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21.2: Titration

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Lesson Objectives

The student will:

  • explain what an acid/base indicator is.
  • explain how acid-base indicators work.
  • explain the difference between natural and synthetic indicators.
  • explain how indicators are used in the lab.
  • explain what a titration is.
  • describe how titrations can be used to determine the concentration of an acid or a base in solution.
  • explain the difference between the equivalence point and the end point.
  • define a standard solution in terms of acid-base titrations.
  • calculate the concentration of an acid or base solution using a standard solution.
  • calculate the concentration of unknown acid or base when given the concentration of the other and the volume needed to reach the equivalence point in a titration.

Vocabulary

  • endpoint
  • equivalence point
  • natural indicator
  • standard solution
  • synthetic indicator
  • titrant
  • titration
  • titration curve

Introduction

The typical laboratory procedure for determining the concentration of acid and/or base in a solution is to complete a titration. There are three main types of titration experiments. As we go through this lesson, we will take apply the knowledge we have obtained about acids and bases, chemical reactions, and molarity calculations to the concept of titrations.

Indicators

Recall from the chapter on “Acids-Bases” that an indicator is a substance that changes color at a specific pH and is used to indicate the pH of the solution. One example of an indicator is litmus paper. Litmus paper is paper that has been dipped in a substance that will undergo a color change when it is exposed to either an acid or a base. If red litmus paper turns blue, the solution is basic (pH > 7), and if blue litmus turns red the solution is acidic (pH < 7).

A natural indicator is an indicator that is a naturally occurring substance. For example, the juice from red cabbage can be used to prepare an indicator paper. It contains the chemical anthrocyanin, which is the active ingredient in the indicator. Red beets, blueberries, and cranberries are other great examples of naturally occurring indicators. These are all due to the same anthocyanin molecule found in the red cabbage.

Some flowers are also natural indicators. Hydrangea is a common garden plant with flowers that come in many colors, depending on the pH of the soil. A hydrangea plant with blue flowers indicates that the soil is acidic, while creamy white flowers mean the soil is neutral and pink flowers mean the soil is basic.

Hydrangeas

A hydrangea plant with blue flowers. What does the flower color indicate about the pH of the soil?

Synthetic indicators are compounds created in a chemistry lab rather than compounds found in nature. Both naturally occurring indicators and synthetic indicators are weak organic acids or bases. For example, a common synthetic indicator used in most chemistry laboratories is phenolphthalein. The chemical structure of phenolphthalein is shown in the figure below.

This indicator changes color at a pH of 8.2. Below 8.2 it is colorless, and above 8.2 it is bright pink. There are many common synthetic indicators that are useful in the chemistry laboratory. When dealing with a more acidic range, chemistry students may use methyl orange. The structure for methyl orange is shown below.

Methyl orange changes color from pH 3.2 to 4.4. Below 3.2, the color of the indicator is red. Above 4.4, the color of the indicator is yellow. In between 3.2 and 4.4, there are various shades of orange, hence the name.

There are two requirements for a substance to function as an acid-base indicator: 1) the substance must have an equilibrium affected by hydrogen ion concentration, and 2) the two forms of the compound on opposite sides of the equilibrium must have different colors. Most indicators function in the same general manner and can be presented by a generic indicator equation. In the equation below, we represent in the indicator ion with a hydrogen ion attached as \mathrm{HIn}, and we represent the indicator ion without the hydrogen attached as \mathrm{In}^-.

Since the indicator itself is a weak acid, the equilibrium between the protonated form and the anionic form is controlled by the hydrogen ion concentration. For the example above, the protonated form is colored red and the anionic form is colored yellow. If we add hydrogen ion to the solution, the equilibrium will be driven toward the reactants and the solution will turn red. If we add base to the solution (reduce hydrogen ion concentration), the equilibrium will shift toward the products and the solution will turn yellow. It is important to note that if this indicator changes color at \mathrm{pH} = 5, then at all pH values less than 5, the solution will be red and at all pH values greater than 5, the solution will be yellow. Therefore, putting this indicator into a solution and having the solution turn yellow does NOT tell you the pH of the solution, it only tells you that the pH is greater than 5. At pH values less than 5, the great majority of the indicator molecules are in the red form and the solution will be red. At pH values greater than 5, the great majority of the indicator particles will be in the yellow form and the solution will be yellow. The equilibrium between these indicator particles is such that the particles will be 50% red form and 50% yellow form at exactly \mathrm{pH} = 5. Therefore, at \mathrm{pH} = 5, the actual color of the solution will be a 50-50 mixture of red and yellow particles and the solution will be orange, as demonstrated in the figure below.

