Mark scheme and accompanying theory for the CAPE past paper question #5 from the 2016 Unit 2 Paper 2.

1. CAPE Chemistry 2016 U2 P2 Q5 – Theory And Mark Scheme
Raoult’s Law
Raoult's Law, as applied to completely miscible binary systems, states that
the partial pressure of a constituent of a binary mixture at any given
temperature is equal to the normal vapor pressure of that constituent at the
stated temperature multiplied by the mole fraction of the constituent in the
mixture.
Because solvent vapor pressure is proportional to the relative number of
solvent molecules, we can write the following equation for the equilibrium
vapor pressure of the solvent over a solution:
Psolvent = xsolvent P°solvent
Where:
Psolvent = vapour pressure of the solvent.
P°solvent = pure solvent equilibrium vapour pressure.
xsolvent = solvent mole fraction.
Ideal Solutions
Ideal solutions obey Raoult’s law. These are solutions in which:
1. The interactions between components are similar to those in pure
components.
2. There is no enthalpy change on mixing.
3. There is no volume change on mixing.
Ideal solutions do not form azeotropes.
Azeotropic Mixtures
An azeotropic mixture is one which boils or distils without change in
composition, and in general it has a boiling point higher or lower than that of
any of its pure constituents.
That a constant boiling mixture (CBM) is not a molecular compound in the
usual sense, however, was demonstrated in 1861 by Sir Henry Roscoe who
showed that the composition of the CBM varied with the pressure at which
the distillation was carried out.
The term "azeotropic" (privative form of the Greek zein, to boil, and tropos,
changing; hence, to boil unchanged) was suggested in 1911 by Wade and
Merriman.
Boiling Point – Composition Diagrams
An understanding of the behaviour of azeotropic mixtures is best obtained by
a consideration of phase equilibrium diagrams, and for the present purpose
those of binary mixtures will be sufficient.
In 1876 it was set forth on theoretical grounds by Willard Gibbs, and
empirically by D. P. Konowaloff in 1881, that in completely miscible binary
mixtures the vapor will be relatively richer in that component the addition of
which to the mixture increases the total vapor pressure.
Just how rich the vapor will be was first shown by F. M. Raoult who, in 1887,
demonstrated the accuracy of what has now become known as Raoult's Law.
A mixture behaving reasonably in accordance with Raoult's Law thus gives
the familiar boiling point-composition diagram shown in Figure 1.
Figure 1.
Any composition m boils at temperature t and at equilibrium gives off a vapor
of composition n richer in the more volatile component A. The residue is
therefore richer in the less volatile component B.
Through repeat distillation, which is accomplished in a fractionating column
any mixture can therefore be separated into pure A and pure B, provided only
that the column is sufficiently effective.
In mixtures where the relative vapor pressures deviate from Raoult's Law
widely enough to give a maximum or minimum total vapor pressure, liquid-
vapor diagrams such as those below are obtained where at one point, k, the
vapor and liquid compositions are identical, and the curves representing
these compositions are thus tangent.
In such cases we have azeotropic mixtures of minimum or maximum boiling
point, respectively.
Figure 2. Figure 3.
In Figure 2, any composition o to the right of k boils at temperature t and
gives off a vapor p richer in A, and a residue remains, richer in B. By
fractionation, any mixture with a composition lying to the right of k can
therefore be separated into pure B as a residue and the pure azeotropic
composition k.
Likewise, any composition o' to the left of k can be separated by fractionation
into pure A as a residue and the pure azeotropic mixture k; hence, no matter
what the composition in the still pot, excepting pure A or pure B, the
distillate, or "overhead product," on fractionation is always the pure
azeotrope k.
The residue left behind, if any, will be pure A or B depending on whether
there was in the starting mixture an excess of A or B over that required by the
azeotropic composition k. Figure 2 is in effect two Figure 1 diagrams. The
curve α is a Figure 1 diagram for a mixture of A and the azeotrope k, while the
curve β is a Figure 1 diagram for a mixture of B and the azeotrope k. At any
given pressure, an azeotrope on fractionation therefore behaves as a pure
component having a boiling point of T.
Figure 3 is a diagram for a mixture of two components which form a CBM of
maximum boiling point. Any composition o to the right of k boils at
temperature t, gives a vapor of composition p richer in B, and leaves a residue
richer in the azeotrope k. Similarly, any composition o' to the left of k can be
fractionated into a distillate of pure A and a residue of the pure azeotrope k.
