Vapour pressure of ideal solutions at 25c the vapour pressure of chloroform and carbon tetrachloride are 26.54 and 15.27 kpa respectively.
If the liquids from ideal solutions.
(A) what is the composition of the vapour in equilibrium with with a solution containing 1mol of each ?
(B) what is the total vapor pressure?
pCHCl3 = XCHCl3*PoCHCl3
pCCl4 = XCCl4*PoCCl4
Total vapor Pressure = pCHCl3 + pCCl4
X each = 1 mol/2 mols = 0.5 for X
In the vapor state,
XCHCl3 = pCHCl3/Ptotal
XCCl4 = pCCl4/Ptotal
To answer these questions, we can use Raoult's law, which states that the vapor pressure of a component in an ideal solution is equal to the product of its mole fraction in the solution and its pure substance vapor pressure.
(A) What is the composition of the vapor in equilibrium with a solution containing 1 mole of each?
To find the composition of the vapor, we need to calculate the mole fraction of each component in the solution. Let's assume that the mole fraction of chloroform (CHCl3) is x and the mole fraction of carbon tetrachloride (CCl4) is (1 - x) since we have 1 mole of each component.
According to Raoult's law, the vapor pressure of chloroform (P1) is equal to x times its pure substance vapor pressure (P1^0), and the vapor pressure of carbon tetrachloride (P2) is equal to (1 - x) times its pure substance vapor pressure (P2^0).
We can set up the following equation:
P1 = x * P1^0
P2 = (1 - x) * P2^0
Substituting the given values:
P1 = x * 26.54 kPa
P2 = (1 - x) * 15.27 kPa
Since the liquids form an ideal solution, the total vapor pressure (PTotal) is the sum of the vapor pressures of the individual components.
PTotal = P1 + P2
(B) What is the total vapor pressure?
To find the total vapor pressure, we need to substitute the values of P1 and P2 into the equation for PTotal:
PTotal = P1 + P2
PTotal = x * 26.54 kPa + (1 - x) * 15.27 kPa
Now, we can solve for x by setting the equation for P1 equal to the equation for P2:
x * 26.54 = (1 - x) * 15.27
Simplifying the equation:
26.54x = 15.27 - 15.27x
26.54x + 15.27x = 15.27
41.81x = 15.27
x = 15.27 / 41.81
x ≈ 0.3657
Now that we have the value of x, we can substitute it into the equation for PTotal:
PTotal = x * 26.54 kPa + (1 - x) * 15.27 kPa
PTotal = 0.3657 * 26.54 kPa + (1 - 0.3657) * 15.27 kPa
Calculating the values:
PTotal ≈ 9.68 kPa + 9.71 kPa
PTotal ≈ 19.39 kPa
So, the total vapor pressure of the solution containing 1 mole of chloroform and 1 mole of carbon tetrachloride is approximately 19.39 kPa.
To solve this problem, we need to use Raoult's law, which states that the vapor pressure of an ideal solution is proportional to the mole fraction of each component in the solution.
(A) To determine the composition of the vapor in equilibrium with a solution containing 1 mol of each chloroform (CHCl3) and carbon tetrachloride (CCl4), we need to find the mole fraction of each component.
Mole fraction (χ) is defined as the ratio of the number of moles of a component to the total number of moles in the solution.
For a solution containing 1 mol of each component, the total number of moles is 2.
Mole fraction of chloroform:
χCHCl3 = moles of CHCl3 / total moles
= 1 mol / 2 mol
= 0.5
Mole fraction of carbon tetrachloride:
χCCl4 = moles of CCl4 / total moles
= 1 mol / 2 mol
= 0.5
Therefore, in equilibrium, the composition of the vapor in the solution containing 1 mol of each chloroform and carbon tetrachloride is 0.5 mol fraction for each component.
(B) Now, to find the total vapor pressure, we can use the equation:
Ptotal = χCHCl3 * PCHCl3 + χCCl4 * PCCl4
where PCHCl3 and PCCl4 are the vapor pressures of chloroform and carbon tetrachloride, respectively.
Given:
PCHCl3 = 26.54 kPa
PCCl4 = 15.27 kPa
Substituting the values:
Ptotal = 0.5 * 26.54 kPa + 0.5 * 15.27 kPa
= 13.27 kPa + 7.64 kPa
= 20.91 kPa
Therefore, the total vapor pressure of the solution containing 1 mol of each chloroform and carbon tetrachloride is approximately 20.91 kPa.