   Chapter 13.5, Problem 2.4ACP

Chapter
Section
Textbook Problem

After opening a 1.0 L soda, what mass of the dissolved CO2 is released to the atmosphere in order to reach equilibrium? Assume that the CO2 dissolved in the soda in the sealed bottle was in equilibrium with the CO2 in the headspace at 4.0 bar pressure.

Interpretation Introduction

Interpretation: It should be determined that what mass of dissolved CO2 which is released to the atmosphere in order to reach equilibrium.

Concept introduction:

• Henry’s law: The solubility of a gas in liquid is directly proportional to the gas pressure.

Sg= kHPg,where,Sgisthegassolubility(inmol/kg)kHis Henry's constant Pg is the partial pressure of the gaseous solute.

• Density=MassVolume
Explanation

Given,partialpressureofCO2=4barHenry'sconstant=0.034mol/kg.barAccordingtoHenry'slaw, Sg=kHPgsolubilityofCO2beforeopening=0.034mol/kg.bar×4bar =0.136mol/kg

Assume that, the density of the solution is 1.0g/cm3. Therefore 1.0L corresponds to 1kg. The amount of CO2 dissolved is 0.136mol.

Solubility of CO2after opening can be calculated as follows:

partialpressureofCO2=3.7×10-4barHenry'sconstant=0.034mol/kg.bar

According to Henry’s law:

Sg =kHPg

Substituting the given values in the above equation, the solubility can be calculated.

Sg=0

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