Acid-base titration

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Intros
Lessons
1. What is titration?
2. How titration works
3. Finding unknown concentration: titration calculations.
4. Titrations with partial neutralization.
5. Percentage purity.
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Examples
Lessons
1. Determine the unknown concentration from acid-base titration results:
A solution of KOH of unknown concentration was titrated by 0.3 M hydrochloric acid. The results below show the volume of HCl required to titrate 25cm3 of the KOH solution:

 Run: Titre volume (cm3) 1 18.60 2 18.35 3 18.40
1. Which two of these readings are concordant and should be used to find the average titre?
2. Calculate the average titre for this experiment.
1. Use your average titre to find the concentration of the potassium hydroxide (KOH) solution.
2. Use an acid-base titration to calculate percentage purity of a sample.
1.17g of sodium hydroxide pellets were used to make a 250mL solution of NaOH. 25.00 mL of this solution was titrated by 0.096 M HNO3, with an average titre of 27.75 mL.

Use this information to find the percentage purity of the sodium hydroxide sample.

Introduction to Acid-Base Titration

Acid-base titration is a fundamental chemistry experiment that plays a crucial role in quantitative analysis. This precise technique allows chemists to determine the concentration of an unknown acid or base solution by neutralizing it with a standard solution of known concentration. The importance of titration in chemistry cannot be overstated, as it forms the basis for numerous analytical procedures in research, industry, and environmental monitoring. Our introductory video provides a visual demonstration of this essential process. In this article, we'll delve into the basics of acid-base titration, exploring the underlying principles and step-by-step procedures. We'll also cover the calculations involved in interpreting titration results, including how to determine equivalence points and calculate unknown concentrations. Finally, we'll examine the wide-ranging applications of titration in various fields, from pharmaceutical quality control to food and beverage analysis, highlighting its significance in real-world scenarios.

Understanding Acid-Base Titration

Acid-base titration is a fundamental analytical technique in chemistry used to determine the concentration of an unknown acid or base solution. This method relies on the principle of neutralization, where an acid and a base react to form water and a salt. The purpose of acid-base titration is to precisely measure the amount of acid or base needed to reach the point of neutralization, also known as the stoichiometric point or equivalence point.

The basic principles involved in acid-base titration revolve around the concept of neutralization. When an acid and a base are combined, they react to form water and a salt. This reaction continues until one of the reactants is completely consumed. The point at which the acid and base have reacted in exactly the right proportions to neutralize each other is called the stoichiometric point.

To perform an acid-base titration, several pieces of equipment are essential. The primary apparatus used is the burette, a long, graduated glass tube with a stopcock at the bottom. The burette allows for the precise delivery of small volumes of solution. A pipette is used to measure and transfer a specific volume of the solution being analyzed. Other equipment includes an Erlenmeyer flask to hold the solution being titrated, a magnetic stirrer for continuous mixing, and a pH meter or indicator for detecting the endpoint.

The concept of neutralization is central to acid-base titration. When an acid and a base react, they form water and a salt. The pH of the solution changes as the titration progresses, starting from either acidic or basic and moving towards neutral. The point of neutralization occurs when the number of moles of acid equals the number of moles of base, resulting in a pH of 7 for strong acid-strong base titrations.

An indicator is often used to visually signal when the neutralization point has been reached. Indicators are substances that change color at specific pH values. Common indicators include phenolphthalein, which turns from colorless to pink in basic solutions, and methyl orange, which changes from red in acidic solutions to yellow in basic solutions.

Performing an acid-base titration requires a step-by-step approach with an emphasis on precision. Here's a general procedure:

1. Prepare the burette by rinsing it with the titrant (the solution of known concentration) and then filling it to the zero mark.
2. Using a pipette, measure a precise volume of the analyte (the solution of unknown concentration) into an Erlenmeyer flask.
3. Add a few drops of indicator to the analyte in the flask.
4. Place the flask under the burette and begin adding the titrant slowly while swirling the flask to ensure thorough mixing.
5. As you approach the endpoint, add the titrant drop by drop, watching for the color change of the indicator.
6. Stop adding titrant as soon as the indicator changes color and remains changed for at least 30 seconds.
7. Record the volume of titrant used from the burette reading.
8. Repeat the titration at least three times to ensure reproducibility and calculate the average volume used.

