Chemistry: The Molecular Nature of Matter and Change
Chemistry: The Molecular Nature of Matter and Change
8th Edition
ISBN: 9781259631757
Author: Martin Silberberg Dr., Patricia Amateis Professor
Publisher: McGraw-Hill Education
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Chapter 5, Problem 5.96P

(a)

Interpretation Introduction

Interpretation:

The partial pressure of each gas in the atmosphere is to be calculated

Concept introduction:

The ideal gas equation can be expressed as follows,

PV=nRT

Here, P is the pressure, V is the volume, T is the temperature, n is the mole of the gas and R is the gas constant.

The expression to calculate the partial pressure of the gas is as follows:

Pgas=XgasPtotal

Here, Pgas is the partial pressure of the gas, Xgas mole fraction of the gas and Ptotal is the total pressure.

The expression to calculate the mole fraction of the gas is as follows,

Xgas=Moles of gasTotal moles

Here, Xgas is the mole fraction of the gas.

(a)

Expert Solution
Check Mark

Answer to Problem 5.96P

The partial pressure of N2 is 597 torr, the partial pressure of O2 is 159 torr, The partial pressure of CO2 is 0.3 torr and the partial pressure of water is 3.5 torr.

Explanation of Solution

The expression to calculatethe mole fraction of nitrogen is as follows:

Pnitrogen=XnitrogenPtotal (1)

Substitute the value 0.786 for Xnitrogen and 1 atm for PTotal in the equation (1)

Pnitrogen=(0.786)(1 atm(760 torr1 atm))=597.36 torr= 597 torr

The expression to calculatethe mole fraction of oxygen is as follows:

Poxygen=XoxygenPtotal (2)

Substitute the value 0.209 for Xoxygen and 1 atm for PTotal in the equation (2)

Poxygen=(0.209)(1 atm(760 torr1 atm))=158.84 torr= 597 torr

The expression to calculatethe mole fraction of carbon dioxide is as follows:

Pcarbon dioxide=Xcarbon dioxidePtotal (3)

Substitute the value 0.0004 for Xcarbon dioxide and 1 atm for PTotal in the equation (3)

Pcarbon dioxide=(0.0004)(1 atm(760 torr1 atm))=0.304 torr= 0.3 torr

The expression tocalculatethe mole fraction of water is as follows:

Pwater=XwaterPtotal (4)

Substitute the value 0.0046 for Xwater and 1 atm for PTotal in the equation (4)

Pwater=(0.0046)(1 atm(760 torr1 atm))=3.496 torr= 3.5 torr

Conclusion

The partial pressure of N2 is 597 torr, the partial pressure of O2 is 159 torr, The partial pressure of CO2 is 0.3 torr and the partial pressure of water is 3.5 torr.

(b)

Interpretation Introduction

Interpretation:

The mole percent of each gas in the alveoli is to be calculated.

Concept introduction:

The ideal gas equation can be expressed as follows,

PV=nRT

Here, P is the pressure, V is the volume, T is the temperature, n is the mole of the gas and R is the gas constant.

The expression to calculate the partial pressure of the gas is as follows:

Pgas=XgasPtotal

Here, Pgas is the partial pressure of the gas, Xgas mole fraction of the gas and Ptotal is the total pressure.

The expression to calculate the mole fraction of the gas is as follows,

Xgas=Moles of gasTotal moles

Here, Xgas is the mole fraction of the gas.

(b)

Expert Solution
Check Mark

Answer to Problem 5.96P

The mole percent of N2 is 74.9 %, the mole percent of O2 is 13.7 %, the mole percent of CO2 is 5.3 % and the mole percent of water is 6.2 %.

