A SodaStream "sparkling water" home carbonation system pressurizes a 1L water bottle to a pressure of 4 bar (400 kPa) in order to dissolve CO2 gas into the liquid to produce carbonated water also known as "Fizzy-Water". Small bubbles are injected to promote mass transfer such that we can assume the liquid-gas system is at equilibrium with water at a typical refrigerator temperature of 2 °C = 275 K. Assuming that both CO2 and water are ideal gases and CO2 is minimally soluble in water such that Henry's Law is an appropriate model for behavior, what mass of CO2 is dissolved in a 1L water bottle and what would be the equivalent volume, in liters, of that mass if released at room temperature of T = 298 K and pressure of 4 bar (during pressurization) and at 1 bar (when drinking the water)? Assume solvent MH20 18.015 kg/kmol, Psat@2c = 2 kPa == solute Mco₂ = 44.01 kg/kmol, Rco₂ = 0.1889 kPa m³/kgK, Hco₂ = 510 bar, Hint: The mass fraction and mole fraction of a mixture are related to each other by (where the subscript m is for "mixture"). = Mi mi = Wi mm Ni Mi NmMm Yi Mm

A SodaStream "sparkling water" home carbonation system pressurizes a 1L water bottle to a pressure of 4 bar (400 kPa) in order to dissolve CO2 gas into the liquid to produce carbonated water also known as "Fizzy-Water". Small bubbles are injected to promote mass transfer such that we can assume the liquid-gas system is at equilibrium with water at a typical refrigerator temperature of 2 °C = 275 K. Assuming that both CO2 and water are ideal gases and CO2 is minimally soluble in water such that Henry's Law is an appropriate model for behavior, what mass of CO2 is dissolved in a 1L water bottle and what would be the equivalent volume, in liters, of that mass if released at room temperature of T = 298 K and pressure of 4 bar (during pressurization) and at 1 bar (when drinking the water)? Assume solvent MH20 18.015 kg/kmol, Psat@2c = 2 kPa == solute Mco₂ = 44.01 kg/kmol, Rco₂ = 0.1889 kPa m³/kgK, Hco₂ = 510 bar, Hint: The mass fraction and mole fraction of a mixture are related to each other by (where the subscript m is for "mixture"). = Mi mi = Wi mm Ni Mi NmMm Yi Mm

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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