Lecture4-Properties -...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: BIOC*2580
Lecture
4:
Properties
of
aqueous
solutions
of
 weak
electrolytes.
 1 Synopsis:
 Biochemical
 reactions
 occur
 in
 aqueous
 solution
 at
 close
 to
 neutral
 pH.
 Many
 biochemical
substances
such
as
amino
acids
include
weak
acid
groups
such
as
carboxylates,
SH
 or
 phenolic
 OH,
 or
 weak
 bases
 such
 as
 amines
 or
 some
 ring
 N
 compounds.
 The
 behaviour
 of
 such
groups
is
highly
dependent
on
whether
they
are
protonated
or
deprotonated.
 READ:

Lehninger
5th
ed
p.
43‐66
(4th
ed
p.89‐95)
 REVIEW:

CHEM*1040
notes
regarding
weak
acids
and
bases.
 
 Amino
acids
as
weak
electrolytes
 
 Normal
 biochemical
 processes
 occur
 in
 aqueous
 solution
 close
 to
 neutral
 pH;
 typical
 physiological
 pH
 is
 about
 7.2
 to
 7.4,
 and
 pH
 7.0
 is
 a
 close
 approximation.
 Certain
 functional
 groups
found
in
biological
molecules,
in
particular
carboxylic
acids
or
amino
groups,
can
gain
or
 lose
H+
depending
on
the
availability
of
hydrogen
ions
(or
protons)
in
the
solution.

 
 pH
expresses
the
availability
of
H+;
pH
=
–
log10
[H+]

 
 Each
 ionic
 functional
 group,
 e.g.
 amino
 groups
 or
 carboxylic
 acid
 groups,
 has
 a
 characteristic
 constant,
pKa,
which
expresses
the
tendency
to
gain
or
lose
H+.


 
 The
Henderson
Hasselbalch
equation
relates
pH
to
pKa
and
the
state
of
ionization:
 deprotonated
 [A − ] pH = pKa + log10 [HA ] 
 protonated
 

 € {} The
Henderson‐Hasselbalch
equation
allows
one
to
do
the
calculations
needed:

 
 1. to
 determine
 the
 pH
 given
 the
 ionic
 conditions
 of
 the
 surroundings;
 if
 pKa
 and
 the
 concentrations
are
known,
pH
can
be
calculated.
 2. to
 determine
 the
 degree
 of
 protonation
 or
 deprotonation
 of
 an
 ionizable
 functional
 group
 at
 a
 given
 pH.
 If
 the
 pH
 and
 pKa
 are
 known,
 the
 ratio
 of
 concentrations
 can
 be
 calculated,
and
this
means
we
can
work
out
what
the
state
of
an
"ionic"
functional
group
 actually
is
at
a
given
pH.

 
 For
each
amino
acid,
there
is
 
 • an
α ‐carboxylic
acid
(typical
pKa
=
2.4±0.5)
 • an
α ‐amino
group
(typical
pKa
9.6±0.5)
 • certain
amino
acids
also
have
a
side
chain
which
may
be
charged.
 
 Exact
pKa
values
for
each
of
the
20
amino
acids
can
be
found
in
Lehninger
p.
73
(4th
ed
p.78)
 Page
1
of
7
 BIOC*2580
Lecture
4:
Properties
of
aqueous
solutions
of
 weak
electrolytes.
 2 We
transform
the
Henderson
Hasselbalch
equation
to
calculate
the
state
of
each
group
at
pH
 7.0
 
 € € € € pH = pKa + log10 

 A− 10pH‐pKa = 
 [[HA ]] 
 

 {} [A − ] [HA ] 
 Given
pKa
=
2.4
for
the
a‐carboxylic
acid
group,
we
can
calculate
the
ratio
of
anionic
carboxylate
 ‐CO2–

to
neutral
carboxylic
acid
‐CO2H
when
pH
=
7.0:

 7.0 −2.4 [A − ] 
 [HA ] This
indicates
that
the
vast
majority
of
a‐carboxylic
acid
groups
are
fully
deprotonated
(i.e.
have
 lost
H+)
and
exists
in
the
carboxylate
ion
state
at
pH
7.0.
 Given
pKa
=
9.6
for
the
a‐amino
group,
 [ ‐NH2 ] 7.0 −9.6 + 
 [‐NH ] This
indicates
that
the
 a‐amino
group
is
essentially
fully
protonated
(have
gained
H+)
and
 exists
 in
the
‐NH3+
state
at
pH
7.0.

