Acid-Base Titration and pH Notes

Aqueous Solutions and the Concept of pH

Main Ideas
- Self-ionization of water forms hydronium and hydroxide ions.
- The concentrations of hydronium and hydroxide ions determine pH and pOH.
- The sum of a solution’s pH and pOH is always 14.
Key Terms
- Self-ionization of water
- pH
- pOH

Self-Ionization of Water

Water undergoes self-ionization, where two water molecules produce a hydronium ion (H_3O^+) and a hydroxide ion (OH^-) by transfer of a proton.
The equilibrium is represented as: H2O(l) + H2O(l) \leftrightarrow H_3O^+(aq) + OH^-(aq)
In pure water at 25°C, the concentrations of hydronium and hydroxide ions are each 1.0 × 10^{-7} mol/L.
Standard notation to show concentration in moles per liter:
- The formula of the particular ion or molecule is enclosed in brackets, [ ].
- For example, the symbol [H3O+] means “hydronium ion concentration in moles per liter,” or “molar hydronium ion concentration.”

Ionization Constant of Water

The mathematical product of [H3O+] and [OH-] remains constant in water and dilute aqueous solutions at constant temperature.
This constant mathematical product is called the ionization constant of water, Kw, and is expressed by the following equation: Kw = [H_3O^+][OH^-]
In water and dilute aqueous solutions at 25°C: Kw = [H3O^+][OH^-] = (1.0 × 10^{-7})(1.0 × 10^{-7}) = 1.0 × 10^{-14}
The ionization of water increases as temperature increases; therefore, the ion product, K_w, also increases as temperature increases.

Neutral, Acidic, and Basic Solutions

In pure water, the hydronium ion and hydroxide ion concentrations are the same; therefore, it is neutral.
Any solution in which [H_3O^+] = [OH^-] is neutral.
Acids increase the concentration of H_3O^+ in aqueous solutions.
Solutions in which the [H_3O^+] is greater than the [OH^-] are acidic.
Bases increase the concentration of OH^- in aqueous solutions.
In basic solutions, the [OH^-] is greater than the [H_3O^+].
At 25°C:
- If the [H_3O^+] is increased to greater than 1.0 × 10^{-7} M, the solution becomes acidic.
- If the [OH^-] is increased to greater than 1.0 × 10^{-7} M, the solution becomes basic.

Calculating [H_3O^+] and [OH^-]

Strong acids and bases are considered completely ionized or dissociated in weak aqueous solutions.
For example, NaOH is a strong base, so 1 mol of it will yield 1 mol of OH^- in an aqueous solution.
- NaOH(s) \rightarrow Na^+(aq) + OH^-(aq)
The K_w of an aqueous solution is a relatively constant 1.0 × 10^{-14} at ordinary room temperatures, the concentration of either ion can be determined if the concentration of the other ion is known.
Kw = [H3O^+][OH^-] = 1.0 × 10^{-14}
[H_3O^+] = \frac{1.0 × 10^{-14}}{[OH^-]}
Increase in either [H_3O^+] or [OH^-] in an aqueous solution causes a decrease in the concentration of the other ion.

Sample Problem A: Calculating Hydronium and Hydroxide Concentrations

A 1.0 × 10^{-4} M solution of HNO_3 has been prepared for a laboratory experiment.
- Calculate the [H_3O^+] of this solution.
- Calculate the [OH^-].
HNO3 is a strong acid, which means that it is essentially 100% ionized in dilute solutions. One molecule of acid produces one hydronium ion. The concentration of the hydronium ions thus equals the concentration of the acid. Because the ion product, [H3O^+][OH^-], is a constant, [OH^-] can easily be determined by using the value for [H3O^+].
- HNO3(l) + H2O(l) \rightarrow H3O^+(aq) + NO3^-(aq)
- (assuming 100% ionization)
- [OH^-] = \frac{1.0 × 10^{-14}}{[H_3O^+]}

The Concentrations of Hydronium and Hydroxide Ions Determine pH and pOH

Expressing acidity or basicity in terms of the concentration of H_3O^+ or OH^- can be cumbersome because the values tend to be very small. A more convenient quantity, called pH, also indicates the hydronium ion concentration of a solution.
The letters pH stand for the French words pouvoir hydrogène, meaning “hydrogen power.”
The pH of a solution is defined as the negative of the common logarithm of the hydronium ion concentration, [H_3O^+].
The pH is expressed by the following equation: pH = -log [H_3O^+]
The common logarithm of a number is the power to which 10 must be raised to equal the number.
Likewise, the pOH of a solution is defined as the negative of the common logarithm of the hydroxide ion concentration, [OH^-].
pOH = -log [OH^-]
The values of [H3O^+] and [OH^-] are related by Kw.
The negative logarithm of K_w at 25°C, 1 × 10^{-14}, is 14.0.
The sum of the pH and the pOH of a neutral solution at 25°C is also equal to 14.0. The following relationship is true at 25°C: pH + pOH = 14.0

The pH Scale

As the concentration of hydronium ions increases, the solution becomes more acidic and the pH decreases.
As the concentration of hydronium ions decreases, the solution becomes more basic and the pH increases.
At 25°C the range of pH values of aqueous solutions generally falls between 0 and 14.
Acidic solutions at 25°C
- The pH of this solution is less than 7
- The pOH is greater than 7.
Basic solutions at 25°C
- the pH is more than 7.0
- the pOH is less than 7.0

The Sum of a Solution’s pH and pOH is Always 14

If either the [H_3O^+] or pH of a solution is known, the other can be calculated.
Because pH represents a logarithm, the number to the left of the decimal only locates the decimal point. It isn’t included when counting significant figures. So there must be as many significant figures to the right of the decimal as there are in the number whose logarithm was found.

