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 = vol of Xat STP total vol of air at STP × 10 6 On a certain November day, the concentration of carbon monoxide in the air in downtown Denver, Colorado, reached 3.0 × 10 2 ppmv. The atmospheric pressure at that time was 628 torr and the temperature was 0°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?

Interpretation: For the given data, partial pressure, number of molecules per cubic meter and number of molecules per cubic centimeter of carbon monoxide should be determined.

Concept introduction:

• Mixing ratio is used to express the concentration of trace compounds in air. Mixing ratios are often expressed as ppmv (parts per million volume);

  ppmv of X = volume of X at STPtotal volume of air at STP×106

• A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

  Equation for mole fraction of a molecule in a mixture of three molecules (A, B and C) is,

  molecule  fraction  of A, ( χA)   =  numbers  of moles of molecule A (nA)total number of moles (nA+nB+nC) 

• Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone.

  Partial pressure of a gas in terms of its mole fraction ( χA ) and total pressure is,

PA  =  χA  ×  PTOTAL

• By combining the three gaseous laws namely Boyle’s law, Charles’s law and Avogadro’s law a combined gaseous equation is obtained. This combined gaseous equation is called Ideal gas law.

According to ideal gas law,

PV=nRT

Where,

P = pressure in atmospheres

V= volumes in liters

n = number of moles

R =universal gas constant ( 0.08206L×atm/K×mol )

T = temperature in kelvins

Total number of moles of gases in the mixture of gases can be determined by using ideal According to ideal gas equation,

Total number of moles    =    Total pressure  ×  Volume R  ×  Temperature    

•    Number of molecules  =Number of moles ×6.022×1023moleculesmol

Explanation

• To determine: The partial pressure of carbon monoxide

Partial pressure of carbon monoxide PCO= 0.19 torr

Partial pressure of a gas in a mixture of gases is the pressure of that gas when it alone. Partial pressure of a gas in terms of its mole fraction ( χCO ) and total pressure is,

` PCO  =  χCO  ×  PTOTAL (1)

A mole fraction of a molecule in a mixture is the ratio of number of moles of particular molecule to the sum of number of moles of all molecules in the mixture.

To calculate the partial pressure,molefraction and volume of carbon monoxide should be determinedmole  fraction  of CO, ( χCO)   =  numbers  of moles of  CO (nCO)total number of moles of mixture(ntotal)  Since,volume of a gas is directly proportional to the number of moles of gas, That is,                 Vµ n So,mole fraction in terms of volume can be written as: χCO = volume of carbonmonoxide (VCO)Total volume of gas (Vtotal)...(2)From the given data,Concentration of carbon monoxide inthe air is 3.0×102ppmvppmv of X = volume of X at STPtotal volume of air at STP×106If we have 1.0×106L of air (Vtotal)3.0×102ppmv = VCO 1.0×106L×106 VCO= 3.0×102ppmv ×1.0×106L106= 3.0×102LBy adding this values to the equation(2)χCO= 3.0×102L1.0×106L =3.0×10-4By adding the value of mole fraction to the equation (1)PCO  =  χCO  ×  PTOTALχCO = 3.0×10-4From the given dataPTOTAL= 628 torrPCO= 3.0×10-4×628 torr= 0.19torr

• To determine: Number of molecules per cubic meter of carbon monoxides.

Number of molecules per cubic meter of carbon monoxides =  6.6×1021moleculesm3

Total number of moles of gases in the mixture of gases can be determined by using ideal gas equation.

According to ideal gas equation,

Total number of moles(n)    =    Total pressure(P)  ×  Volume(V) R  ×  Temperature(T)    

Number of molecules per cubic meter of carbon monoxides, nCO =    PCO×VR×T

Here,Assuming 1.0m3air, 1 m3= 1000 LV= 1.0×103LPCO =0.19 torr = 0.00025 atm           Since, 1 torr = 760 atm                                                                               0