Many indicators are available to help determine the pH of solutions. A list of the most common indicators is found in Table below, along with their respective color change pH valuess and corresponding color changes.

Colors and pH Ranges for Common Indicators
Indicator pH Range Color Change
Methyl Violet 0.0~-~1.6 Yellow - Blue
Thymol Blue 1.2~-~2.8 Red - Yellow
Orange IV 1.3~-~3.0 Red - Yellow
Methyl Orange 3.2~-~4.4 Red - Orange
Bromophenol Blue 3.0~-~4.7 Orange/Yellow - Violet
Congo Red 3.0~-~5.0 Blue - Red
Bromocresol Green 3.8~-~5.4 Yellow - Blue
Methyl Red 4.8~-~6.0 Red - Yellow
Litmus 5.0~-~8.0 Red - Blue
Chlorophenol Red 4.8~-~6.2 Yellow - Red
Bromothymol Blue 6.0~-~7.6 Yellow - Blue
Phenol Red 6.4~-~8.2 Yellow - Red/Violet
Thymol Blue 8.0~-~9.6 Yellow - Blue
Phenolphthalein 8.2~-~10.0 Colorless - Pink
Alizarin Yellow R 10.1~-~12.0 Yellow - Red
Methyl Blue 10.6~-~13.4 Blue - Pale Violet
Indigo Carmine 11.4~-~13.0 Blue - Yellow

There are many more indicators than are shown in Table above, but these are ones that you may find in common chemistry classroom laboratories. One example of an indicator not found in the table is known as the universal indicator. The universal indicator is a solution that has a different color for each \mathrm{pH} from 0-14. Universal indicator is produced by creatively mixing many of the individual indicators together so that a different color is achieved for each different pH. It is used for many types of experiments to determine if solutions are acids or bases and where on the pH scale the substance belongs. The chart below indicates the colors of universal indicator for different pH values.

Example:

If the \mathrm{pH} of the solution is 4.8, what would be the color of the solution if the following indicators were added?

  1. Universal indicator
  2. Bromocresol Green
  3. Phenol red

Solution:

  1. Universal indicator = Orange to orange-yellow
  2. Bromocresol Green = green (midway \mathrm{pH} = 4.6)
  3. Phenol red = yellow

Example:

A solution found in the laboratory was tested with a number of indicators. These were the results:

  • Phenolphthalein was colorless
  • Bromocresol green was blue
  • Methyl red was yellow
  • Phenol red was yellow

What was the \mathrm{pH} of the solution?

Solution:

  • Phenolphthalein was colorless, \mathrm{pH} < 8.0
  • Bromocresol green was blue, \mathrm{pH} > 5.4
  • Methyl red was yellow, \mathrm{pH} > 6.0
  • Phenol red was yellow, \mathrm{pH} < 6.4

Therefore, the \mathrm{pH} of the solution must be between 6.0 and 6.4.

The Titration Process

One of the properties of acids and bases is that they neutralize each other. In the laboratory setting, an experimental procedure where an acid is neutralized by a base (or vice versa) is known as titration. Titration is the addition of a known concentration of base (or acid), also called the titrant, to a solution of acid (or base) of unknown concentration. Since both volumes of the acid and base are known, the concentration of the unknown solution is then mathematically determined.

When doing a titration, you need to have a few pieces of equipment. A burette like the one shown below is used to accurately dispense the volume of the solution of known concentration. An Erlenmeyer flask is used to hold a known volume of the solution whose concentration is unknown. A few drops of the indicator are added to the flask before you begin the titration. The endpoint is the point where the indicator changes color, which tells us that the acid is neutralized by the base. The equivalence point is the point where the number of moles of acid exactly equals the number of moles of base.

Some laboratories have \mathrm{pH} meters that measures this point more accurately than the indicator. The diagram below shows a simplified version of a pH meter with the probe from the meter immersed in a mildly alkaline solution (pH = 8.03). The two knobs on the meter are used to calibrate the instrument.

