### Video Transcript

In this video, we will learn how to
calculate the pH of a solution and describe the ion-product constant of water. We’ll also learn how to calculate
the pOH and examine how pH, pOH, and the ion-product constant of water are
related. Before we look at any calculations,
let’s first review acids and bases.

According to the Brønsted–Lowry
definition, an acid is a substance that can lose protons in a reaction. We can think of a Brønsted–Lowry
acid as a hydrogen ion donor. For example, hydrochloric acid can
donate a proton to water to produce H3O+ called hydronium and a chloride ion. On the other hand, a Brønsted–Lowry
base is a substance that can gain protons in a reaction. We can think of a Brønsted–Lowry
base as a hydrogen ion acceptor. An example of a Brønsted–Lowry base
is ammonia. Ammonia can accept a proton from a
water molecule to produce an ammonium ion and OH−, the hydroxide ion.

Notice in the first reaction that
water accepts a hydrogen ion from a hydrochloric acid molecule. Thus, water in this reaction is
acting as a Brønsted–Lowry base. But in the second reaction, water
donates a hydrogen ion to ammonia and is therefore acting as a Brønsted–Lowry
acid. These two reactions show that water
is an amphoteric substance. An amphoteric substance is a
substance that can behave as both an acid and a base. If water can behave as both an acid
and a base, then two water molecules could undergo an acid–base reaction with one
another. One water molecule can act as an
acid and donate a hydrogen ion to the other water molecule acting as a base.

The products of this reaction are
hydronium ions and hydroxide ions. The acid–base reaction between two
water molecules is known as the autoionization of water. This reaction is sometimes
simplified by leaving out one of the water molecules. The reaction written this way shows
the dissociation of water into hydrogen ions and hydroxide ions. Free hydrogen ions don’t
technically exist in solution as they would immediately react with other water
molecules to form hydronium ions. As all hydrogen ions in solution
would immediately be converted into hydronium ions, it’s common in acid–base
chemistry to write H+ as a shorthand for H3O+.

The autoionization of water occurs
in all aqueous samples. However, the equilibrium lies very
far to the left. This means that only a very small
number of water molecules react to produce hydronium and hydroxide ions at any given
time. So we should expect the
concentration of hydronium and hydroxide ions to be quite low. In fact, in a sample of pure water
at 25 degrees Celsius, the concentration of hydronium ions and hydroxide ions is
only 0.0000001 moles per liter, or one times 10 to the negative seventh molar.

Since the autoionization of water
is an equilibrium reaction, the relationship between the equilibrium concentrations
of the products and reactants at a given temperature can be expressed with an
equilibrium constant. For the given reaction, the
following equilibrium expression can be written to calculate the equilibrium
constant. In the reaction equation and
expression, the capital letters represent the chemical formulas of the reactants and
products. The lowercase letters represent the
molar coefficients. And the brackets indicate that we
must use the concentration in moles per liter.

Let’s apply what we know about
equilibrium constants to the autoionization of water. We can substitute hydronium and
hydroxide into the expression for capital C and D and water for capital A and B. The molar coefficients are all
ones. As only a very small amount of
water reacts during autoionization, the concentration of water remains virtually
unchanged, so we can omit water from the expression. Thus, the equilibrium constant for
the autoionization of water is equal to the concentration of hydronium ions times
the concentration of hydroxide ions. This equilibrium constant is given
the symbol K subscript W and is called the ion-product constant.

Equilibrium constants and thus the
ion-product constant are dependent on temperature. We stated earlier in the video that
the concentration of hydronium and hydroxide ions in pure water at 25 degrees
Celsius is one times 10 to the negative seventh molar. We can substitute these
concentrations into the ion-product constant expression to determine that this
constant is equal to one times 10 to the negative 14th at 25 degrees Celsius.

Notice that although we multiplied
two concentrations together, the ion-product constant is given as a dimensionless
value. The reason as to why this is the
case is beyond the scope of this video. We just need to recognize that when
using the ion-product constant expression that the unit of concentration must always
be moles per liter and the ion-product constant will always be reported as a
dimensionless value.

Let’s consider three beakers of
pure water at 25 degrees Celsius. In each beaker, the concentration
of hydronium and hydroxide ions is the same. When the concentrations are equal,
we consider the substance to be neutral. If we add an acid to one of the
beakers, such as hydrochloric acid, the concentration of hydronium ions will
increase. As the ion-product constant is
equal to the concentration of hydronium ions times the concentration of hydroxide
ions, an increase in the hydronium ion concentration must correspond with a decrease
in the hydroxide ion concentration. Thus, acidic solutions will have a
greater concentration of hydronium ions than hydroxide ions.

The opposite is true of basic
solutions. Addition of a base increases the
concentration of hydroxide ions which corresponds to a decrease in the concentration
of hydronium ions. Thus in basic solutions, the
concentration of hydronium ions will be less than the concentration of hydroxide
ions. When using concentrations to
determine if a solution is acidic, basic, or neutral, we tend to focus on the
hydronium ion concentration. So we could also say that when the
hydronium ion concentration is greater than one times 10 to the negative seventh
molar, the solution is acidic. And when the concentration is less
than one times 10 to the negative seventh molar, the solution is basic. Working with hydronium ion
concentrations can be difficult because the values tend to be very small. Shown here is the hydronium ion
concentration of pure water at 25 degrees Celsius and the approximate hydronium ion
concentrations of ammonia and stomach acid.

