Lesson Video: Calculating pH | Nagwa Lesson Video: Calculating pH | Nagwa

# Lesson Video: Calculating pH Chemistry

In this video, we will learn how to calculate the pH of a solution and describe the ion-product constant of water.

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### 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.