(a)
Interpretation:
The mole fraction of benzene in vapour phase, y1and constant total pressure, P at temperature 100°C is to be calculated.
Concept introduction:
Raoult’s Law states that the partial pressure of liquid A above the solution is equal to the mole fraction of the liquid in a solution times the partial pressure of the pure liquid. This holds for ideal solutions. An ideal solution is approached by binary solutions of molecules that have similar properties (e.g. benzene and toluene). The law is mathematically expressed as-
Where
A solution behaves ideally when
- The solute and the solvent molecules have similar sizes and similar intermolecular forces,
- The excess volume of mixing is zero, and
- The heat of mixing is zero when both the solute and the solvent are liquids
(a)
Answer to Problem 13.1P
(a)
Explanation of Solution
The Raoult’s law expression for two components A and B to give the equilibrium partial pressure of the components in a binary mixture is written as follows-
and
The total pressure:
Where
The mole fraction of A in the vapor phase is given by -
Similarly, mole fraction of B in vapor phase is given by -
Now vapor pressures
Now, For benzene (1)
And For toluene (2)
Given
Now vapor pressure for benzene (1) can be calculated using Antoine equation as follows: -
Now vapor pressure for toluene (2) can be calculated using Antoine equation as follows:
Using formula
Using the formula
we find mole fraction of benzene (1) in vapor phase,
Therefore,
(b)
Interpretation:
The mole fraction of benzene in liquid phase, x1and constant total pressure, P at temperature 100°C is to be calculated.
Concept introduction:
Raoult’s Law states that the partial pressure of liquid A above the solution is equal to the mole fraction of the liquid in a solution times the partial pressure of the pure liquid. This holds for ideal solutions. An ideal solution is approached by binary solutions of molecules that have similar properties (e.g. benzene and toluene). The law is mathematically expressed as-
Where
A solution behaves ideally when
- The solute and the solvent molecules have similar sizes and similar intermolecular forces,
- The excess volume of mixing is zero, and
- The heat of mixing is zero when both the solute and the solvent are liquids
(b)
Answer to Problem 13.1P
Explanation of Solution
The Raoult’s law expression for two components A and B to give the equilibrium partial pressure of the components in a binary mixture is written as follows-
and
The total pressure:
Where
The mole fraction of A in the vapor phase is given by -
Similarly, mole fraction of B in vapor phase is given by -
Now vapor pressures
Now, For benzene (1)
And For toluene (2)
Given
Now vapor pressure for benzene (1) can be calculated using Antoine equation as follows: -
Now vapor pressure for toluene (2) can be calculated using Antoine equation as follows:
Using the formula
we find mole fraction of benzene (1) in liquid phase,
Using formula
Therefore,
(c)
Interpretation:
The mole fraction of benzene in vapor phase, y1and temperature of the solution, T at total pressure P =120 kPa is to be calculated.
Concept introduction:
Raoult’s Law states that the partial pressure of liquid A above the solution is equal to the mole fraction of the liquid in a solution times the partial pressure of the pure liquid. This holds for ideal solutions. An ideal solution is approached by binary solutions of molecules that have similar properties (e.g. benzene and toluene). The law is mathematically expressed as-
Where
A solution behaves ideally when
- The solute and the solvent molecules have similar sizes and similar intermolecular forces,
- The excess volume of mixing is zero, and
- The heat of mixing is zero when both the solute and the solvent are liquids
(c)
Answer to Problem 13.1P
Explanation of Solution
The Raoult’s law expression for two components A and B to give the equilibrium partial pressure of the components in a binary mixture is written as follows-
and
The total pressure:
Where
The mole fraction of A in the vapor phase is given by -
Similarly, mole fraction of B in vapor phase is given by -
Now vapor pressures
Now, For benzene (1)
And For toluene (2)
Given
Now,
Using formula
Solving this equation, we find
Now vapor pressure for benzene (1) can be calculated using Antoine equation as follows: -
Now vapor pressure for toluene (2) can be calculated using Antoine equation as follows:
Using the formula
we find mole fraction of benzene (1) in vapor phase,
Therefore,
(d)
Interpretation:
The mole fraction of benzene in liquid phase, x1and temperature of the solution, T at total pressure P =120 kPa is to be calculated.