An example of a typical electronic pH meter with the attached probes is shown below. The main purpose of a \mathrm{pH} meter in this experiment is to measure the changes in pH as the titration goes from start to finish.

A typical titration setup is shown below. The burette is upright and ready to drip the solution into the flask holding the solution of unknown concentration and the few drops of indicator. When the indicator changes color, the number of moles of acid equals the number of moles of base and the acid (or base) has been neutralized.

There are three types of titrations that are normally performed in the laboratory in order to determine the unknown concentration of the acid or base. These three types are:

  1. Strong acid vs. Strong base
  2. Strong acid vs. Weak base
  3. Weak acid vs. Strong base

In these titrations, a pH meter may be used to measure the changes in the pH as the titration goes to completion. If so, a titration curve can be constructed. A titration curve is a graph of the pH versus the volume of titrant added. Let’s take a look at how each of these types of titrations differs in terms of their pH curves and their pH at the equivalence point.

(1) Strong Acid vs. Strong Base

For a strong acid vs. a strong base titration, let’s assume the strong base is the titrant. Therefore, the Erlenmeyer flask contains the strong acid and a few drops of your indicator. The initial pH of the solution in the flask will likely be low since the solution is a strong acid. As the base is added, the acid is slowly neutralized. At first the change in pH is minimal. This is due to the fact that the flask has a much greater number of \mathrm{H}_3\mathrm{O}^+ ions than \mathrm{OH}^- ions available from the added titrant.

As more and more base is added, more \mathrm{OH}^- ions are added and thus more \mathrm{H}_3\mathrm{O}^+ ions get neutralized. Let’s stop here and look at the reaction. The equation below shows the total ionic equation of a reaction between a strong acid and a strong base:

\mathrm{H}^+_{(aq)} + \mathrm{Cl}^-_{(aq)} + \mathrm{Na}^+_{(aq)} + \mathrm{OH}^-_{(aq)} \rightarrow \mathrm{Na}^+_{(aq)} + \mathrm{Cl}^-_{(aq)} + \mathrm{H}_2\mathrm{O}_{(l)}

The next equation shows the net ionic equation for the reaction between the strong acid and the strong base:

\mathrm{H}^+_{(aq)} + \mathrm{OH}^-_{(aq)} \rightarrow \mathrm{H}_2\mathrm{O}_{(l)}

As we add more \mathrm{OH}^- ions, more \mathrm{H}_3\mathrm{O}^+ (or \mathrm{H}^+) ions are being neutralized. Since these two ions react to form water, a neutral solution will eventually be formed. For a strong acid and a strong base, this means the \mathrm{pH} = 7.0 at the point of neutralization. If we continue to add the titrant (containing \mathrm{OH}^- ions) after all of the \mathrm{H}_3\mathrm{O}^+ ions have been neutralized, the pH will continue to rise as more base is added and there are excess \mathrm{OH}^- ions.

Now that we know what happens in a strong acid-strong base titration, what does the titration curve look like? The main points described above are shown in the titration curve below.

The points A through D sum up the description of the events that take place during the titration. Point A is the start of the titration. Point B is the midpoint, the point where half of the \mathrm{H}^+ ions have been neutralized. Point D is the equivalence point.

(2) Strong Acid vs. Weak Base

What would happen if we were to titrate a strong acid with a weak base or vice versa? The titration curve for a weak base-strong acid titration is shown below. Try to determine what is happening in the titration just by looking at the graph.

As the acid (the titrant) is added, the pH decreases as the \mathrm{H}_3\mathrm{O}^+ ions begin to neutralize the \mathrm{OH}^- ions. Point D is the equivalence point. Notice that for a weak base and a strong acid titration, the pH at equivalence point is acidic. The equation for the reaction between \mathrm{NH}_3, a weak base, and \mathrm{HCl}, a strong acid, is shown below:

\mathrm{NH}_{3(aq)} + \mathrm{HCl}_{(aq)} \rightarrow \mathrm{NH}_4\mathrm{Cl}_{(aq)} + \mathrm{H}_2\mathrm{O}_{(l)}

The ionic equation is:

\mathrm{NH}_{3(aq)} + \mathrm{H}^+_{(aq)} + \mathrm{Cl}^-_{(aq)} \rightarrow \mathrm{NH}^+_{4(aq)} + \mathrm{Cl}^-_{(aq)} + \mathrm{H}_2\mathrm{O}_{(l)}

