7.03 pH
Sample Data Table: What is being measured // Measurement Initial volume of titrant // 0.0 mL NaOH Final volume of titrant // 25.0 mL NaOH Molarity of titrant // 0.50 M NaOH Volume of solution in flask // 15.0 mL H2SO4 2 NaOH + H2SO4 → 2 H2O + Na2SO4 Use subtraction to determine the amount of titrant added from the buret into the flask. final volume of titrant − initial volume of titrant = volume of titrant used 25.0 mL NaOH - 0.0 mL NaOH = 25.0 mL NaOH Starting with the volume of titrant added and the known molarity of the titrant, you can use stoichiometry to solve for the molarity of the substance in the flask. volume of titrant (mL) = 1 L NaOH /1000 mL titrant x ? mol titrant / 1 L titrant x mol other reactant / mol titrant = moles of the reactant in the flask 25.0 mL NaOH x 1 L titrant / 1000 mL titrant x 0.50 mol NaOH / 1 L titrant x 1 mol H2SO4 / 2 mol NaOH = 0.00625 mol H2SO4 Once you have solved for the moles of solute in the flask, divide the moles by the measured volume of the solution in the flask to determine the unknown molarity of the solution in the flask. moles of reactant (calculated above) / volume (L) of solution in the flask = concentration (M) of the solution in the flask 0.00625 mol H2SO4 / 0.0150 L H2SO4 solution = 0.42 M H2SO4
Example Problem with Data
Water has the ability to behave as both an acid and as a base, depending on the properties of the other reactant. This means that water molecules can react with each other in a sample of pure water. One water molecule, acting as an acid, donates a hydrogen ion to another water molecule, acting as a base. This reaction forms a hydroxide ion and a hydronium ion, which can also react together to re-form the water molecules.
H2O
When water molecules react together, equal numbers of hydroxide and hydronium ions are formed. This means that in pure water, the concentrations of hydroxide and hydronium ions are equal, making the solution neutral. Experiments have revealed that the concentrations of hydroxide and hydronium ions in pure water are extremely low, around 0.0000001 molar for each at room temperature. This is why pure water behaves as a very weak acid or base, and is also a very poor electrolyte. Water is neutral because it contains equal amounts of hydroxide and hydronium ions, not because of the low concentrations of these ions. The acidic, basic, or neutral property of a solution is determined by the balance between the hydronium and hydroxide ions in the solution. When the concentrations of the hydronium and hydroxide ions are equal, the solution is neutral. H3O+ and OH- are balanced In an acidic solution, the concentration of hydronium ions is greater than the concentration of hydroxide ions. Adding an acid, such as hydrochloric acid, to pure water will increase the concentration of hydronium ions present. In an acidic solution, the concentration of hydronium ions is greater than the concentration of hydroxide ions. Adding an acid, such as hydrochloric acid, to pure water will increase the concentration of hydronium ions present. When the hydronium ion concentration is greater than the hydroxide ion concentration, the solution is acidic. H3O+ is greater than the OH-
H2O + H2O ⇄ OH- + H3O+
1. Use subtraction to determine the amount of titrant added from the buret into the flask. final volume of titrant − initial volume of titrant = volume of titrant used 2. Starting with the volume of titrant added and the known molarity of the titrant, you can use stoichiometry to solve for the molarity of the substance in the flask. volume of titrant (mL) = 1 L NaOH /1000 mL titrant x ? mol titrant / 1 L titrant x mol other reactant / mol titrant = moles of the reactant in the flask 3. Once you have solved for the moles of solute in the flask, divide the moles by the measured volume of the solution in the flask to determine the unknown molarity of the solution in the flask. moles of reactant (calculated above) / volume (L) of solution in the flask = concentration (M) of the solution in the flask
More on Titration
In a basic solution, the concentration of hydroxide ions is greater than the concentration of hydronium ions. Adding a base, such as ammonia, to pure water will increase the concentration of hydroxide ions present. When the hydroxide ion concentration is greater than the hydronium ion concentration, the solution is basic. OH- is greater than the H3O+
NH3 + H2O → NH4+ + OH-
What is the concentration of hydronium ions in a solution with a pH of 6.3? [H3O+] = 10^-6.3 [H3O+] = 5.0 × 10^-7 M
Practice Problem #1
What is the pH of a solution with a concentration of 6.8 x 10^-4 molar H3O+? pH = -log [6.8 × 10^-4] pH = 3.17
Practice Problem #1
What is the concentration of hydroxide ions in a solution with a pH of 12.6? [H3O+] = 10^-12.6 [H3O+] = 2.51 × 10^-13 M [OH-] = 1.0 x 10 ^-14 / H3O- [OH-] = 1.0 x 10^-14 / 2.51 x 10^-13 [OH-] = 3.98 × 10^-2 M
Practice Problem #2
What is the pH of a solution with a concentration of 4.2 x 10^-5 molar OH-? Formula: [H3O+] × [OH-] = 1.0 × 10^-14 M Rearrange to solve for [H3O+]: [H3O+] = 1 x 10^-14 M / [OH-] Plug in [OH-] from the problem: [H3O+] = 1 x 10^-14 M / 4.2 x 10^-5 M [H3O+] = -2.4 × 10^-10 M Solve for pH: pH = -log [H3O+] pH = -log (-2.4 × 10^-10 M) pH = 9.62
Practice Problem #2
Pure water is considered neutral pH with regards to being acidic or basic. The gaining and losing of hydrogen atoms is balanced in pure water. Thus, pure water is the standard for determining if something is acidic (more hydronium ions than pure water, H3O+) or basic (more hydroxyl ions than pure water, OH-).
