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 5.124P
Interpretation Introduction

Interpretation:

The number of metric tons of each gas are emitted per year 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.

Expert Solution & Answer
Check Mark

Answer to Problem 5.124P

The number of metric tons of CO2 emitted per year is 4.83×102 t/year.

The number of metric tons of CO emitted per year is 9.61 t/year.

The number of metric tons of H2O emitted per year is 1.5×102 t/year.

The number of metric tons of SO2 emitted per year is 1.70×102 t/year.

The number of metric tons of S2 emitted per year is 4×101 t/year.

The number of metric tons of H2 emitted per year is 2.1×101 t/year.

The number of metric tons of HCl emitted per year is 6×101 t/year.

The number of metric tons of H2S emitted per year is 2×101 t/year.

Explanation of Solution

The expression to calculate the moles of gas/day is as follows,

PV=nRT        (1)

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

Rearrange the equation (1) to calculate n as follows,

n=PVRT        (2)

Substitute the value 1.0 atm for P, 298 K for T, 1.5×103 m3 for V and 0.0821 LatmmolK for R in the equation (2).

n=(1.0 atm)(1.5×103 m3)(1000 L1 m3)(0.0821 LatmmolK)(298 K)=6.13101×105 mol/day

The expression to calculate the moles of gas/year is as follows,

Moles of gas/year=[(Moles of gas/day)(Total number of days in year)]        (3)

Substitute the value 6.13101×105 mol/day the moles of gas/year and 365.25 day/year for total number of days in year in the equation (3).

Moles of gas/year=[(6.13101×105 mol/day)(365.25 day/year)]=2.23935×107mol/year

The expression to calculate the mass of CO2 is as follows:

Mass of CO2=[(Mole fraction of CO2)(Moles of gas/year)(Molar mass of CO2)]        (4)

Substitute the value 2.23935×107mol/year for moles of gas/year, 0.4896 for mole fraction of CO2 and 44.01 g/mol for molar mass of CO2 in the equation (4)

Mass of CO2=(0.4896)(2.23935×107mol/year)(44.01 g/mol)(1 kg1000 g)(1 t1000 kg)=482.519 t/year

The expression to calculate the mass of CO is as follows:

Mass of CO=[(Mole fraction of CO)(Moles of gas/year)(Molar mass of CO)]        (5)

Substitute the value 2.23935×107mol/year for moles of gas/year, 0.0146 for mole fraction of CO and 28.01 g/mol for molar mass of CO in the equation (5)

Mass of CO=(2.23935×107mol/year)(28.01 g/mol)(1 kg1000 g)(1 t1000 kg)=9.15773 t/year9.16 t/year

The expression to calculate the mass of H2O is as follows:

Mass of H2O=[(Moles of gas/year)(mole fraction of H2O)(Molar mass of H2O)]        (6)

Substitute the value 2.23935×107mol/year for moles of gas/year, 0.3710 for mole fraction of H2O and 18.02 g/mol for molar mass of H2O in the equation (6)

Mass of H2O=(0.3710)(2.23935×107mol/year)(18.01 g/mol)(1 kg1000 g)(1 t1000 kg)=149.70995 t/year1.5×102 t/year

The expression to calculate the mass of SO2 is as follows:

Mass of SO2=[(Moles of gas/year)(mole fraction of SO2)(Molar mass of H2O)]        (7)

Substitute the value 2.23935×107mol/year for moles of gas/year, 0.1185 for mole fraction of SO2 and 64.06 g/mol for molar mass of SO2 in the equation (7)

Mass of SO2=(0.1185)(2.23935×107mol/year)(64.06 g/mol)(1 kg1000 g)(1 t1000 kg)=169.992 t/year1.7×102 t/year

The expression to calculate the mass of S2 is as follows:

Mass of S2=[(Moles of gas/year)(mole fraction of S2)(Molar mass of S2)]        (8)

Substitute the value 2.23935×107mol/year for moles of gas/year, 0.0003 for mole fraction of S2 and 64.12 g/mol for molar mass of S2 in the equation (8)

Mass of S2=(0.0003)(2.23935×107mol/year)(64.12 g/mol)(1 kg1000 g)(1 t1000 kg)=0.4307614 t/year4.3×101 t/year

The expression to calculate the mass of H2 is as follows:

Mass of H2=[(Moles of gas/year)(mole fraction of H2)(Molar mass of H2)]        (9)

Substitute the value 2.23935×107mol/year for moles of gas/year, 0.0047 for mole fraction of H2 and 2.016 g/mol for molar mass of H2 in the equation (9)

Mass of H2=(0.0047)(2.23935×107mol/year)(2.016 g/mol)(1 kg1000 g)(1 t1000 kg)=0.21218 t/year2.1×101 t/year

The expression to calculate the mass of HCl is as follows:

Mass of HCl=[(Moles of gas/year)(mole fraction of HCl)(Molar mass of HCl)]        (10)

Substitute the value 2.23935×107mol/year for moles of gas/year, 0.0008 for mole fraction of HCl and 36.46 g/mol for molar mass of HCl in the equation (10)

Mass of HCl=(0.0008)(2.23935×107mol/year)(36.46 g/mol)(1 kg1000 g)(1 t1000 kg)=0.6531736 t/year6×101 t/year

The expression to calculate the mass of H2S is as follows:

Mass of H2S=[(Moles of gas/year)(mole fraction of H2S)(Molar mass of H2S)]        (11)

Substitute the value 2.23935×107mol/year for moles of gas/year, 0.0003 for mole fraction of H2S and 34.08 g/mol for molar mass of H2S in the equation (11)

Mass of H2S=(0.0003)(2.23935×107mol/year)(34.08 g/mol)(1 kg1000 g)(1 t1000 kg)=0.228951 t/year2×101 t/year

Conclusion

The number of metric tons of CO2 emitted per year is 4.83×102 t/year.

The number of metric tons of CO emitted per year is 9.61 t/year.

The number of metric tons of H2O emitted per year is 1.5×102 t/year.

The number of metric tons of SO2 emitted per year is 1.70×102 t/year.

The number of metric tons of S2 emitted per year is 4×101 t/year.

The number of metric tons of H2 emitted per year is 2.1×101 t/year.

The number of metric tons of HCl emitted per year is 6×101 t/year.

The number of metric tons of H2S emitted per year is 2×101 t/year.

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Chapter 5 Solutions

Chemistry: The Molecular Nature of Matter and Change

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