(3) Weak Acid vs. Strong Base

The third type of titration is that of a weak acid with a strong base. When we follow through with the same procedure as the previous two titrations, we can determine a great deal of information simply by looking at the pH curve. For example, let’s consider the titration of a solution of acetic acid, \mathrm{HC}_2\mathrm{H}_3\mathrm{O}_2, with a solution of potassium hydroxide, \mathrm{KOH}. We can write the chemical reaction for this acid-base neutralization and begin to draw a rough sketch of a titration curve:

\mathrm{H}^+_{(aq)} + \mathrm{C}_2\mathrm{H}_3\mathrm{O}^-_{2(aq)} + \mathrm{K}^+_{(aq)} + \mathrm{OH}^-_{(aq)} \rightarrow \mathrm{K}^+_{(aq)} + \mathrm{C}_2\mathrm{H}_3\mathrm{O}^-_{2(aq)} + \mathrm{H}_2\mathrm{O}_{(l)}

The points on the curve represent the same points as with the other two titration curves. Look, however, at the equivalence point. Notice how the pH for the equivalence point of the weak acid-strong base titration is above 7.0.

Example:

Draw a rough sketch of the titration curve between nitric acid and ethylamine, \mathrm{CH}_3\mathrm{NH}_2. Assume the acid is in the burette. What is the estimated pH at the equivalence point?

Solution:

The <H at the equivalence point is approximately 4.6 from this graph.

The titrant is the solution of known concentration. For accuracy reasons, this titrant is normally titrated to find its exact concentration before beginning the desired titration. The purpose of this initial titration is to determine, with as much accuracy as possible, the exact concentration of the solution in the burette. To determine the exact concentration of the titrant, we use a standard solution. A standard solution is a solution whose concentration is known exactly. Standard solutions have this property because these chemicals are normally found in pure, stable forms. Examples of chemicals used to prepare standard solutions are potassium hydrogen phthalate, \mathrm{KHC}_8\mathrm{H}_4\mathrm{O}_4 (sometimes referred to as \mathrm{KHP}), and sodium carbonate, \mathrm{Na}_2\mathrm{CO}_3.

When using a standard solution, the standard is first prepared by dissolving the solid in a known volume of water, adding a few drops of indicator, and titrating with the solution that you want to standardize.

Example:

What is the concentration of a sodium hydroxide solution if 32.34 \ \mathrm{mL} is required to neutralize a solution prepared by dissolving 1.12 \ \mathrm{g} of \mathrm{KHC}_8\mathrm{H}_4\mathrm{O}_{4(s)} in 25.00 \ \mathrm{mL} of \mathrm{H}_2\mathrm{O}?

Solution:

Step 1: Find the moles of \mathrm{KHC}_8\mathrm{H}_4\mathrm{O}_4.

moles \mathrm{KHC}_8\mathrm{H}_4\mathrm{O}_4 = \frac {\mathrm{mass}} {\mathrm{molar \ mass}} = \frac {1.12 \mathrm{g}} {204.2 \ \mathrm{g/mol}} = 5.48 \times 10^{-3} \ \mathrm{mol}

Step 2: Use mole ratio from the reaction to find the moles of \mathrm{NaOH}.

\mathrm{KHC}_8\mathrm{H}_4\mathrm{O}_{4(aq)} + \mathrm{NaOH}_{(aq)} \rightarrow \mathrm{KNaC}_8\mathrm{H}_4\mathrm{O}_{4(aq)} + \mathrm{H}_2\mathrm{O}_{(l)}

Since the reaction is 1:1, 1 mole of \mathrm{KHP} reacts with every mole of \mathrm{NaOH}.

\mathrm{mol \ NaOH} = 5.48 \times 10^{-3} \ \mathrm{mol}

Step 3: Determine the concentration of \mathrm{NaOH}.

[\mathrm{NaOH}] = \frac {5.48 \times 10^{-3} \ \mathrm{mol}} {0.03234 \ \mathrm{L}} = 0.170 \ \mathrm{M}

Therefore, the exact concentration of the sodium hydroxide solution used in the titration is 0.170 \ \mathrm{mol/L}.