Sample Problem B: Calculating pH

What is the pH of a 1.0 × 10^{-3} M NaOH solution?
- NaOH is completely dissociated when it is dissolved in water. A 1.0 × 10^{-3} M NaOH solution therefore produces a [OH^-] equal to 1.0 × 10^{-3} M. The ion product of [H3O^+] and [OH^-] is a constant, 1.0 × 10^{-14}. By substitution, the [H3O^+] can be determined. The pH can then be calculated.

Calculating pH from [H_3O^+]

The pH of a solution is the exponent of the hydronium ion concentration with the sign changed.
Most scientific calculators have a “log” key.

Sample Problem C: Calculating pH

What is the pH of a solution if the [H_3O^+] is 3.4 × 10^{-5} M?
- pH = -log [H_3O^+]. You can convert numbers to logarithms on most calculators by using the “log” key.

Calculating [H_3O^+] and [OH^-] from pH

pH = -log [H_3O^+]
log [H_3O^+] = -pH
[H_3O^+] = antilog (-pH)
[H_3O^+] = 10^{-pH}

Sample Problem D: Calculating Hydronium Concentration Using pH

Determine the hydronium ion concentration of an aqueous solution that has a pH of 4.0.

Sample Problem E: Calculating Hydronium and Hydroxide Concentrations

The pH of a solution is measured and determined to be 7.52.
- What is the hydronium ion concentration?
- What is the hydroxide ion concentration?
- Is the solution acidic or basic?

pH Calculations and the Strength of Acids and Bases

Solutions of weak acids, such as acetic acid, CH3COOH, present a different problem. The [H3O^+] cannot be calculated directly from the molar concentration because not all of the acetic acid molecules are ionized. The same problem occurs for weak bases such as ammonia, NH3. The pH of these solutions must be measured experimentally. The [H3O^+] and [OH^-] can then be calculated from the measured pH values.

Determining pH and Titrations

Main Ideas
- Indicators can determine pH, pOH, and strength.
- Titration is used to determine exact concentrations.
- A standard solution is used to titrate unknowns.

Indicators Can Determine pH, pOH, and Strength

An approximate value for the pH of a solution can be obtained using acid-base indicators.
Acid-base indicators are compounds whose colors are sensitive to pH. In other words, the color of an indicator changes as the pH of a solution changes.
Indicators change colors because they are either weak acids or weak bases.
In solution, a weak-acid indicator (HIn) can be represented by the equation below:
- HIn \leftrightarrow H^+ + In^-
- Because the reaction is reversible, both HIn and In- are present.
- The colors displayed result from the fact that HIn and In- are different colors.
In acidic solutions, any In- ions that are present act as Brønsted bases and accept protons from the acid. The indicator is then present in largely nonionized form, HIn. The indicator has its acid-indicating color.
In basic solutions, the OH^- ions combine with the H^+ ions produced by the indicator. The indicator molecules further ionize to offset the loss of H^+ ions. The indicator is present largely in the form of its anion, In-. The solution now displays the base-indicating color.

Transition Interval

The pH range over which an indicator changes color is called its transition interval.
Different indicators change color at different pH values.
Universal indicators are made by mixing several different indicators.
Paper soaked in universal indicator solution is called pH paper.

pH Meters

If a more precise value for the pH of a solution is needed, a pH meter should be used.
A pH meter determines the pH of a solution by measuring the voltage between the two electrodes that are placed in the solution. The voltage changes as the hydronium ion concentration in the solution changes.

Titration is Used to Determine Exact Concentrations

Neutralization reactions occur between acids and bases. The OH^- ion acquires a proton from the H_3O^+ ion, forming two molecules of water.
- H3O^+(aq) + OH^-(aq) \leftrightarrow 2H2O(l)
Neutralization occurs when hydronium ions and hydroxide ions are supplied in equal numbers by reactants.
Titration is the controlled addition and measurement of the amount of a solution of known concentration required to react completely with a measured amount of a solution of unknown concentration.

Equivalence Point

The point at which the two solutions used in a titration are present in chemically equivalent amounts is the equivalence point.
Indicators and pH meters can be used to determine the equivalence point. The pH will change rapidly as the equivalence point is approached.
The point in a titration at which an indicator changes color is called the end point of the indicator.
Indicators that undergo transition at about pH 7 are used to determine the equivalence point of strong-acid/strong-base titrations because the neutralization of strong acids with strong bases produces a salt solution with a pH of 7.
Indicators that change color at pH lower than 7 are useful in determining the equivalence point of strong-acid/weak-base titrations.
Indicators that change color at pH higher than 7 are useful in determining the equivalence point of weak-acid/strong-base titrations.

A Standard Solution is Used to Titrate Unknowns

If the concentration of one solution is known precisely, the concentration of the other solution in a titration can be calculated from the chemically equivalent volumes.
The solution that contains the precisely known concentration of a solute is known as a standard solution, it is often called simply the “known” solution.
To be certain of the concentration of the known solution, that solution must first be compared with a solution of a primary standard.
A primary standard is a highly purified solid compound used to check the concentration of the known solution in a titration.

Calculating the Molarity of an Acid Solution

Sample Problem F: In a titration, 27.4 mL of 0.0154 M Ba(OH)2 is added to a 20.0 mL sample of HCl solution of unknown concentration until the equivalence point is reached. What is the molarity of the acid solution?
Steps:
- Start with the balanced equation for the neutralization reaction, and determine the chemically equivalent amounts of the acid and base.
- Determine the moles of acid (or base) from the known solution used during the titration.
- Determine the moles of solute of the unknown solution used during the titration.
- Determine the molarity of the unknown solution.