Thus, any composition whatever yields on fractionation a residue of pure
azeotrope boiling at the temperature T and an overhead product of pure A or
pure B depending on whether the starting material contained excess of A or B
over that required by the azeotrope k.
Again, Figure 3 is actually two Figure 1 diagrams. α is a diagram for mixtures
of A and k, and β is a diagram for mixtures of B and k.
Partition Coefficient
If we take two immiscible solvents A and B in a beaker, they form separate
layers. When a solute X which is soluble in both solvents is added, it gets
distributed or partitioned between them. Molecules of X pass from solvent A
to B and from solvent B to A.
Finally a dynamic equilibrium is set up. At equilibrium, the rate, at which
molecules of X pass from one solvent to the other is balanced (Figure 4).
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2. CAPE Chemistry 2016 U2 P2 Q5 - Theory And Mark Scheme
Figure 4.
Nernst (1891) studied the distribution of several solutes between different
appropriate pairs of solvents. He gave a generalization which governs the
distribution of a solute between two non-miscible solvents. This is called
Nernst’s Distribution law (or Nernst’s Partition law) or simply Distribution law
or Partition law.
If a solute X distributes itself between two immiscible solvents A and B
at constant temperature and X is in the same
molecular condition in both solvents,
If C1 denotes the concentration of the solute in solvent A and C2 the
concentration in solvent B, Nernst’s Distribution law can be expressed as:
The constant KD (or simply K) is called the Distribution coefficient or Partition
coefficient or Distribution ratio.
The process of a solute dissolved in one solvent being extracted into a new
solvent actually involves an equilibrium process. We can thus write the
following:
Aorig ⇌ Aext
in which A refers to analyte and, orig and ext refer to original solvent and
extracting solvent, respectively. The partition coefficient can be defined as
follows:
or
in which Wext is the weight of the solute extracted into the extracting solvent,
Vext is the volume of the extracting solvent used, Worig is the weight of the
solute in the original solvent, and Vorig is the volume of the original solvent
used.
IUPAC recommends that: “In equations relating to aqueous/organic systems
the organic phase concentration is, by convention, the numerator and the
aqueous phase concentration the denominator.”
Sample Calculation
The partition coefficient of A between ether and water is 4.0. 5 g of A were
dissolved in 100 cm3 of water and mixed with 10 cm3 of ether. Calculate the
mass extracted into the ether.
K = [A]ether/[A]water
therefore (x/10)/((5-x)/100) = 4, and
x/10 = 4(5-x)/100 so 100x = 200 - 40x which gives
140x = 200, so x = 1.43.
The value of x is 1.43 so the mass that is dissolved in the ether at equilibrium
is x g. Therefore the mass extracted is 1.43 g.
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SUGGESTED MARK SCHEME – CAPE CHEMISTRY
JUNE 2016 UNIT 2 PAPER 2
Question 5
(a)(i) As applied to completely miscible binary
systems, states that the partial pressure
of a constituent of a mixture at any
given temperature (1) is equal to the
normal vapor pressure of that
constituent at the stated temperature
multiplied by the mole fraction of the
constituent in the mixture.(1)
(a)(ii) The interactions between components are
similar to those in pure components. (1)
There is no enthalpy change on mixing.(1)
(b)(i) One which boils or distils without change
in composition, and in general it has a
boiling point higher or lower than that
of any of its pure constituents. (1)
(b)(ii) Their composition varies with the
pressure at which distillation is carried
out. (1)
(b)(iii)
Minimum of two tie lines and
corresponding vertical lines down to Y
and Z. (1)
T1, T2, Y and Z labelled. (1)
Liquid mixture X boils at temperature T1
to produce vapour of composition Y which
is richer in A. (1)
Continued distillation further enriches
vapour in A as shown at Z. (1)
Sufficiently effective column will yield
azeotrope of composition M as the
distillate. (1)
Pure B remains as residue. (1)
(c) Mass of compound initially in 100 cm3
aqueous solution = 5 g.
Mass of compound extracted by organic
solvent = x g.
Mass of compound remaining in water =
(5-x)g. (1)
K = [cpd.]water/[cpd.]organic solvent
0.200 = ((5-x)/100)/(x/25) (1)
x = 2.8 g (1)
Total 15 marks
KC UK XS
2
2
1
1
6
3
6 9
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