 The
backbone
portion
of
a
free
amino
acid
at
pH
7
is
therefore
best
represented
as
 ‐ +NH3‐CHR‐CO2 

 When
 an
 amino
 acid
 is
 linked
 up
 as
 part
 of
 a
 peptide
 chain,
 the
 situation
 is
 different.
 The
 a‐ amino
 groups
 and
 a‐carboxylate
 groups
 combine
 to
 form
 amide
 or
 peptide
 bonds.
 When
 combined
 as
 an
 amide,
 the
 a‐amino
 groups
 and
 a‐carboxylate
 groups
 are
 not
 free
 to
 protonate
 or
 deprotonate,
 so
 in
 the
 peptide
 bonded
 state,
 the
 amino
 acid
 backbone
 is
 uncharged:

 x‐NH‐CHR‐CO‐NH‐CHR‐CO‐NH‐CHR‐CO‐x
 

 

 = 10 = 40000 = 10 = 0.0025 Meaning
of
pKa
 
 The
value
of
pKa
tells
you
where
in
the
 pH
scale
a
functional
group
 undergoes
 protonation
or
deprotonation
 e.g.
for
glutamate:
 
 Each
group
has
its
own
pKa
value.
The
 exact
 value
 of
 a
 group’s
 pKa
 depends
 on
its
chemical
context.
 The
presence
 of
 the
 positive
 NH3+
 near
 the
 a‐ carboxylic
acid
position
favours
deprotonation
to
 the
negative
carboxylate,
 hence
this
group
is
 more
acidic
(lower
pKa)
than
the
g‐carboxylate.
 Page
2
of
7
 BIOC*2580
Lecture
4:
Properties
of
aqueous
solutions
of
 weak
electrolytes.
 3 When
 glutamate
 is
 part
 of
 a
 peptide
 chain,
 the
 α‐amino
is
part
of
a
neutral
 amide
bond,
 so
in
the
absence
of
a
 nearby
positive
charge,
 the
glutamate
 side
chain
carboxylate
has
pKa
 =
5.
 
 If
we
start
with
a
sample
of
free
glutamic
acid
 initially
 at
 very
 low
 pH,
 all
 functional
 groups
 will
 be
 protonated.
 As
 pH
 is
 increased,
 each
 functional
group
will
start
to
lose
H+
when
the
 pH
 approaches
 the
 pKa
 of
 that
 group.
 
 For
 example,
 deprotonation
 of
 the
 a‐carboxylic
 acid
group
 occurs
around
pH
2.1.

When
pH
=
 2.1,
 the
 α‐carboxylic
 acid
 will
 be
 exactly
 50%
 deprotonated.


 
 Above
 pH
 3.1,
 the
 α‐carboxylate
 group
 is
 essentially
fully
deprotonated.

 
 If
 the
 pH
 continues
 to
 increase,
 as
 it
 approaches
 the
 pKa
 of
 the
 γ‐carboxylic
 acid
 group,
 this
 will
 deprotonate
 in
 turn
 to
 yield
 the
γ‐carboxylate.
 
 Ultimately,
if
pH
is
increased
much
 above
pH
 9,
 the
 α‐amino
 group
 will
 start
 to
 be
 deprotonated.

 
 Page
3
of
7
 BIOC*2580
Lecture
4:
Properties
of
aqueous
solutions
of
 weak
electrolytes.
 4 Note
 that
 the
 transition
 of
 a
 given
 group
 from
 fully
 protonated
 to
 fully
 deprotonated
 occurs
 over
 a
 narrow
 range
 of
 pH,
 essentially
 over
 a
 range
 of
 1
 pH
 unit
 on
 either
 side
 of
 pKa.
 
