Concept explainers
(i)
Interpretation: Under the given conditions, the solubility of CO2 gas in water has to be calculated.
Concept introduction: Henry’s law states that the partial vapor pressure of a solute B is directly proportional to the mole fraction of solute B. Hence, for dilute solution the compositions can be determined by Henry’s law, which is expressed as,
pB=KB×χB
(i)
Answer to Problem 5A.10AE
The solubility of CO2 in water at pCO2=0.10 atm is 3.37×10-3 kg-1 mol_.
Explanation of Solution
Carbon dioxide is dissolving in water, which is in small amount. Therefore, CO2 acts as a solute in water. Since the amount of CO2 in water is small, it means solution is very dilute. The Henry’s law for CO2 is expressed as,
pCO2=KCO2×χCO2 (1)
Where,
- pCO2 is the partial vapor pressure of CO2.
- χCO2 is the mole fraction of CO2.
- KCO2 is the Henry’s law constant.
Since, χCO2 is the mole fraction of CO2, it represents the number of moles or amount of CO2 dissolved in water. Therefore solubility of CO2 in water can be expressed in terms of mole fraction of CO2.
Therefore, the equation (1) can be written as,
pCO2=KCO2×bCO2 (2)
Where,
- bCO2 is the solubility of CO2 gas in water.
Rearrange the equation (2) in terms of bCO2.
bCO2=pCO2KCO2 (3)
It is given that,
The value of Henry’s law constant, KCO2 is 3.01×103 kPa kg mol−1.
The Partial pressure, pCO2 is 0.1 atm.
The conversion of atm to kPa is done as,
1 atm=101.325 kPa
Therefore the conversion of 0.1 atm to kPa is done as,
0.1 atm=0.1×101.325 kPa=10.1325 kPa
Substitute KCO2=3.01×103 kPa kg mol−1 and pCO2=10.1325 kPa in equation (3)
bCO2=10.1325 kPa3.01×103 kPa kg mol−1=3.37×10-3 kg-1 mol_
Therefore, the solubility of CO2 in water at pCO2=0.1 atm is 3.37×10-3 kg-1 mol_.
(ii)
Interpretation: Under the given conditions, the solubility of CO2 gas in water has to be calculated.
Concept introduction: Henry’s law states that the partial vapor pressure of a solute B is directly proportional to the mole fraction of solute B. Hence, for dilute solution the compositions can be determined by Henry’s law, which is expressed as,
pB=KB×χB
(ii)
Answer to Problem 5A.10AE
The solubility of CO2 in water at pCO2=1 atm is 33.7×10-3 kg-1 mol_.
Explanation of Solution
Carbon dioxide is dissolving in water, which is in small amount. Therefore, CO2 acts as a solute in water. Since the amount of CO2 in water is small, it means solution is very dilute. The Henry’s law for CO2 is expressed as,
pCO2=KCO2×χCO2 (1)
Where,
- pCO2 is the partial vapor pressure of CO2.
- χCO2 is the mole fraction of CO2.
- KCO2 is the Henry’s law constant.
Since, χCO2 is the mole fraction of CO2, it represents the number of moles or amount of CO2 dissolved in water. Therefore solubility of CO2 in water can be expressed in terms of mole fraction of CO2.
Therefore, the equation (1) can be written as,
pCO2=KCO2×bCO2 (2)
Where,
- bCO2 is the solubility of CO2 gas in water.
Rearrange the equation (2) in terms of bCO2.
bCO2=pCO2KCO2 (3)
It is given that,
The value of Henry’s law constant, KCO2 is 3.01×103 kPa kg mol−1.
The Partial pressure, pCO2 is 1 atm.
The conversion of atm to kPa is done as,
1 atm=101.325 kPa
Substitute the value of KCO2=3.01×103 kPa kg mol−1 and pCO2=101.325 kPa in equation (3)
bCO2=101.325 kPa3.01×103 kPa kg mol−1=33.7×10-3 kg-1 mol_
Therefore, the solubility of CO2 in water at pCO2=1 atm is 33.7×10-3 kg-1 mol_.
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Chapter 5 Solutions
PHYSICAL CHEMISTRY-WEBASSIGN
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