Choosing an Appropriate Indicator

To choose an appropriate indicator for a titration, a titration curve is useful. Knowing the pH at equivalence for the different types of titrations (see Table below) is also necessary.

pH at Equivalence for Titrations
Type of Titration pH at Equivalence
Strong Acid – Strong Base pH = 7
Strong Acid – Weak Base pH < 7
Weak Acid – Strong Base pH > 7

Choosing an indicator close to the equivalence point is essential to see the point where all of the \mathrm{H}^+ ions and \mathrm{OH}^- ions have been neutralized. The color change should occur on or around the equivalence point. So, for example, with a strong acid-strong base titration, the pH at equivalence is 7.0. Indicators such as bromothymol blue (pH range = 6.0 - 7.6) and phenol red (pH range = 6.6 - 8.0) are common. Notice the midpoint color (green) for bromothymol blue would appear at a pH = 6.8, which is close to 7.0. For phenol red, the midpoint color (orange) would appear at pH = 7.3, again close to 7.0.

The same process is used for other titration types. For a strong acid-weak base titration where the pH at equivalence is less than 7, the indicators normally chosen are methyl red (pH range = 4.8 - 6.0) and chlorophenol red (pH range = 4.8 - 6.2). For a weak acid-strong base titration, where the pH at equivalence is greater than 7, the indicators normally chosen are phenolphthalein (pH range = 8.2 - 10) and thymol blue (pH range = 8.0 - 9.6). As with strong acid-strong base titrations, the visual observation of the indicator's midpoint color should signal close proximity to the equivalence point.

Example:

Look at the graph below and determine the appropriate indicator.

Solution:

We first look at the graph and mark the vertical stretch of the titration curve in order to find the half-way mark on this vertical stretch. Looking at the graph, when we follow this half-way mark over to the y-axis, we can see that the equivalence point occurs at approximately pH = 8.8. The indicator appropriate to use would be phenolphthalein pH range = 8.2 - 10). As soon as the pink color forms, we are at the equivalence point.

There is an interesting observation about the endpoint that has yet to be mentioned. The endpoint was defined earlier as the point where the indicator changes color. In an acid-base neutralization reaction, this point may not be the point where all of the \mathrm{H}^+ ions have been neutralized by \mathrm{OH}^- ions, or vice versa. The experimenter continues titration until the indicator changes color, that is, the endpoint has been reached. The equivalence point is the point where the moles of hydrogen ion and the moles of hydroxide ion are equal. It requires knowledge by the experimenter to select an indicator that will make the endpoint as close as possible to the equivalent point.

The Mathematics of Titration

For the calculations involved here, we will only use our acid and base examples where the stoichiometric ratio of \mathrm{H}^+ and \mathrm{OH}^- is 1:1. To determine the volume required to neutralize an acid or a base, or in other words, to reach the equivalence point, we will use a formula similar to the dilution formula:

M_a \times V_a = M_b \times V_b

where M_a is the molarity of the acid, V_a is the volume of the acid, M_b is the molarity of the base, and V_b is the volume of the base. Note that if the acid and base do not neutralize each other in a 1:1 ratio, this equation does not hold true.

Example:

When 10.0 \ \mathrm{mL} of a 0.125 \ \mathrm{mol/L} solution of hydrochloric acid, \mathrm{HCl}, is titrated with a 0.100 \ \mathrm{mol/L} solution of potassium hydroxide, \mathrm{KOH}, what is the volume of the hydroxide solution required to neutralize the acid? What type of titration is this?

Solution:

Step 1: Write the balanced ionic chemical equation.

\mathrm{H}^+ + \mathrm{Cl}^- + \mathrm{K}^+ + \mathrm{OH}^- \rightarrow \mathrm{K}^+ + \mathrm{Cl}^- + \mathrm{H}_2\mathrm{O}

Step 2: Use the formula and fill in all of the given information.

M_a \times V_a = M_b \times V_b
M_a = 0.125 \ \mathrm{mol/L}
V_a = 10.0 \ \mathrm{mL}
M_b = 0.100 \ \mathrm{mol/L}
V_b = ?
M_a \times V_a = M_b \times V_b
V_b = \frac {M_a \times V_a} {M_b} = \frac {(0.125 \ \mathrm{mol/L})(10.0 \ \mathrm{mL}} {0.100 \ \mathrm{mol/L}} = 12.5 \ \mathrm{mL}

Therefore, for this strong acid-strong base titration, the volume of base required is 12.5 \ \mathrm{mL}.