Precision is crucial in acid-base titration. Even small errors in measurement can lead to significant inaccuracies in the final result. It's important to read the burette at eye level to avoid parallax errors and to add the titrant slowly near the endpoint to avoid overshooting. The use of a white background can help in observing color changes more clearly.

The data obtained from the titration can be used to calculate the concentration of the unknown solution using stoichiometric relationships. This involves considering the balanced chemical equation for the neutralization reaction and applying concepts of molarity and volume.

Acid-base titration finds applications in various fields, including environmental analysis, quality control in industries, and medical diagnostics. It's used to determine the acidity of foods, analyze water quality, and in the production of pharmaceuticals. The principles of acid-base titration also form the foundation for more complex titration techniques used in analytical chemistry.

In conclusion, acid-base titration is a powerful and precise method for quantitative analysis in chemistry.

Titration Calculations

Titrations are fundamental analytical techniques in chemistry used to determine the concentration of an unknown solution. The mathematical calculations involved in titrations are crucial for accurate results and rely on the principle of stoichiometry. Understanding these calculations is essential for students and professionals working in chemistry and related fields.

The core equation used in titration calculations is c1v1 = c2v2, where c represents concentration and v represents volume. This equation is based on the concept that the number of moles of the reactant in the titrant (the solution of known concentration) is equal to the number of moles of the reactant in the analyte (the solution of unknown concentration) at the equivalence point.

To determine the concentration of an unknown solution, you need to know the concentration and volume of the titrant, as well as the volume of the analyte used. Let's walk through an example to illustrate this process:

Suppose we have 25.0 mL of an unknown concentration of hydrochloric acid (HCl) that is titrated with 0.100 M sodium hydroxide (NaOH). If it takes 20.0 mL of NaOH to reach the endpoint, we can calculate the concentration of HCl as follows:

c1v1 = c2v2
(0.100 M NaOH)(20.0 mL) = (x M HCl)(25.0 mL)
2.00 mmol = 25.0x mmol
x = 0.0800 M HCl

This calculation demonstrates how we can use the known concentration and volume of NaOH to determine the unknown concentration of HCl. The molar ratio between the reactants is crucial in these calculations, which is why balanced chemical equations are so important in titration math.

Balanced chemical equations provide the stoichiometric ratios between reactants and products. In the case of the HCl and NaOH reaction, the balanced equation is:

HCl + NaOH NaCl + H2O

This 1:1 ratio allows us to use the c1v1 = c2v2 equation directly. However, not all titrations have a 1:1 ratio. For example, consider the titration of sulfuric acid (H2SO4) with sodium hydroxide:

H2SO4 + 2NaOH Na2SO4 + 2H2O

In this case, the molar ratio is 1:2, which means we need to adjust our calculations accordingly. Let's look at an example:

If 30.0 mL of 0.150 M NaOH is required to neutralize 25.0 mL of H2SO4, we calculate the concentration of H2SO4 as follows:

(0.150 M NaOH)(30.0 mL) = (2)(x M H2SO4)(25.0 mL)
4.50 mmol NaOH = 50.0x mmol H2SO4
x = 0.0900 M H2SO4

Note the factor of 2 in the equation, which accounts for the 1:2 molar ratio between H2SO4 and NaOH. This example highlights the importance of using balanced chemical equations to determine the correct stoichiometric relationships in titration calculations.

The molar ratio concept is not limited to acid-base titrations. It applies to all types of titrations, including redox reactions, complexometric titrations, and precipitation reactions. In each case, the balanced chemical equation provides the necessary information to perform accurate calculations.

For instance, in a redox titration of Fe2+ with MnO4-, the balanced equation is:

5Fe2+ + MnO4- + 8H+ 5Fe3+ + Mn2+ + 4H2O

Polyprotic Acids in Titration

Polyprotic acids are a fascinating class of compounds that play a crucial role in various chemical processes, particularly in titration experiments. These acids are characterized by their ability to donate multiple protons (hydrogen ions) in aqueous solutions, making them distinct from monoprotic acids. Understanding polyprotic acids is essential for chemists, biochemists, and environmental scientists, as they are prevalent in nature and have significant implications in analytical chemistry.