Pure Water
orange juice: 2-4 toilet cleaner: 8-10 window cleaner: 11-14 deodorant: 2-4 milk: 5-6 detergent: 8-10 vinegar: 2-4 distilled water: 7 dish soap: 8-10 drain cleaner: 11-14
Substances with pH values greater than 7 are basic, equal to 7 are neutral, and less than 7 are acidic.
Titration is a laboratory method that allows you to determine the precise amount of one reactant needed to react with a given amount of another reactant. A buret is a long, narrow piece of glassware that is used to deliver small amounts of one reactant to a flask containing the other reactant. The bottom of the buret can be adjusted, using the stopcock, to release a small stream of liquid or add the reactant drop by drop. This allows you to carefully add the reactant until you reach the end of the reaction. For an acid-base titration, an acid-base indicator or pH meter is used to determine when you have reached the end of the reaction, called the endpoint. You will begin a titration by preparing the buret. The buret should be cleaned, and then it should be rinsed with small amounts of the solution that will be used in the buret during the titration. Once the buret has been cleaned and rinsed, you can fill the buret with the solution that will be used in the titration. The solution that is added to a reaction from a buret is often referred to as the titrant. Once you have filled the buret, it is important to remove all air bubbles and to make sure the dropper end of the buret is filled with solution as well. This will ensure that your volume readings are accurate. It is important to record the initial volume of solution in the buret in your data table or notebook before the titration begins. Next, you will prepare the second solution and pour it into an Erlenmeyer flask. Be sure to record all of the measurements regarding this solution, such as volume or mass, in your data table or notebook. If an acid-base indicator will be used to determine the end point of the reaction, a few drops of the indicator should be added to the flask as well. Different indicators work at different pH ranges, so it is important to choose an indicator that will work well for the reaction being examined. Acid-base indicators are weak acid or base dyes that are sensitive to changes in pH. Indicators change color at certain pH values, so it is important to choose the correct indicator when performing a titration. Universal indicators, like the pH paper you used in the introduction, are actually a mixture of several indicators that can identify a range of pH values. This table gives some commonly used acid-base indicators and the pH range where they change color. Indicator // Color at lower pH // Color at higher pH // Range when color change occurs Phenolphtalein // colorless // pink // 8.2-10.6 Litmus // red // blue // 5.5-8.0 Bromothymol blue // yellow // blue // 6.0-7.6 When you start combining the reactants, use the buret to deliver a few milliliters of titrant to the flask at a time. You will see the indicator change color when the titrant first contacts the solution in the flask, but the color change disappears upon stirring. As the color change begins to linger, it is time to slow down the addition of the titrant and carefully add it drop by drop. Be sure to constantly stir the solution inside the flask by carefully moving the flask in small circles as the titrant is being added. If any titrant from the buret drips down the inside wall of the Erlenmeyer flask, you may use a wash bottle filled with distilled water to rinse the sides of the flask. This helps ensure that all of the titrant that leaves the buret is added to the mixture in the flask. Make sure you know what the endpoint should look like. When using the indicator phenolphthalein, the endpoint is the first very pale, but permanent, pink. The color change should stay after the solution has been stirred for 10 seconds, but it should be so light that you may need to hold a piece of white paper behind the flask to notice the color change. When you have reached the endpoint, read the final volume in the buret and record it in your data table or notebook. Remember, the buret's scale is opposite of the graduated cylinder, so the volume will be larger than your initial volume. Titration with a pH meter follows the same procedure as a titration with an indicator, except that the endpoint is detected by a rapid change in pH, rather than the color change of an indicator. If the titration is between a strong acid and strong base, the endpoint is reached when the pH is 7.0.