 This
 gives
 us
 a
 simple
 set
 of
 rules
 for
 determining
 the
 ionic
 state
 of
 the
 functional
 groups
 in
 a
 molecule
at
any
given
pH:
 
 If
pH
is
one
unit
or
more
above
its
pKa,
a
group
may
be
considered
fully
deprotonated,
 e.g.
carboxylate
groups
with
pKa
=
2.4
exist
as
‐CO2–
at
pH
7.
 
 If
pH
is
equal
to
pKa,
the
group
is
exactly
50%
protonated
and
50%
deprotonated.

 
 If
pH
is
one
unit
or
more
below
its
pKa,
a
group
may
be
considered
fully
protonated,
 e.g.
amino
groups
with
pKa
=
9.6
exist
as
+NH3‐
at
pH
7.
 
 Hence
it
is
easy
to
determine
by
inspection
that
glutamate
exists
with
its
two
carboxylate
groups
 deprotonated,
and
its
amino
group
protonated
at
physiological
pH.
 
 There
are
seven
amino
acids
with
side
chains
that
undergo
deprotonation
 
 
 pKa
 State
at
pH
7
 State
at
low
pH
 State
at
high
pH
 Aspartate
 4.0
 ‐CO2–
 ‐CO2H
below
pH
4
 same
as
pH
7
 Glutamate
 5.0
 ‐CO2–
 ‐CO2H
below
pH
5
 same
as
pH
7
 Histidine
 6.5
 76%
ring
N:
 ring
NH+
below
pH
6.5
 ring
N:
 Cysteine
 8.5
 Neutral
‐SH
 same
as
pH
7
 ‐S–
above
pH
8.5
 Tyrosine
 10.0
 Phenol‐OH
 same
as
pH
7
 Phenolate‐O–
above
pH
10
 Lysine
 10.2
 ‐NH3+
 same
as
pH
7
 ‐NH2
above
pH
10.2
 Arginine
 12.5
 ‐NH3+
 same
as
pH
7
 =NH
above
pH
12.5
 
 pKa
values
given
 are
for
the
side
chain
of
the
amino
acid
 in
a
polypeptide.

Values
are
slightly
 different
for
the
free
amino
acid
(see
Lehninger
p.
73
(4th
ed
p.78)).
 
 Cysteine
 and
 Tyrosine
 were
 not
 included
 as
 negative
 in
 the
 pyramid
 table
 of
 amino
 acids,
 because
they
are
neutral
at
pH
7.
 
 Important
Note:
these
rules
can
tell
you
whether
a
group
is
 protonated
or
deprotonated,
but
 not
 immediately
 whether
 the
 group
 is
 positively
 or
 negatively
 charged.
 
 It
 is
 also
 necessary
 to
 apply
a
little
knowledge
of
the
chemistry
of
the
group:
 
 Groups
that
ionize
on
O
or
S
are
neutral
when
protonated
and
negative
when
deprotonated.
 Groups
that
ionize
on
N
are
positive
when
protonated
and
neutral
when
deprotonated.
 No
group
can
go
from
positive
to
negative
in
a
single
deprotonation
step.
 Page
4
of
7
 BIOC*2580
Lecture
4:
Properties
of
aqueous
solutions
of
 weak
electrolytes.
 5 Many
functional
groups
contain
O,
N
or
S
but
do
not
undergo
ionization,
e.g.
alcohols
or
amides.
 Simple
 alcohols
 (R‐OH)
 such
 as
 the
 side
 chains
 of
 serine
 or
 threonine,
 and
 the
 amides
 (R‐ CONH2)
such
as
the
side
chains
of
 asparagine
or
glutamine,
do
not
deprotonate
or
 protonate
 appreciably
in
aqueous
solution
and
their
side
chains
are
neither
weak
acids
nor
weak
bases.
 