Explanation of Solution

The expression to calculate the mole fraction percent of nitrogen is as follows:

Pnitrogen=XnitrogenPtotal (5)

Rearrange the equation (5) to calculate the percent of Xnitrogen as follows:

Xnitrogen=(PnitrogenPtotal)(100 %) (6)

Substitute the value 569 torr for Pnitrogen and 760 torr for PTotal in the equation (6)

Xnitrogen=(569 torr760 torr)(100 %)=74.8684%=74.9 %

The expression to calculate the mole fraction percent of oxygen as follows:

Poxygen=XoxygenPtotal (7)

Rearrange the equation (7) to calculate the percent of Xoxygen as follows:

Xoxygen=(PoxygenPtotal)(100 %) (8)

Substitute the value 104 torr for Poxygen and 760 torr for PTotal in the equation (8)

Xoxygen=(104 torr760 torr)(100 %)=13.6842%=13.7 %

The expression to calculate the mole fraction percent of carbon dioxide as follows:

Pcarbon dioxide=Xcarbon dioxidePtotal (9)

Rearrange the equation (5) to calculate the percent of Xcarbon dioxide as follows:

Xcarbon dioxide=(Pcarbon dioxidePtotal)(100 %) (10)

Substitute the value 40 torr for Pcarbon dioxide and 760 torr for PTotal in the equation (10)

Xcarbon dioxide=(40 torr760 torr)(100 %)=5.263%=5.3 %

The expression to calculate the mole fraction percent of water as follows:

Pwater=XwaterPtotal (11)

Rearrange the equation (11) to calculate Xwater as follows:

Xwater=(PwaterPtotal) (12)

Substitute the value 47 torr for Pwater and 760 torr for PTotal in the equation (12)

Xwater=(47 torr760 torr)(100 %)=6.184%=6.2 %

Conclusion

The mole percent of N2 is 74.9 %, the mole percent of O2 is 13.7 %, the mole percent of CO2 is 5.3 % and the mole percent of water is 6.2 %.

(c)

Interpretation Introduction

Interpretation:

The number of O2 molecules in 0.50 L of alveoli air at 37 °C is to be calculated.

Concept introduction:

The relationship between pressure and volume can be expressed as follows,

PV=constant

Here, P is the pressure and V is the volume.

According to Charles's law, the volume occupied by the gas is directly proportional to the temperature at the constant pressure.

The relationship between pressure and temperature can be expressed as follows,

V α T

Here, T is the temperature and V is the volume.

According to Avogadro’s law, the volume occupied by the gas is directly proportional to the mole of the gas at the constant pressure and temperature.

The relationship between volume and mole can be expressed as follows,

α n

Here, n is the mole of the gas and V is the volume.

The ideal gas equation can be expressed as follows,

PV=nRT

Here, P is the pressure, V is the volume, T is the temperature, n is the mole of the gas and R is the gas constant.

(c)

Expert Solution
Check Mark

Answer to Problem 5.96P

The number of O2 molecules in 0.50 L of alveoli air at 37 °C is 1.6×1021 molecules.

Explanation of Solution

The formula to convert °C to Kelvin is:

TK=T°C+273.15 (12)

Substitute 37 °C for T°C in equation (12).

TK=37+273.15=310.15 K

The pressure in torr is converted into atm is as follows,

P=104 torr=(104 torr)(1 atm760 torr )=0.136842105 atm

The expression to calculate the moles of the O2 is as follows,

PV=nRT (13)

Here, P is the pressure, V is the volume, T is the temperature, n is the mole of the NO and R is the gas constant.

Rearrange the equation (13) to calculate n as follows,

n=PVRT                                                                                                                     (14)

Substitute the value 0.136842105 atm for P, 310.15 K for T, 0.50 L for V and 0.0821 LatmmolK for R in the equation (14).

n=(0.50 L)(0.136842105 atm)(0.0821 LatmmolK)(310.15 K)=0.0026870 mol

The expression to calculate the molecules of O2 is as follows:

Moles of O2=Molecules of O2Avogadro's number (15)

Rearrange the equation (15) to calculate the molecules of O2.

(Molecules of O2)=(Moles of O2)(Avogadro's number) (16)

Substitute the value 0.0026870 mol for moles of O2 and 6.022×1023 molecules for the Avogadro's number in the equation (16).

(Molecules of O2)=(0.0026870 mol)(6.022×1023)=1.681×1021 molecules

Conclusion

The number of O2 molecules in 0.50 L of alveoli air at 37 °C is 1.6×1021 molecules.

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Chapter 5 Solutions

Chemistry: The Molecular Nature of Matter and Change

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