Concept introduction:
Raoult’s Law states that the partial pressure of liquid A above the solution is equal to the mole fraction of the liquid in a solution times the partial pressure of the pure liquid. This holds for ideal solutions. An ideal solution is approached by binary solutions of molecules that have similar properties (e.g. benzene and toluene). The law is mathematically expressed as-
Where
A solution behaves ideally when
- The solute and the solvent molecules have similar sizes and similar intermolecular forces,
- The excess volume of mixing is zero, and
- The heat of mixing is zero when both the solute and the solvent are liquids
(d)
Answer to Problem 13.1P
Explanation of Solution
The Raoult’s law expression for two components A and B to give the equilibrium partial pressure of the components in a binary mixture is written as follows-
and
The total pressure:
Where
The mole fraction of A in the vapor phase is given by -
Similarly, mole fraction of B in vapor phase is given by -
Now vapor pressures
Now, For benzene (1)
And For toluene (2)
Given
Now,
Solving these two equations, we find
Therefore,
(e)
Interpretation:
The mole fraction of benzene in liquid phase, x1and mole fraction of benzene in vapour phase, y1at total pressure P =120 kPa and temperature T=105 °C is to be calculated.
Concept introduction:
Raoult’s Law states that the partial pressure of liquid A above the solution is equal to the mole fraction of the liquid in a solution times the partial pressure of the pure liquid. This holds for ideal solutions. An ideal solution is approached by binary solutions of molecules that have similar properties (e.g. benzene and toluene). The law is mathematically expressed as-
Where
A solution behaves ideally when
- The solute and the solvent molecules have similar sizes and similar intermolecular forces,
- The excess volume of mixing is zero, and
- The heat of mixing is zero when both the solute and the solvent are liquids
(e)
Answer to Problem 13.1P
Explanation of Solution
The Raoult’s law expression for two components A and B to give the equilibrium partial pressure of the components in a binary mixture is written as follows-
and
The total pressure:
Where
The mole fraction of A in the vapor phase is given by -
Similarly, mole fraction of B in vapor phase is given by -
Now vapor pressures
Now, For benzene (1)
And For toluene (2)
Given
Now,
Now vapor pressure for benzene (1) can be calculated using Antoine equation as follows: -
Now vapor pressure for toluene (2) can be calculated using Antoine equation as follows:
Using formula
Using the formula
Therefore,
(f)
Interpretation:
The overall mole fraction of benzene is z1=0.33 at total pressure P =120 kPa and temperature T=105 °C is given. The mole fraction of benzene and toluene in vapor phase needs to calculated.
Concept introduction:
Raoult’s Law states that the partial pressure of liquid A above the solution is equal to the mole fraction of the liquid in a solution times the partial pressure of the pure liquid. This holds for ideal solutions. An ideal solution is approached by binary solutions of molecules that have similar properties (e.g. benzene and toluene). The law is mathematically expressed as-
Where
A solution behaves ideally when
- The solute and the solvent molecules have similar sizes and similar intermolecular forces,
- The excess volume of mixing is zero, and
- The heat of mixing is zero when both the solute and the solvent are liquids
(f)
Answer to Problem 13.1P
Vapor fraction, V is 0.231923 and liquid fraction is 0.768077
Explanation of Solution
The Raoult’s law expression for two components A and B to give the equilibrium partial pressure of the components in a binary mixture is written as follows-
and
The total pressure:
Where
The mole fraction of A in the vapor phase is given by -
Similarly, mole fraction of B in vapor phase is given by -
Now vapor pressures
Now, For benzene (1)
And For toluene (2)
Given
Now,
Now vapor pressure for benzene (1) can be calculated using Antoine equation as follows: -
Now vapor pressure for toluene (2) can be calculated using Antoine equation as follows:
Using formula
Using the formula
Now,
Therefore, vapor fraction, V is 0.231923 and liquid fraction is 0.768077.
(g)
Interpretation:
To explain why Raoul’s law is likely to be an excellent VLE model for this system at the stated conditions.
Concept introduction:
Raoult’s Law states that the partial pressure of liquid A above the solution is equal to the mole fraction of the liquid in a solution times the partial pressure of the pure liquid. This holds for ideal solutions. An ideal solution is approached by binary solutions of molecules that have similar properties (e.g. benzene and toluene). The law is mathematically expressed as-
Where
A solution behaves ideally when
- The solute and the solvent molecules have similar sizes and similar intermolecular forces,
- The excess volume of mixing is zero, and
- The heat of mixing is zero when both the solute and the solvent are liquids
(g)
Explanation of Solution
Benzene and toluene are both non-polar. They are similar in shape and size. Therefore, one would expect little chemical interaction between the two substances. Moreover, the temperature is sign enough and the pressure is low, so it is expected to behave ideally.
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Chapter 13 Solutions
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