Titration
When you are given to concentration of hydronium ions in a solution, or the concentration of a strong acid (assumed to ionize 100%), you can determine the pH by using the following formula: pH = -log [H3O+] For example: We can determine the pH of a 1.2 × 10-3 molar nitric acid solution by plugging into the formula above, because nitric acid is a strong acid that will ionize 100% to produce 1.2 × 10-3 molar H3O+. pH = -log [1.2 × 10-3] pH = 2.92 Be sure to notice that there is a negative sign in the formula for calculating pH values. In most cases, the pH value will come out to be a positive number. If the concentration of hydronium ions is high, the pH value may come out to be less than zero. When you are given the concentration of hydroxide ions in a basic solution, you can use that value to find the concentration of the hydronium ions present using the following relationship: [H3O+] × [OH-] = 1.0 × 10-14 M The value 1.0 × 10-14 is called the ionization constant of water. The relationship above can be used to compare the hydronium and hydroxide ion concentrations in any aqueous solution at 25°C. For example, we can determine the pH of a 2.3 × 10-2 molar NaOH solution by first using the hydroxide ion concentration to determine the hydronium ion concentration in the solution. NaOH is a strong base that ionizes completely in water, so the concentration of the base is equal to the concentration of the hydroxide ions in the solution. Dividing the ionization constant of water by the concentration of the hydroxide ions will give you the concentration of hydronium ions in the same solution. [H3O+] × [OH-] = 1.0 × 10-14 M [H3O+] = 1.0 x 10^-14 / [OH -] [H3O+] = 1.0 x 10^-14 / 2.3 x 10^-2 [H3O+] = 4.3 × 10^-13 M H3O+ pH = -log [4.3 × 10^-13] pH = 12.4 Notice that the concentrations of hydronium and hydroxide are inversely related—the higher the concentration of one, the lower the concentration of the other.
Using Concentration to Solve for pH
When you are given the pH value of a solution, this value is a logarithm. To determine the concentration of hydronium ions from a given pH, you must take the negative antilogarithm of the pH value. [H3O+] = 10^-pH For example, we can determine the concentration of hydronium and hydroxide ions in a solution that has a pH of 2.3 by plugging into the formula above. [H3O+] = 10^-2.3 [H3O+] = 0.0050 M Using the ionization constant of water, we can use the concentration of hydronium ions to determine the concentration of hydroxide ions in the solution.
Using pH to solve for concentration
Acidic Solution: [H3O+] > [OH-] Neutral Solution:[H3O+] = [OH-] Basic Solution: [H3O+] < [OH-]
comparing the properties of acidic, basic, and neutral solutions... (brackets are used to represent concentration in molarity)
In addition to describing a solution as acidic, basic, or neutral, scientists use numerical values to express the acidity of a solution in more detail. Because the concentrations of hydronium and hydroxide ions in a solution can vary greatly, chemists use values called pH to conveniently express a solution's hydronium ion concentration. The letters pH stand for the French words pouvoir hydrogène, meaning "hydrogen power." The pH scale is a numeric scale used to indicate the hydronium ion concentration of a solution. The pH of a solution is determined by calculating the negative base-10 logarithm of the hydronium ion concentration (in molarity). According to the Brønsted-Lowry definition of acids and bases, acids increase the concentration of hydronium ions in a solution by donating hydrogen ions, while bases decrease the concentration of hydronium ions by accepting hydrogen ions. This means that the acidic or basic nature of a substance can both be measured and described by its hydrogen ion, or hydronium ion, concentration. This is why pH values can be used to describe acidic and basic solutions, even though the values are calculated using the concentration of hydronium ions. The range of pH values of aqueous solutions generally falls between 0 and 14, which is a more reasonable range for comparison than the possible range of concentrations. The pH scale and its values are dependent on temperature, so we will be comparing and calculating pH values at 25 degrees Celsius. The pH of a neutral solution, when the concentrations of hydroxide and hydronium ions are equal, at 25°C is 7.0. When the amount of hydronium ions is greater than the amount of hydroxide ions in the solution, the solution is acidic and will have a pH value that is lower than 7.0. In a basic solution, the amount of hydroxide ions is greater than the amount of hydronium ions, and the pH will be greater than 7.0. Refer to the pH scale to compare the pH values of some common solutions. Notice that as the concentration of hydronium ions increases, the pH value decreases (becomes more acidic). It can be easy to confuse this, so be careful when you use the pH scale or compare pH values.
pH Scale
pH = -log [H3O+] (brackets are used to represent concentration in molarity)
pH of a Solution