One of the key features of polyprotic acids is their stepwise dissociation, which leads to multiple dissociation constants. This property significantly affects titration experiments, as it results in multiple endpoints during the neutralization process. For instance, phosphoric acid (H3PO4), a common example of a polyprotic acid, has three dissociable protons, each with its own dissociation constant (Ka1, Ka2, and Ka3).

The concept of partial neutralization is crucial when dealing with polyprotic acids. As a strong base is added to a polyprotic acid solution, the acid undergoes stepwise neutralization. This process leads to the formation of intermediate species, each with its own pH range. In the case of phosphoric acid, the first proton is neutralized to form dihydrogen phosphate (H2PO4-), then hydrogen phosphate (HPO4^2-), and finally phosphate (PO4^3-).

Titration curves for polyprotic acids exhibit multiple inflection points, corresponding to each proton dissociation. These points represent the partial neutralization stages and are critical for determining the equivalence points. However, identifying these endpoints can be challenging, especially when the dissociation constants are close in value. This complexity often requires advanced techniques and careful analysis to accurately determine each endpoint.

The challenges in titrating polyprotic acids arise from several factors. Firstly, the overlapping of buffer regions between successive dissociations can make it difficult to distinguish individual endpoints. Secondly, the strength of each acidic proton varies, with the first proton typically being the strongest and subsequent protons becoming progressively weaker. This variation affects the sharpness of the pH change at each endpoint, making some transitions more subtle than others.

To illustrate these concepts, let's consider the titration of phosphoric acid with sodium hydroxide. The first endpoint occurs when one mole of NaOH has been added per mole of H3PO4, forming NaH2PO4. The second endpoint is reached when two moles of NaOH have been added, resulting in Na2HPO4. The final endpoint occurs after the addition of three moles of NaOH, forming Na3PO4. Each of these stages has a distinct pH range and buffer capacity.

The practical implications of polyprotic acids in titration experiments are significant. They require careful selection of indicators or the use of potentiometric methods to accurately determine all endpoints. In some cases, only the first or second endpoint may be practically measurable, depending on the relative strengths of the acid dissociations. This limitation can affect the accuracy of quantitative analysis and must be considered when designing experimental procedures.

Understanding polyprotic acids and their behavior in titrations is not only important for analytical chemistry but also has broader applications. In biochemistry, many important biological molecules, such as amino acids and nucleic acids, are polyprotic. In environmental science, the behavior of polyprotic acids is crucial for understanding water chemistry, soil pH, and the cycling of nutrients in ecosystems.

In conclusion, polyprotic acids present both challenges and opportunities in titration experiments. Their stepwise dissociation, partial neutralization, and multiple endpoints require a nuanced approach to analysis. By mastering the concepts related to polyprotic acids, chemists can more accurately interpret titration data, design better analytical methods, and gain deeper insights into complex chemical systems. Whether in the laboratory or in natural environments, the principles of polyprotic acid titration curves continue to be fundamental to our understanding of acid-base chemistry and its wide-ranging applications.

Percentage Purity Determination

Titration is a powerful analytical technique used to determine the percentage purity of a sample by comparing the expected concentration with the actual concentration obtained through the titration process. This method is particularly useful in identifying the presence and quantity of impurities in a given substance.

To begin, it's essential to understand that percentage purity refers to the amount of pure substance present in a sample, expressed as a percentage. Impurities can significantly affect the properties and reactivity of a compound, making their identification and quantification crucial in various fields, including chemistry, pharmaceuticals, and quality control.

The process of determining percentage purity through titration involves several steps:

1. Prepare a solution of known concentration (the standard solution) and the sample solution of unknown purity.
2. Perform the titration, carefully measuring the volume of standard solution required to reach the endpoint.
3. Calculate the actual concentration of the sample based on the titration results.
4. Compare the actual concentration with the expected concentration to determine the percentage purity.

Calculating the expected concentration versus the actual concentration is a critical step in this process. The expected concentration is based on the assumption that the sample is 100% pure, while the actual concentration is derived from the titration results. Here's a step-by-step guide to performing these calculations:

1. Calculate the expected number of moles of the substance based on its mass and molecular weight, assuming 100% purity.
2. Determine the actual number of moles reacted during the titration using the volume and concentration of the standard solution.
3. Calculate the actual concentration by dividing the actual number of moles by the volume of the sample solution.
4. Compare the actual concentration to the expected concentration to determine the percentage purity.

