Chemistry for Engineering Students
Chemistry for Engineering Students
3rd Edition
ISBN: 9781285199023
Author: Lawrence S. Brown, Tom Holme
Publisher: Cengage Learning
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Chapter 5, Problem 5.43PAE

39 A sample containing only NO2 and SO2, has a total pressure of 120. torr. Measurements show that the partial pressure of NO2 is 43 torr. 1f the vessel has a volume of 800.0 mL and the temperature is 22.0°C, how many moles of each gas are present?

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Interpretation Introduction

Interpretation:

The moles number of each gas (NO2 and SO2) present in the sample has to be calculated

Concept Introduction:

  • An ideal gas has is a hypothetical gas that is formed by a few molecules so that, its density is low, and the intermolecular forces are null. The model of gas facilitates mathematical calculations to study gases.
  • The ideal gas law can be expressed in the following way,

    P x V= n x R x T

    Where P is the gas pressure (atm), V is the gas volume (L), T is the gas absolute temperature (K), n is the moles number of the gas and R is the ideal gas constant ( R=0.082 atm LK mol )

  • Absolute temperature (K) = T (°C )+ 273. where, T (°C) is the temperature in Celsius degrees (°C).

  • 1 atm = 760 torr
  • The ideal gas mixture is a mixture of two or more ideal gases that has the following characteristics,

    Each component of the mixture behaves as ideal gas that occupies all the mixture volume at the mixture temperature.

    Each component exercises a partial pressure. The sum of the partial pressure of the components is equal to the total pressure of the mixture.

  • The mole fraction is the ratio between the moles number of the component in the mixture and the total number of moles of gas in the mixture. It can be expressed in the following way,

    yi=nintotal

    Where, yi is the molar fraction of component i, ni is the moles number of component i and n total is the total moles number of the mixture.

  • The partial pressure is the pressure that a gas of the mixture exercises if it occupies all the volume of the mixture.
  • The partial pressure of each component in the mixture is directly proportional to its molar fraction. It can be expressed in the following way,

    Pi=yi x Ptotal

    Where, Pi is the partial pressure of component i, Ptotal is the total pressure of the mixture and yi is the molar fraction of component i.

Answer to Problem 5.43PAE

Solution:

n NO2= 1.865 x 10-3 moln SO2= 3.396 x 10-3 mol

Explanation of Solution

Given Information:

Ptotal=120 torrP NO2=43 torrVvessel=800.0 mLTsample=22.0 °C

1-Convert the T in K

Tsample=22.0 °C + 273 =295.0 °C

2-Convert the pressure in atm

Ptotal=120 torr x 1 atm760 torr=0.158 atmP NO2=43 torr x 1 atm760 torr=0.056 atm

3-Convert the volume in L

Vvessel=800.0 mL x 1 L1000 mL=0.800 L

4-Calculate the partial pressure of SO2

PSO2=Ptotal - PNO2 =0.158 atm - 0.056 atm = 0.102 atm

5-Calculate the total moles number of the sample

0.158 atm x 0.800 L= ntotal x 0.082 atm LK mol x 295.0 Kntotal=0.158 atm x 0.800 L0.082 atm  L K  mol x 295.0 K=5.261 x 10-3 mol

6-Calculate the moles number of each component

0.056 atm = n NO 2 5 .261 x 10 -3 mol x 0.158 atm0.056 atm 0.158 atmn NO 2 5 .261 x 10 -3 mol  n NO2=0.056 atm 0.158 atmx 5.261 x 10-3 mol= 1.865 x 10-3 mol0.102 atm = n SO 2 5 .261 x 10 -3 mol x 0.158 atm0.102 atm 0.158 atmn SO 2 5 .261 x 10 -3 mol  n SO2=0.102 atm 0.158 atmx 5.261 x 10-3 mol= 3.396 x 10-3 mol

Conclusion

The sample is formed by 1.865 x 10-3 mol of NO2 and  3.396 x 10-3 mol of SO2.

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Chapter 5 Solutions

Chemistry for Engineering Students

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