pH
and
pOH
Calculations
Section
6.2
pg.
238
‐
244
Pure
Water
 
Pure
water
actually
self
ionizes
(called
“auto‐ioniza6on”),
so
it
contains
H+(aq)
and
OH‐(aq)
ions,
but
their
concentra6ons
are
so
low
that
a
conduc6vity
test
is
nega6ve.
 
In
a
sample
of
pure
water,
about
two
out
of
every
billion
molecular
collisions
are
successful
in
forming
hydronium
and
hydroxide
ions
 
2H2O(l)

H3O+(aq)
and
OH‐(aq)
In
pure
water
at
SATP,
the
hydronium
ion
concentra6on
is
very
low;
about
1
x
10‐7
mol/L
 
This
concentra6on
is
oRen
negligible
and
will
show
no
conduc6vity
unless
very
sensi6ve
equipment
is
used
(pg.
238
–
Figure
1)
Pure
Water
 
 
 
Adding
acid
to
water
adds
H+(aq)
ions
causing
the
H+(aq)
concentra6on
to
increase,
thus
it
makes
the
solu6on
conduc(ve
Adding
base
to
water
adds
OH‐(aq)
ions
causing
the
OH‐(aq)
concentra6on
to
increase,
thus
it
makes
the
solu6on
conduc(ve
Aqueous
solu6ons
exhibit
a
wide
range
of
hydronium
ion
concentra6ons
–
from
more
than
10
mol/L
for
concentrated
HCl(aq)
to
less
than
10‐15
mol/L
for
concentrated
NaOH(aq)
 
This
range
is
called
pH;
meaning
“power
of
hydrogen”
 
“the
nega)ve
of
the
base
ten
exponent
for
the
hydronium
ion
concentra)on”
[H3O
+(aq)]
=
10
‐pH
pH
–
power
of
hydrogen
 
 
This
range
is
called
pH;
meaning
“power
of
hydrogen”
“The
nega)ve
of
the
base
ten
exponent
for
the
hydronium
ion
concentra)on”
[H3O
+(aq)]
=
10
–pH
1
x
101
mol/L
Acidic
solution
pH
=
‐1
1
x
10‐7
mol/L
Neutral
pH
=
7
1
x
10‐15
mol/L
Basic
solution
pH
=
15
pH
–
power
of
hydrogen
[H3O
+(aq)]
=
10
‐pH
The
pH
scale
is
used
to
communicate
a
broad
range
of
hydronium
ion
concentrations.
Most
common
acids
and
bases
have
pH
values
between
0
and
14
pH
changes
Changes
in
pH
can
be
deceptive.
Adding
vinegar
to
pure
water
might
change
the
pH
from
7
to
4.
While
this
change
of
3
pH
units
may
not
appear
significant,
the
change
in
hydronium
ion
concentration
is
103
or
1000
times
larger
Practice
 
Try
pg.
239
#1‐3
pH
Calculations
 
Do
you
think
solu6ons
always
have
a
pH
that
is
an
integer
or
simply
a
power
of
10?
No,
scien6sts
oRen
need
pH
measurements
to
one
or
more
decimal
places
 
 
So
our
defini6on
of
[H3O
+(aq)]
=10
–pH
must
be
improved
so
we
can
convert
numbers
like
6.7
x
10‐8
mol/L
to
a
pH
Our
new
defini6on:
 
pH
=
‐log
[H3O
+(aq)]
pH
=
‐log
[
6.7
x
10‐8]
*
the
units
are
dropped
because
a
log
has
no
units
pH
=
‐
(‐7.1739252)
pH
=
7.1739252
–
but
how
many
sig
digs
can
it
have?
pH
Calculations
Sig
digs
for
pH:
 
“The
number
of
digits
following
the
decimal
point
in
the
pH
value
is
equal
to
the
number
of
sig
digs
in
the
hydronium
ion
concentra)on.”
[H3O
+(aq)]
=
6.7
x
10
‐8
(two
sig
digs)
pH
=
7.17
(two
sig
digs)
pH
Calculations
 
So
from
[H3O
+(aq)]
to
pH
we
use:
pH
=
‐log
[H3O
+(aq)]
pH
=
‐log
(4.5
x
10‐10)
pH
=
9.35
(two
sig
digs)
 
But
to
go
from
pH
to
[H3O
+(aq)]
we
can
s6ll
use:
[H3O
+(aq)]
=10
–pH
[H3O
+(aq)]
=
10
‐9.35
[H3O
+(aq)]
=
4.5
x
10
‐10
mol/L
Since
pH
has
no
units,
the
defini6on
of
pH
includes
the
requirement
that
concentra6on
be
in
mol/L;
you
will
need
to
add
the
units
to
your
answer.
Using
your
calculator:
 
 
 
Go
to
pg.
241
and
read
the
two
Learning
Tips
Numbers
in
scientific
notation
are
best
entered
using
the
exponent
key
(EE)
–
because
the
calculator
treats
the
entry
as
one
value.
The
10x
key
is
not
recommended
because
you
may
obtain
the
incorrect
result
in
some
situations
Try
it:
Turn
[H3O
+(aq)]
=
4.7
x
10‐11
mol/L
into
a
pH
value
Calculator:
(‐)
log
4
.
7
2nd
,
(‐)
1
1
enter
Using
your
calculator:
 
A
solution
has
a
pH
of
5.3.
Calculate
its
hydronium
ion
concentration.
[H3O
+(aq)]
=10
–pH
[H3O
+(aq)]
=10
–5.3
[H3O
+(aq)]
=
5.0118
x
10‐6
Sig
digs?
(pH
=
5.3
–
only
1
sig
dig)
=
0.5
x
10
‐5
mol/L
Try
it
with
your
calculator:
Calculator:
2nd
log
(‐)
5
.
3
enter
pOH
and
Hydroxide
ion
Concentration
 
 
Although
pH
is
used
more
commonly,
in
some
applications
it
is
more
practical
to
describe
hydroxide
ion
concentration.
The
definition
of
pOH
follows
the
same
format
as
pH
pOH
=
‐log
[OH
‐(aq)]
 
[OH
‐(aq)]
=10
–pOH
Example:
Calculate
the
hydroxide
ion
concentration
of
water
with
a
pOH
of
6.3.
[OH
‐(aq)]
=10
–pOH
[OH
‐(aq)]
=10
–
6.3
=
5
x
10‐7
mol/L
Summary
 
 
pH
=
‐log
[H3O+(aq)]
[H3O+(aq)]
=10
–pH
pOH
=
‐log
[OH
‐(aq)]
[OH
‐(aq)]
=10
–pOH
The
number
of
digits
following
the
decimal
point
in
a
pH
or
pOH
value
is
equal
to
the
number
of
significant
digits
in
the
corresponding
hydronium
or
hydroxide
concentration.
For
both
pH
and
pOH,
an
inverse
relationship
exist
between
the
ion
concentration
and
the
pH
or
pOH.
The
greater
the
hydronium
ion
concentration,
the
lower
the
pH
is.
Practice
 
Pg.
242
#4‐7
(pH)
 
Pg.
243
#9‐11
(pOH)