Let's walk through an example to illustrate this process:

Suppose we have a 2.5 g sample of impure sodium hydroxide (NaOH) dissolved in 250 mL of water. We titrate this solution against 0.1 M hydrochloric acid (HCl), and it takes 45 mL of HCl to reach the endpoint.

Step 1: Calculate the expected concentration (assuming 100% purity)
Moles of NaOH = 2.5 g ÷ 40 g/mol = 0.0625 mol
Expected concentration = 0.0625 mol ÷ 0.250 L = 0.25 M

Step 2: Calculate the actual concentration based on titration results
Moles of HCl used = 0.1 M × 0.045 L = 0.0045 mol
Moles of NaOH (actual) = 0.0045 mol (1:1 ratio with HCl)
Actual concentration = 0.0045 mol ÷ 0.250 L = 0.018 M

Step 3: Calculate the percentage purity
Percentage purity = (Actual concentration ÷ Expected concentration) × 100
Percentage purity = (0.018 M ÷ 0.25 M) × 100 = 72%

In this example, we can conclude that the sodium hydroxide sample is 72% pure, with the remaining 28% consisting of impurities. This information is valuable for assessing the quality of the sample and determining its suitability for various applications.

Titration-based percentage purity determination is a versatile and accurate method for analyzing the composition of chemical samples. By comparing the expected concentration with the actual concentration obtained through careful titration, chemists and researchers can gain valuable insights into the purity of substances and the presence of impurities. This technique finds applications in diverse fields, from quality control in manufacturing to environmental monitoring and pharmaceutical research.

Applications and Importance of Titration

Acid-base titration is a fundamental technique in analytical chemistry with widespread applications across various industries. This versatile method plays a crucial role in quality control and analysis, making it an indispensable tool for researchers and professionals alike. In environmental science, titrations help monitor water quality by measuring acidity levels in lakes, rivers, and soil samples. This information is vital for assessing ecosystem health and implementing effective conservation strategies. The food industry relies heavily on titration for quality assurance. It's used to determine the acidity of products like fruit juices, wines, and dairy items, ensuring consistency and safety for consumers. Titration also aids in measuring the vitamin C content in beverages and ascertaining the freshness of oils by quantifying their free fatty acid levels. In the pharmaceutical sector, titration is essential for drug development and quality control. It's employed to determine the purity and potency of medications, ensuring that each batch meets stringent regulatory standards. Titration helps in analyzing the active ingredients in drugs, verifying their concentration, and assessing their stability over time. The technique is also valuable in forensic science for analyzing blood alcohol content and identifying unknown substances. Titration's importance in analytical chemistry stems from its accuracy, reliability, and versatility. It allows for precise quantitative analysis of substances, providing crucial data for research and development across multiple fields. The method is relatively simple to perform yet yields highly accurate results, making it a cost-effective choice for many laboratories. In quality control, titration serves as a cornerstone technique. It enables manufacturers to maintain consistent product quality by precisely measuring key components. This is particularly important in industries where slight variations can significantly impact product performance or safety. Titration's role extends to environmental monitoring, where it helps in assessing pollution levels and compliance with regulatory standards. The technique's adaptability allows it to be automated, increasing efficiency in high-volume testing environments. As analytical needs evolve, titration continues to be refined and integrated with modern technologies, enhancing its capabilities and expanding its applications. From ensuring the safety of our food and water to advancing medical treatments, titration remains an essential technique in the toolkit of analytical chemists, playing a vital role in maintaining quality and safety standards across numerous industries.

Conclusion

In conclusion, mastering acid-base titration is crucial for developing essential chemistry skills. This analytical technique forms the foundation for understanding complex chemical reactions and equilibria. By grasping the concepts of equivalence points, indicators, and titration curves, students can confidently approach various laboratory experiments and real-world applications. The introduction video provides a visual demonstration of these key concepts, making them more accessible and easier to comprehend. We encourage readers to watch the video to reinforce their understanding of acid-base titration principles. To further enhance your proficiency in this vital analytical technique, consider practicing titration exercises, exploring advanced titration curves methods, and applying these skills to diverse chemical systems. Remember, a solid grasp of acid-base titration will serve you well throughout your chemistry journey, whether in academic pursuits or professional endeavors. Take the next step in your chemistry education by delving deeper into titration techniques and expanding your analytical capabilities.