 Partial
ionization
 If
 pH
 is
 less
 than
 one
 unit
 greater
 or
 less
 than
 pKa,
 we
 can’t
 say
 that
 a
 given
 group
 is
 fully
 protonated
or
deprotonated.
It
is
still
possible
to
say
that
the
major
form
is
deprotonated
if
pH
 is
 above
the
pKa,
and
protonated
if
pH
is
below
the
pKa,
but
the
minor
form
is
still
present
in
 significant
 amounts.
 
 If
 we
 want
 to
 be
 more
 exact,
 we
 can
 use
 the
 Henderson‐Hasselbalch
 equation
to
determine
the
exact
state
of
deprotonation.
 
 The
histidine
side
chain
has
pKa
=
6.5.

At
 pH
 7,
 the
 major
 form
 is
 deprotonated,
 but
the
pH
is
not
a
full
 unit
 higher,
 so
 is
 nowhere
 near
 being
 "fully
 deprotonated",
 and
 the
 positively
 charged
form
is
still
present
in
 significant
 amounts.

 
 What
 is
 the
 degree
 of
 deprotonation
 of
 the
 side
 chain
 of
 His
 (pKa
 =
 6.5)
 at
 pH
 7.0?
 
 Degree
of
deprotonation
is
the
fraction
of
the
total
that
is
in
the
deprotonated
state.
 [deprotonated] [deprotonated ] α 
 

 = [ total ] = [protonated +deprotonated ] 
 
 We
get
the
ratio
of
deprotonated
[His]
to
protonated
[HisH+]
from
the
Henderson‐Hasselbalch
 equation:
 € € € € { [His pH = pKa + log10 [HisH+] ] 




 deprotonated 
 protonated 

 [His 107.0 ‐6.5 = [HisH+] ] = 3.2 

 
 [His] α= 






divide
top
and
bottom
by
[HisH+ ] 
 + 

 [HisH ] + [His] [His] + 3.2 α = [HisH ] = = 0.76 
 [His] 1 + [HisH+ ] 1 + 3.2 

 } The
histidine
side
chain
is
76%
deprotonated
at
pH
=
7.0
 Page
5
of
7
 € BIOC*2580
Lecture
4:
Properties
of
aqueous
solutions
of
 weak
electrolytes.
 6 Relating
charge
to
degree
of
deprotonation
 The
 degree
 of
 deprotonation
 α
 tells
 you
 what
 fraction
 is
 deprotonated.
 You
 need
 to
 know
 something
 about
 the
 chemistry
 of
 the
 functional
 group
 to
 deduce
 the
 charge,
 and
 since
 histidine
has
a
N‐base
in
its
side
chain,
the
protonated
form
is
positive,
and
the
deprotonated
 form
is
neutral.

 
 If
76%
is
deprotonated,
(charge
0)
then
24%
must
be
protonated
(charge
+1).
 
 Now
sum
the
contributions
to
average
charge:
 
 (0.76
× 
0)

+

(0.24
× 
+1)


=


+0.24

 
 fraction
neutral





fraction
positive






average
charge
 At
pH
7.0,
Histidine
behaves
as
if
it
has
a
side
chain
charge
of
+0.24.
 
 Although
no
one
molecule
can
carry
a
fractional
charge,
the
+ve
HisH+
and
neutral
His
molecules
 exchange
 H+
 very
 rapidly
 (millions
 of
 times
 per
 second.
 Averaged
 over
 a
 period
 of
 time,
 each
 molecule
behaves
as
if
it
has
+0.24
charge.

 
 A
calculation
similar
to
the
above
gives
degree
of
deprotonation
=
0.074
for
Cysteine
(pKa
=
8.5)
 at
pH
7.4.
For
cysteine,
the
side
chain
states
are:
 
 If
7.4
%
is
deprotonated
single
negative
‐S–,
then
92.6%
is
protonated
neutral
–SH
 
 (0.074
× 
–1)

+

(0.926
× 
0)


=


–
0.074
 
 fraction
negative







fraction
neutral 




average
charge 
 Effective
charge
of
cysteine
side
chain
at
pH
7.4
=
–
0.074.
This
is
low
enough
that
it
is
 usually
 ignored.

