^3\) c. Find the concentration of CO in molecules per cubic centimeter

07

Convert the concentration to molecules per cubic centimeter

Finally, we convert the concentration of CO from molecules per cubic meter to molecules per cubic centimeter by using the conversion factor 1 m³ = 10⁶ cm³: Concentration of CO (molecules/cm³) = \(6.68 × 10^{21}\, \text{molecules/m}^3 × \frac{1\, \text{cm}^3}{10^6\, \text{m}^3} = 6.68 × 10^{15}\, \text{molecules/cm}^3\) So, the answers are: a. The partial pressure of CO is \(2.478 × 10^{-4}\, \text{atm}\) b. The concentration of CO is \(6.68 × 10^{21}\, \text{molecules/m}^3\) c. The concentration of CO is \(6.68 × 10^{15}\, \text{molecules/cm}^3\)

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!