What is Titration? How Titration Works

Step 1: Introduction to Titration

Titration is a chemical experiment conducted in a laboratory setting to determine the unknown concentration of an acid or a base. This technique involves a series of steps that allow for precise measurements and calculations, making it a valuable tool in both educational and professional chemistry environments.

Step 2: Purpose and Benefits of Titration

The primary purpose of titration is to find the unknown concentration of a substance by reacting it with a known amount of another substance. This method is particularly useful for acids and bases, as their reactions are well-understood and easily measurable. Titration can also be used to determine the percentage purity of a substance, which is crucial in various industrial and research applications.

Step 3: Basic Principles of Titration

Titration involves the gradual addition of a known reagent (chemical A) to a solution containing the unknown reagent (chemical B) until the reaction reaches a stoichiometric point. The stoichiometric point is when the ratio of moles of the two chemicals matches the ratio in the balanced chemical equation. This point is often indicated by a noticeable change, such as a color change, facilitated by an indicator.

Step 4: Setting Up the Experiment

The experimental setup for titration typically includes a burette, which is a precise measuring instrument used to add the known reagent (A) to the unknown solution (B). The unknown solution is placed in a beaker, and the known reagent is added from the burette until the stoichiometric point is reached. The volume of the known reagent used is recorded for further calculations.

Step 5: Performing the Titration

To perform a titration, the known reagent (A) is added to the unknown solution (B) gradually. Initially, the reagent can be added quickly, but as the stoichiometric point approaches, it should be added drop by drop to ensure precision. An indicator is used to signal the stoichiometric point, which is when the reaction is complete, and the exact volume of reagent A used is recorded.

Step 6: Calculating the Results

Once the titration is complete, the volume of the known reagent (A) used is used to calculate the number of moles of A. Using the stoichiometry of the reaction, the number of moles of the unknown reagent (B) can be determined. With the moles and the precisely measured volume of B, the concentration of B can be calculated using the formula:
Concentration (C) = Moles (n) / Volume (V).

Step 7: Ensuring Precision

Precision is crucial in titration. To ensure accurate results, a trial run is often performed to get an approximate range of the volume needed. The final titration is then conducted with more precision, adding the reagent drop by drop near the stoichiometric point. Multiple titrations are performed to ensure consistency, and the results are averaged to obtain the final concentration.

Step 8: Importance of Indicators

Indicators play a vital role in titration by signaling the stoichiometric point through a color change. Different indicators are used depending on the pH range of the reaction. Universal indicators are not suitable for titrations due to their gradual color change. Instead, specific indicators with a clear and distinct color change at a particular pH are used to ensure accuracy.

Step 9: Recording and Repeating the Experiment

Each titration run is called a titer. Multiple titers are performed to ensure the results are reliable. The volume of the known reagent used in each titer is recorded, and the titers are repeated until the results are within a small margin of error, typically 0.05 cm³ or milliliters. This repetition ensures the precision and accuracy of the titration results.

Step 10: Conclusion

Titration is a precise and reliable method for determining the concentration of an unknown substance. By following the steps outlined above, chemists can accurately measure and calculate the concentration of acids and bases, ensuring the reliability of their results. The use of indicators, trial runs, and precise measurements all contribute to the effectiveness of this essential laboratory technique.

FAQs

1. How do you calculate titration?

To calculate titration results, use the equation c1v1 = c2v2, where c is concentration and v is volume. Knowing the concentration and volume of the titrant, along with the volume of the analyte, you can determine the unknown concentration. For example, if 20 mL of 0.1 M NaOH neutralizes 25 mL of HCl, you'd calculate: (0.1 M)(20 mL) = (x M)(25 mL), solving for x to find the HCl concentration.