To simplify working with these
concentrations, Danish chemist Soren Sorensen proposed the use of pH in 1909. pH is
a way to represent the concentration of hydronium ions and is calculated by taking
the negative logarithm of the hydrogen ion concentration. Remember that hydrogen ions are
often used interchangeably with hydronium ions in acid–base chemistry. For the remainder of this video, we
will use hydrogen ions in place of hydronium ions. The pH equation uses a base 10
logarithm. To better understand this function,
let’s consider a number that is a multiple of 10. For example, 1000 is equal to 10
times 10 times 10 or 10 to the third power. The base 10 logarithm of 𝑥 will be
equal to the power to which 10 must be raised in order to obtain the value 𝑥. Since the number 1000 is equal to
10 to the third power, the log of 1000 will be three.

Let’s take a look at the logarithm
of a number less than one. 0.001 is equal to one divided by 10
times 10 times 10 or 10 to the negative third power. Thus, the log of 0.001 is negative
three. Now that we understand the basics
of logarithms, let’s calculate the pH of stomach acid, pure water, and ammonia. We’ll first calculate the logarithm
of the hydrogen ion concentration. This will be a negative value as
each of the concentrations is less than one. Then, since pH is equal to the
negative log of the hydrogen ion concentration, we need to change the sign to give
us the pH values 11, seven, and two.

Notice that although the hydrogen
ion concentration is in molar or moles per liter, the pH is a dimensionless
value. The pH of a solution is easily
measured with a pH meter. If we know the pH, we can easily
calculate the hydrogen ion concentration using the equation hydrogen ion
concentration equals 10 to the negative pH. For example, a cup of coffee has a
pH of approximately five. If we substitute the pH value into
the equation, we get a hydrogen ion concentration of 10 to the negative fifth molar
or 0.00001 molar. Drain cleaner has a pH of
approximately 14. So the hydrogen ion concentration
would be 10 to the negative 14th molar.

Let’s connect what we know about
hydrogen ion concentration, pH, and hydroxide ion concentration. The typical hydrogen ion
concentration of a solution ranges from one times 10 to the negative 14th molar to
one molar. These concentrations correspond to
pH values ranging from zero to 14, what we call the pH scale. The pH scale is often accompanied
by a chart that shows the color of a solution with a particular pH to which
universal indicator has been added. We already know that pure water is
considered neutral. Solutions with a greater hydrogen
ion concentration than pure water are acidic. And solutions that have a lower
hydrogen ion concentration than pure water are basic. So solutions with a pH of seven are
neutral, solutions with a pH less than seven are acidic, and solutions with a pH
greater than seven are basic.

Let’s add hydroxide ion
concentration to the chart. If we assume the temperature is 25
degrees Celsius, we can set the ion-product constant expression equal to one times
10 to the negative 14th. To calculate the hydroxide ion
concentration of coffee, we substitute the hydrogen ion concentration into the
equation and rearrange to solve. The numerical answer is one times
10 to the negative ninth. We should recognize that although
the ion-product constant is dimensionless, the concentration of hydroxide ions
should have the unit of molarity. Using the ion-product constant
expression, we can calculate all of the hydroxide ion concentrations.

We can simplify the hydroxide ion
concentration by using pOH. pOH is equal to the negative logarithm of the
concentration of hydroxide ions. So the pOH of drain cleaner is
equal to the negative logarithm of one which is zero. And the pOH of ammonia is equal to
the negative logarithm of one times 10 to the negative three which is equal to
three. We can use the pOH equation to fill
in the rest of the chart. We know we can calculate the
hydrogen ion concentration if the pH is known. Likewise, we can calculate the
hydroxide ion concentration if the pOH is known using the equation concentration of
hydroxide ions equals 10 to the negative pOH.

We can see from the chart that
neutral solutions have a hydroxide ion concentration of one times 10 to the negative
seventh molar and a pOH of seven. The acidity of a solution increases
with decreasing hydroxide ion concentration and increasing pOH, while the basicity
of a solution increases with increasing hydroxide ion concentration and decreasing
pOH. We may also notice from the chart
that the sum of the pH and pOH of a solution is equal to 14. This equation allows us to easily
relate the pH and pOH.

Altogether, PH, pOH, hydrogen ion
concentration, and hydroxide ion concentration can be related to one another via six
different equations. If only one quantity is known, the
remaining three can be determined. It’s important to recognize that
the relationships pH plus pOH equals 14 and hydrogen ion concentration times
hydroxide ion concentration equals one times 10 to the negative 14th only hold true
when the solution is at 25 degrees Celsius.

Now let’s summarize what we’ve
learned. The autoionization of water is an
acid–base equilibrium reaction between two water molecules. This reaction can be expressed by
the ion-product constant, which is equal to one times 10 to the negative 14th at 25
degrees Celsius. pH is a representation of the concentration of hydronium ions in
solution. In acid–base chemistry, hydrogen
ions are often used in place of hydronium ions. If the pH is known, we can
determine the hydrogen ion concentration by taking 10 to the negative pH. pOH is a
representation of the hydroxide ion concentration.

As with hydrogen ion concentration
and pH, we can determine the hydroxide ion concentration from the pOH. At 25 degrees Celsius, the sum of
the pH and pOH will be 14. Solutions with an equal
concentration of hydrogen ions and hydroxide ions will have a pH and pOH of seven
and are neutral. Solutions with a greater
concentration of hydrogen ions than hydroxide ions will have a pH less than seven, a
pOH greater than seven, and are acidic. Solutions that have a greater
concentration of hydroxide ions than hydrogen ions will have a pH greater than
seven, a pOH less than seven, and are basic.