 
 The
following
section
will
not
be
covered
in
lecture,
but
is
provided
to
refresh
your
memory
of
 how
to
work
with
buffers
from
first
year
Chemistry.

 You
should
also
read
the
 introduction
to
 Laboratory
exercise
1,
which
goes
through
buffer
theory
and
calculations
in
detail.
 
 Buffers
 A
buffer
is
a
substance
present
in
solution
in
sufficiently
high
concentration
to
control
the
pH
of
 its
 environment.
 This
 occurs
 by
 creating
 a
 mixture
 of
 the
 protonated
 (or
 weak
 acid)
 and
 deprotonated
(or
weak
base)
forms
of
the
buffer
such
that
the
mixture
is
at
equilibrium
with
the
 desired
 concentration
 [H+].
 
 The
 resulting
 pH
 will
 be
 close
 to
 the
 pKa
 of
 the
 buffer.
 Buffering
 occurs
 in
 living
 cells
 due
 to
 the
 presence
 of
 bicarbonate
 ions,
 phosphate
 ion
 and
 phosphate
 esters,
all
of
which
have
pKa
values
close
to
7.

 
 In
 the
 biochemical
 experiments
 in
 the
 lab,
 two
 buffers
 are
 widely
 used,
 chosen
 because
 their
 pKa
is
close
to
physiological
pH
7‐7.4:

 dihydrogen
phosphate
H2PO4–
in
equilibrium
with
HPO42–

(pKa
=
6.8).
 trishydroxymethylaminomethane,
 or
 tris
 for
 short,
 in
 equilibrium
 with
 its
 protonated
 form
trisH+
(pKa
=
8.08).
 Page
6
of
7
 BIOC*2580
Lecture
4:
Properties
of
aqueous
solutions
of
 weak
electrolytes.
 7 A
primer
on
buffers
 
 The
Henderson
Hasselbalch
equation
is
used
for
buffer
calculations.

 
 If
the
pKa
and
the
composition
of
protonated
and
deprotonated
forms
is
known,
you
can
 calculate
the
resulting
pH
 
 If
pH
and
pK
are
known,
you
can
calculate
the
desired
proportions
needed
to
make
the
 buffer.
 To
 calculate
 the
 pH
 of
 a
 buffer,
 you
 need
 to
 determine
 the
 molar
 concentration
 of
 the
 protonated
and
deprotonated
forms
of
the
buffer.

 e.g.
a
solution
is
prepared
so
that
it
contains
[tris]
=
0.025
M
and
[trisH+]
=
0.075
M,
where
pKa
 =
8.08
for
trisH+

 This
mixture
describes
the
actual
concentrations
of
weak
base
(tris)
and
its
conjugate
(trisH+),
so
 you
can
go
substitute
directly
into
the
Henderson‐Hasselbalch
equation.

 pH = pKa + log10 

 € { }
 [A − ] [HA ] pH
=
8.08
+
log
(0.025/0.075)

 pH
=
7.6

 
 This
 buffer
 could
 be
 made
 by
 weighing
 out
 the
 appropriate
 masses
 of
 tris
 base
 (molar
 mass
 121.1
g/mol)
and
trisHCl
(molar
mass
157.6
g/mol)
and
dissolving
in
the
required
total
volume
of
 H2O.
 
 
 Example
Question
 
 How
many
moles
of
NaOH
must
be
added
to
0.040
mol
NaH2PO4
(pKa
=
6.8)
to
get
a
 solution
of
 pH
7.0?

 
 Let
x
=
mol
NaOH
required

 Moles
HPO42‐
formed
=
x
 Moles
H2PO‐
remaining
unreacted
=
0.040
‐
x

 
 Set
up
Henderson‐Hasselbalch
equation:

 7.0
=
6.8
+
log
x
/
(0.040
‐
x)

 100.2
=
x
/
(0.040
‐
x)

 1.58
*
0.040
‐
1.58
x
=
x

 
 x
=
1.58
*
0.04
/
2.58
=
0.024
mol
NaOH
required
 
 Page
7
of
7
 ...
View Full Document

Ask a homework question - tutors are online