2. What is the definition of titration in math?

In mathematical terms, titration is a process of determining the concentration of a solution by reacting it with a known volume of another solution of known concentration. It's represented by the equation c1v1 = c2v2, where c1 and v1 are the concentration and volume of the known solution, and c2 and v2 are those of the unknown solution.

3. What is titration for dummies?

Titration for beginners can be explained as a method of finding out how much of a substance is in a solution by slowly adding another substance that reacts with it until the reaction is complete. It's like filling a bathtub to a specific level - you add water slowly until it reaches the right mark, then you know how much water you've added.

4. Is titration always 1 to 1?

No, titration is not always 1 to 1. The ratio depends on the stoichiometry of the reaction. While many acid-base titrations are 1:1, some reactions, like the titration of sulfuric acid (H2SO4) with sodium hydroxide (NaOH), have a 1:2 ratio. Always refer to the balanced chemical equation to determine the correct ratio for calculations.

To get the best titration results: 1) Use clean, calibrated glassware. 2) Rinse the burette with the titrant before filling. 3) Remove air bubbles from the burette tip. 4) Add titrant slowly, especially near the endpoint. 5) Use a white background to see color changes clearly. 6) Perform at least three trials for consistency. 7) Calculate the average of your results. 8) Use a suitable indicator or pH meter for accurate endpoint detection.

Prerequisite Topics for Acid-Base Titration

Understanding acid-base titration is crucial in chemistry, but to truly grasp this concept, it's essential to have a solid foundation in certain prerequisite topics. Two key areas that significantly contribute to comprehending acid-base titration are balancing chemical equations and the acid dissociation constant.

Let's start with the importance of balanced chemical equations. In acid-base titration, we're dealing with reactions between acids and bases. To accurately predict and analyze these reactions, it's crucial to work with properly balanced equations. Balancing ensures that we account for all atoms and charges on both sides of the equation, which is fundamental for stoichiometric calculations in titration. Without this skill, students might struggle to determine the correct amounts of reactants or products, leading to inaccurate titration results.

Moreover, understanding how to balance equations helps in visualizing the neutralization process that occurs during titration. It allows students to see how protons are transferred between the acid and base, and how this affects the overall reaction. This visualization is key to grasping the concept of equivalence point in titration.

Equally important is the concept of the acid dissociation constant. This fundamental principle is crucial for understanding the strength of acids and bases, which directly impacts titration procedures and calculations. The acid dissociation constant, often denoted as Ka, provides information about how readily an acid gives up its protons in solution. This knowledge is essential for predicting the behavior of acids and bases during titration and for interpreting titration curves.

Furthermore, familiarity with polyprotic acid dissociation is particularly relevant in more complex titrations. Many real-world titrations involve polyprotic acids, which have multiple dissociation steps. Understanding how these acids behave at different stages of dissociation is crucial for accurately interpreting titration data and identifying multiple equivalence points.

By mastering these prerequisite topics, students build a strong foundation for understanding acid-base titration. They'll be better equipped to perform titrations, interpret results, and solve related problems. The ability to balance equations ensures accurate stoichiometric calculations, while knowledge of acid dissociation constants allows for a deeper understanding of acid-base behavior and strength. Together, these skills enable students to approach acid-base titration with confidence and precision, paving the way for success in more advanced chemistry concepts.

In this lesson, we will learn:

• Why titrations are performed and their purpose as an experiment.
• How to use reaction stoichiometry to find moles and unknown concentrations from titrations.
• How to use titrations and mole calculations to find percentage purity of a sample.

Notes:

• A titration is a lab experiment used to find the unknown concentration of an acid or base. We can use an acid or base sample with a known concentration (let’s call the ‘known’ chemical A) in a chemical reaction with a sample of a base or acid of unknown concentration that we’re investigating (let’s call the ‘unknown’ chemical B).
Chemicals A and B will react in proportional amounts (moles) to each other, so the amounts of A we used, in the end, tells us the amounts of B that’s present.
• Titration experiments work because volume AND concentration of chemical A are known, so we can calculate moles of A, which is related to moles of B (in their reaction), which is used with its volume to calculate A’s unknown concentration! Finding this works in a sequence as shown in the table below:

• The practical experiment goes like this:
• Known chemical A is gradually added to a precise volume of unknown B until the stoichiometric point is reached. The stoichiometric point is when the ratio of moles of A to B is the same as in the balanced chemical equation. This point is clear from a large change in pH (and color change with indicator added) because neutralization occurs.
The molar ratio in the reaction equation (the stoichiometry) and the volume of A that was needed to neutralize B is then used to find the number of moles of B. Now that moles and volume of ‘unknown’ B are known, the concentration of the unknown chemical B sample can be calculated.