This video shows the technique for performing a titration using an indicator: http://www.youtube.com/watch?v=9DkB82xLvNE (5:03).

Lesson Summary

  • An indicator is a substance that changes color at a specific pH and is used to indicate the pH of the solution relative to that point.
  • A natural indicator is an indicator that is a naturally occurring substance.
  • Indicators are normally weak organic acids or bases with complicated structures.
  • Universal indicator is a mixture of indicators that produces a different color for each pH from 0 – 14.
  • A titration is the addition of a known concentration of base (or acid) to a solution of acid (or base) of unknown concentration.
  • The titrant is the solution of known concentration. This solution is normally in the burette.
  • The endpoint is the point in the titration where the indicator changes color.
  • The equivalence point is the point in the titration where the number of moles of acid equals the number of moles of base.
  • The three types of titrations usually performed in the laboratory are: strong acid vs. strong base, strong acid vs. weak base, and weak acid vs. strong base.
  • A titration curve is a graph of the pH versus the volume of titrant added.
  • For a strong acid vs. strong base titration, the pH at equivalence is 7.0. For a strong acid vs. weak base titration, the pH at equivalence is less than 7.0. For a weak acid vs. strong base titration, the pH at equivalence is greater than 7.0.
  • A standard solution is a solution whose concentration is known exactly and is used to find the exact concentration of the titrant.
  • For titrations where the stoichiometric ratio of mol \mathrm{H}^+ to mol \mathrm{OH}^- is 1:1, the concentrations or volumes for the unknown acid or base can be calculated with the formula Ma \times Va = Mb \times Vb.

Further Reading / Supplemental Links

The following link is to a video about acid-base neutralization and titration.

The video at the link below shows the lab techniques needed for titration.

This video is a ChemStudy film called “Acid Base Indicators.” The film is somewhat dated but the information is accurate.

Review Questions

  1. Why do you think there would be more experimental error when using an indicator instead of a pH meter during a titration?
  2. Which of the following definitions best suits that of an endpoint?
    1. The stoichiometric point where the number of moles of acid equals the number of moles of base.
    2. The visual stoichiometric point where the number of moles of acid equals the number of moles of base.
    3. The midpoint of the vertical stretch on the titration curve.
    4. None of the above
  3. In the following titration curve, what pair of aqueous solutions would best represent what is shown to be happening in the curve?
    1. \mathrm{HCOOH}_{(aq)} + \mathrm{NH}_{3(aq)}
    2. \mathrm{HCOOH}_{(aq)} + \mathrm{NaOH}_{(aq)}
    3. \mathrm{H}_2\mathrm{SO}_{4(aq)} + \mathrm{Ba(OH)}_{2(aq)}
    4. \mathrm{HClO}_{4(aq)} + \mathrm{NH}_{3(aq)}

  4. What would be the best indicator to choose for the pH curve shown in question 3?
    1. Methyl red
    2. Litmus
    3. Phenolphthalein
    4. Phenol red
  5. What is the best indicator to use in the titration of benzoic acid with barium hydroxide?
    1. Methyl violet, range = 0.0 - 1.6
    2. Bromothymol blue, range = 3.0 - 4.7
    3. Phenolphthalein, range = 8.2 - 10.0
    4. Methyl blue, range = 10.6 - 13.4
    5. Indigo carmine, range = 11.4 - 13.0
  6. If 22.50 \ \mathrm{mL} of a sodium hydroxide solution is necessary to neutralize 18.50 \ \mathrm{mL} of a 0.1430 \ \mathrm{mol/L} \mathrm{HNO}_3 solution, what is the concentration of \mathrm{NaOH}?
    1. 0.1176 \ \mathrm{mol/L}
    2. 0.1430 \ \mathrm{mol/L}
    3. 0.1740 \ \mathrm{mol/L}
    4. 2.64 \ \mathrm{mol/L}
  7. Calculate the concentration of hypochlorous acid if 25.00 \ \mathrm{mL} of \mathrm{HClO} is neutralized by 32.34 \ \mathrm{mL} of a 0.1320 \ \mathrm{mol/L} solution of sodium hydroxide.

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