Chapter 13, Problem 5PS

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

What mass of Na2CO3 must you add to 125 g of water to prepare 0.200 m Na2CO3? What is the mole fraction of Na2CO3 in the resulting solution?

Interpretation Introduction

Interpretation: The mass and mole fraction of Na2CO3 has to be identified.

Concept introduction:

Mole fraction: Amount of that component divided by the total amount of all of the components of the mixture ( nA +  nB +  n...).

Mole fraction of A (χA)= nA nA +  nB +  n...

Explanation
• The Mole fraction:

Given data:

Massâ€‰ofâ€‰Na2CO3â€‰=â€‰?Massâ€‰ofâ€‰waterâ€‰=â€‰125â€‰gÂ â€‰=â€‰â€‰0.125Â kgMolalityâ€‰ofâ€‰Na2CO3â€‰=â€‰0.200â€‰m

Molality of a solute is defined as the amount of solute dissolves in kilogram of solvent.

Â Â MolalityÂ ofÂ soluteÂ =Â â€‰AmountÂ ofÂ soluteÂ (mol)MassÂ ofÂ solventÂ (Kg)

Molalityâ€‰=Molesâ€‰ofâ€‰Na2CO3Amountâ€‰ofâ€‰waterâ€‰(inâ€‰Kg)0.200â€‰mâ€‰=â€‰â€‰Molesâ€‰ofâ€‰Na2CO3â€‰0.125Â kgMolesâ€‰ofâ€‰Na2CO3â€‰=(0.200â€‰m)â€‰â€‰(0.125Â kg)=â€‰0.025â€‰mol

From the number of moles, mass of sodium carbonate can be determined:

Massâ€‰ofâ€‰Na2CO3â€‰â€‰=â€‰(molesâ€‰ofâ€‰Na2CO3)â€‰â€‰(molarâ€‰massâ€‰ofâ€‰Na2CO3)â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰(0

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