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# 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?

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### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

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### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 8, Problem 121E
Textbook Problem
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## 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 × 102 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 Introduction

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);

ppmvofX=volumeofXatSTPtotalvolumeofairatSTP×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,

moleculefractionofA,(χA=numbersof moles ofmolecule 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 numberofmoles=Total pressure×VolumeR×Temperature

•   Numberofmolecules=Numberofmoles×6.022×1023moleculesmol

### Explanation of Solution

Explanation

• To determine: The partial pressure of carbon monoxide

Partial pressure of carbon monoxide PCO=0.19torr

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.

Tocalculatethepartialpressure,molefractionandvolumeofcarbonmonoxideshouldbedeterminedmolefractionofCO,(χCO=numbersof moles of CO(nCO)total number of molesofmixture(ntotal) Since,volumeofagasisdirectlyproportionaltothenumberofmolesofgas,Thatis,nSo,molefractionintermsofvolumecanbewrittenas:χCO=volumeofcarbonmonoxide(VCO)Totalvolumeofgas(Vtotal)...(2)Fromthegivendata,Concentrationofcarbonmonoxideintheairis3.0×102ppmvppmvofX=volumeofXatSTPtotalvolumeofairatSTP×106Ifwehave1.0×106Lofair(Vtotal)3.0×102ppmv=VCO1.0×106L×106VCO=3.0×102ppmv×1.0×106L106=3.0×102LByaddingthisvaluestotheequation(2)χCO=3.0×102L1.0×106L=3.0×10-4Byaddingthevalueofmolefractiontotheequation(1)PCO=χCO×PTOTALχCO=3.0×10-4FromthegivendataPTOTAL=628torrPCO=3.0×10-4×628torr=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 numberofmoles(n)=Total pressure(P)×Volume(V)R×Temperature(T)

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

Here,Assuming1.0m3air,1m3=1000LV=1.0×103LPCO=0.19torr=0.00025atm Since,1torr=760atm0

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