- [Instructor] The autoionization of water refers
to the reaction of water molecules to form two ions,
the hydronium ion, which is H3O+,
and the hydroxide ion, which is OH-.
Water can function as an acid or a base,
and in this reaction,
one water molecule functions as a Bronsted-Lowry acid
and donates a proton
and another water molecule functions
as a Bronsted-Lowry base
and accepts a proton.
In the reaction,
the base takes an H+ ion from the acid
and these two electrons are left behind on this oxygen.
Adding an H+ to H2O gives the hydronium ion H3O+,
and taking away an H+ from H2O gives the hydroxide ion OH-.
We can write an equilibrium constant expression
for this reaction.
So we would write the equilibrium constant K is equal to,
we would start with our products.
We'd have the concentration of hydronium ions.
And since we have a coefficient of one in front of hydronium
in the balanced equation,
it'd be the concentration of hydronium ions
raised to the first power
times the concentration of hydroxide ions.
And once again, there's a coefficient of one,
the balanced equation.
So it's the concentration of hydroxide ions
raised to the first power.
For the reactants,
liquid water is left out
of the equilibrium constant expression.
Normally we would write KC,
where the C stands for concentration
for the equilibrium constant,
since we're dealing with concentrations.
However, this is a special equilibrium constant expression
for the autoionization of water,
so instead of writing KC,
we're gonna write KW,
where W stands for water.
KW is equal to 1.0 times 10 to the negative 14
at 25 degrees Celsius,
And with such a low value for KW,
so this value is much less than one,
that tells us at equilibrium,
we have an extremely small concentration of hydronium
and hydroxide ions.
So mostly we have H2O molecules at equilibrium.
Let's go ahead and solve for the concentration
of hydronium ions and hydroxide ions at equilibrium.
In the balanced equation,
there's a coefficient of one
in front of both hydronium and hydroxide.
Therefore, at equilibrium,
these two concentrations are equal.
Since we don't know what those concentrations are,
we're gonna represent it by writing in here X.
So this would be X times X is equal to 1.0
times 10 to the negative 14.
So we would have X squared is equal to 1.0
times 10 to the negative 14.
And taking the square root of both sides,
we would find that X is equal to 1.0
times 10 to the negative seven.
Therefore, if we had a sample of pure water
at 25 degrees Celsius,
the concentration of hydronium ions
and the concentration of hydroxide ions
would be equal to 1.0
times 10 to the negative seventh molar.
Instead of using two water molecules
to show the autoionization of water,
it's also possible to show it using only one water molecule.
So H2O could break up to form H+ and OH-.
So H+, which is the hydrogen ion,
is sometimes used interchangeably with H3O+,
which is the hydronium ion.
We've just seen that pure water has a concentration
of hydronium ions equal to the concentration
of hydroxide ions.
Therefore, pure water is a neutral substance,
and for any aqueous solution where the concentration
of hydronium ion is equal
to the concentration of hydroxide ion,
we would classify that as a neutral solution.
If an aqueous solution has a concentration
of hydronium ions that's greater than the concentration
of hydroxide ions,
we would classify the solution as an acidic solution.
And if an aqueous solution has a concentration
of hydronium ions that's less than the concentration
of hydroxide ions,
or you could say the concentration of hydroxide ions
is greater than that of hydronium,
the solution would be considered a basic solution.
In the equation that we've already talked about,
the concentration of hydronium ions
times the concentration of hydroxide ions
is equal to KW,
which is equal to 1.0 times 10 to the negative 14
at 25 degrees Celsius.
This equation is true
if you're dealing with an acidic solution,
a neutral solution,
or a basic solution.
And I'll call this equation the KW equation from now on.
Let's say we have an aqueous solution
and the concentration of hydronium ions in the solution
is equal to 4.0 times 10 to the negative six molar
at 25 degrees Celsius,
and our goal is to calculate the concentration
of hydroxide ions in the solution at 25 degrees Celsius.
To solve for the concentration of hydroxide ion,
we can use our KW equation.
So we need to plug in for the concentration
of hydronium ion.
So that gives us 4.0 times 10 to the negative six
times the concentration of hydroxide ion,
which we'll just go ahead and make X here,
and all that's equal to KW,
which is equal to 1.0 times 10 to the negative 14.
Solving for X,
we find the X is equal to 2.5 times 10 to the negative nine.
And since X is equal to the concentration of hydroxide ion,
the concentration of hydroxide ion is equal to 2.5
times 10 to the negative ninth molar.
For this aqueous solution,
the concentration of hydronium ion is greater
than the concentration of hydroxide ion.
Therefore, this is an acidic solution.
So let me go ahead and write that in here.
This is an acidic solution.
An equilibrium constant is only constant
at a specific temperature.
For example, at 25 degrees Celsius,
KW is equal to 1.0 times 10 to the negative 14.
But if you change the temperature,
you change the value for KW.
At 50 degrees Celsius,
KW is equal to 5.5 times 10 to the negative 14.
So an increase in temperature from 25 degrees Celsius
to 50 degrees Celsius causes an increase
in the value for KW.
So increase in temperature causes an increase in KW.
And we can use Le Chatelier's principle to predict
if the autoionization of water is an endothermic reaction
or an exothermic reaction.
An increase in KW means an increased concentration
of hydronium ion and hydroxide ion at equilibrium.
Therefore, the net reaction must have gone to the right
to increase the amount of our products.
And if we treat heat as a reactant
and we increase the temperature,
it's as if we've increased
the amount of one of our reactants.
Therefore, according to Le Chatelier's principle,
the net reaction is gonna shift to the right
to make more of the product.
Since that's what we observed
by increasing the value for KW,
we know that the autoionization of water
is an endothermic reaction.
If we had put heat on the product side
and treated this like an exothermic reaction,
we would've gotten a shift in the wrong direction.
We would've got a shift back to the left.
So we know it's not exothermic.
Finally, let's calculate the concentration of hydronium ions
and hydroxide ions in a sample of pure water
at 50 degrees Celsius.
We can still use the KW equation.
So KW is equal to the concentration of hydronium ions
times the concentration of hydroxide ions.
However, since the temperature is now 50 degrees Celsius,
we can't use 1.0 times 10 to the negative 14
because that's the KW at 25 degrees Celsius.
We need to use the KW at 50 degrees Celsius,
which is 5.5 times 10 to the negative 14.
For the autoionization of water,
the mole ratio of hydronium ion
to hydroxide ion is one-to-one.
Therefore the concentration of hydronium ion
is equal to the concentration of hydroxide ion.
So when we plug in for hydronium,
if we say that concentration is X,
then the concentration of hydroxide would also be X.
So we have X times X is equal to KW,
which is equal to 5.5 times 10 to the negative 14.
So X squared is equal to 5.5 times 10 to the negative 14.
And to solve for X,
we simply take the square root of both sides.
So X is equal to 2.3 times 10 to the negative seven.
So the concentration of hydronium ions
is equal to the concentration of hydroxide ions,
which is 2.3 times 10 to the negative seventh molar.
Notice that this is a higher concentration
than we got at 25 degrees Celsius,
which makes sense because the value for KW has increased.
However, since the concentration of hydronium
is still equal to the concentration of hydroxide ions,
pure water is still neutral.