General Chemistry
General Chemistry
7th Edition
ISBN: 9780073402758
Author: Chang, Raymond/ Goldsby
Publisher: McGraw-Hill College
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Chapter 3, Problem 3.111QP
Interpretation Introduction

Interpretation:

The fraction of CH4 in the mixture of the given reaction has to be determined when 13.43g of mixture produces CO2 and H2O in a total mass of 64.84g.

Concept introduction:

  • Balanced chemical equation of a reaction is written according to law of conservation of mass.
  • Equation for Number of moles of a substance, from its given mass is,

Number of moles=GivenmassMolecularmass

  • Mole ratio between the reactant and a product of a reaction are depends upon the coefficients of reactant and product in a balanced chemical equation.

Expert Solution & Answer
Check Mark

Answer to Problem 3.111QP

The fraction of CH4 in the mixture is 0.387.

Explanation of Solution

In given reaction,

Mixture of CH4 and C2H6 are burned in O2.

Therefore,

The chemical equation for this reaction is,

CH4+O2CO2+H2O

C2H6+O2CO2+H2O

Balanced chemical equation of a reaction is written according to law of conservation of mass.

Therefore,

The total number of each atoms in the reactant side should equal to the total number of each atoms in the product side.

So, in order to balance a chemical equation, the coefficients of compounds or atoms are needed to be changed in such a way that total number of each atoms in the reactant side and the total number of each atoms in the product side is to become equal.

Hence,

The balanced equations for the given reactions are,

CH4+2O2CO2+2H2O

2C2H6+7O24CO2+6H2O

Assumes mass of CH4is ‘x’ and mass of C2H6is ‘13.43-x’.

The mass of Mixture of CH4 and C2H6 is given as 13.43g.

Let’s take mass of CH4 is x.

So, the number of moles of CH4 in the reaction is,

x gCH4×1molCH416.04gCH4=x16.04mol.

The balanced chemical equation of the reaction is,

CH4+2O2CO2+2H2O

The mole ratio between CH4 and CO2 in the reaction is 1:1.

The mole ratio between CH4 and H2O in the reaction is 1:2.

So, the number of moles of CO2 produced in the reaction is x16.04mol and the number of moles of H2O produced in the reaction is 2x16.04mol=x8.02mol.

Then,

The mass of CO2 is,

x16.04molCO2×44.01gCO2=2.744xgCO2.

The mass of H2O is,

x8.02molH2O×18.02gH2O=2.247xgH2O.

The mass of Mixture of CH4 and C2H6 is given as 13.43g.

Let’s take mass of C2H6 is 13.43-x.

So, the number of moles of C2H6 in the reaction is,

(13.43-x) gC2H6×1molC2H630.07gC2H6=13.43-x30.07molC2H6

The balanced chemical equation of the reaction is,

2C2H6+7O24CO2+6H2O

The mole ratio between C2H6 and CO2 in the reaction is 1:2.

The mole ratio between C2H6 and H2O in the reaction is 1:3.

So, the number of moles of CO2 produced in the reaction is 2(13.43-x)30.07mol=13.43-x15.035mol and the number of moles of H2O produced in the reaction is 3(13.43-x)30.07mol=13.43-x10.02mol.

Then,

The mass of CO2 is,

13.43-x15.035molCO2×44.01gCO2=2.927(13.43-x)gCO2.

The mass of H2O is,

13.43-x10.02molH2O×18.02gH2O=1.798(13.43-x)gH2O.

The mass of CO2 is produced by CH4 is found as 2.744xg.

The mass of H2O is produced by CH4 is found as 2.247xg.

The mass of CO2 is produced by C2H6 is found as 2.927(13.43-x)g.

The mass of H2O is produced by C2H6 is found as 1.798(13.43-x)g.

The total mass of CO2andH2O produced by the mixture is given that 64.84g.

Therefore,

2.744xg+2.247xg+2.927(13.43-x)g+1.798(13.43-x)g=64.84g 0.266xg+63.4568g=64.84g 0.266xg=1.383g x=5.2

So, the mass of CH4 is 5.2g.

Hence,

The fraction of CH4 in the mixture is,

5.2g13.43g=0.387.

Conclusion

The fraction of CH4 in the mixture of the given reaction was determined as 0.387

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Chapter 3 Solutions

General Chemistry

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