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2.500 Desalination and Water Purification
Spring 2009
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MASSACHUSETTS
INSTITUTE
OF
TECHNOLOGY
DEPARTMENT
OF
MECHANICAL
ENGINEERING
2.500
Desalination
and
Water
Puriﬁcation
Homework
Set
#2
Due
19
March
2009
Problem
1:
Two
ways
to
compute
Π
We
have
seen
that
the
osmotic
pressure,
Π
,
may
be
determined
by
considering
the
partial
molar
Gibbs
energy
of
a
solvent,
i
,
as
a
function
of
pressure
and
composition
at
constant
temperature,
G
i
(p,x
i
,T)
.
To
further
investigate
this,
consider
a
pure
solvent
at
a
pressure
p
I
and
a
solution
having
mole
fraction
of
solvent
x
i
II
at
a
pressure
p
II
.
At
osmotic
equilibrium,
p
II
−
p
I
=
Π
,
the
partial
molar
Gibbs
energies
are
equal,
G
i
(p
I
,x
i
I
,T)
=
G
i
(p
II
,x
i
II
,T)
.
Calculate
Π
in
two
ways.
First,
assume
a
two
step
process
going
from
(i)
pure
solvent
at
p
I
to
pure
solvent
at
p
II
,
followed
by
(ii)
change
in
composition
from
x
i
I
=
1to
x
i
II
at
ﬁxed
pressure
p
II
.
Second,
assume
a
two
step
process
having
(i)
a
change
in
composition
from
x
i
I
=
1to
x
i
II
at
ﬁxed
pressure
p
I
,
followed
by
(ii)
a
change
in
pressure
from
p
I
to
p
II
at
ﬁxed
composition,
x
i
II
.
Bear
in
mind
that
V
i
≡
∂G
i
/∂p
.
How
do
these
two
results
diﬀer?
What
do
you
conclude
about
the
physical
properties
in
volved?
Problem
2:
Constant
volume
model
for
density
of
salt
water
To
estimate
the
density
of
salt
water
(aqueous
NaCl),
we
could
try
assuming
that
the
volume
of
solution
remains
ﬁxed
when
salt
is
added
to
water,
so
that
salt
water
containing
1
kg
of
H
2
O
would
have
a
the
same
volume
as
1
kg
of
pure
water.
Calculate
the
density
of
salt
water
as
a
function
of
molality
on
this
basis
can
compare
it
to
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This note was uploaded on 02/27/2012 for the course MECHANICAL 2.500 taught by Professor Miriambalaban during the Spring '09 term at MIT.
 Spring '09
 MiriamBalaban

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