• Titrations are excellent for finding acid/base concentrations because:
• Acids and bases are complementary in their chemistry so there are lots of ideal ‘partner’ chemicals for them.
• It is easy to measure pH and pH change of a mixture, and the pH can be used to find the concentration and moles of H3O+ or OH- in that same mixture. This is perfect for chemicals that produce these ions, like acids and bases!

• The most important factor in a successful titration is precision. The titration needs to stop precisely at the stoichiometric point (AKA equivalence point). To make sure this is accurate and precise, a few steps are taken in the practical method:
• A chemical called an indicator is added to the mixture. This chemical indicates a change in pH by a clear color change, and the equivalence point is exactly when the titration mixture changes color permanently. There are many different indicators for different pH ranges and combinations of weak/strong acids reacting with weak/strong bases. They are very sensitive to pH change – the addition of one extra drop of acid or base might cause a permanent color change.
• A trial run is performed on the very first titration experiment. This is a ‘rough run’ to establish roughly the volume of chemical A needed to reach the equivalence point. This is done to save time and still allow chemists to be precise in the approximate range where the color change – and equivalence point – is found.
• The final amounts of the known chemical A are added dropwise to get as precise a reading as possible. A single titration run with a volume reading obtained is called a ‘titer’.
• The precise runs – titers – are repeated until two readings fall within 0.05cm3 of each other. An average titer is then taken from these two readings.

• Once an average titer has been obtained, this is taken to be the volume where there is an equal number of moles of both acid and base.
Remember that your titer volumes will be in milliliters or cm3 but concentration is measured in moles per LITER, or dm3. You must convert the volume to liters! Dividing milliliters by 1000 will give you a value in liters.
The number of moles of chemical B can be calculated because its concentration and volume are both known:

$concentration \; (M) = \frac{moles\; (mol)}{Volume \; (L)}$

Rearrange to give:

$moles \; (mol) = concentration \;(M)\; * \; Volume \; (L)$

With this moles of B value obtained, recall the reaction stoichiometry:

aA + bB $\;$$\;$ cC + dD

The molar ratio is important for finding moles of B. The equivalence point occurs when b moles of A is equal to a moles of B. Use this to find the number of moles of unknown chemical B in the titration mixture at equivalence point.

• Once the number of moles of chemical B is found, you have moles and volume:

$concentration \; (M) = \frac{moles\; (mol)}{Volume \; (L)}$

Now the unknown concentration can be calculated!

• Titrations involving partial neutralization can also be performed; this is where polyprotic acids (acids with more than one proton to donate) donate a proton one by one, so no one step completely neutralizes the acid. Take the example with phosphoric acid, H3PO4:

Reaction 1: H3PO4 + OH- $\;$$\;$ H2PO4- + H2O

Reaction 2: H3PO4 + 2OH- $\;$$\;$ HPO42- + 2H2O

Reaction 3: H3PO4 + 3OH- $\;$$\;$ PO43- + 3H2O

If you are asked to do a calculation with partial neutralization, you might need to find out the acid:base molar ratio in the reaction. For this, you’ll be given the volume and concentration of both acid and base so that moles of both can be found – then divide the larger number of moles by the smaller to find the ratio between them! To find the moles, the rearranged equation for concentration can still be used:

$moles \; (mol) = concentration \;(M)\; * \; Volume \; (L)$

This is sometimes written as:

n = C * V $\quad$ Where $\,$ n = moles, C = concentration (M), V = volume (L or dm3)

• Titration results can be used to find the percentage purity of a sample as well. This is done in the following method:
• Find the number of moles of the acid/base you added to the solvent to create the solution. For example, a 1.13g sample of NaOH was used. Find the number of moles of this by dividing the mass used by molar mass:

$moles = \frac{mass \; (g)}{molar \; mass\; (gmol^{-1})}$

$moles = \frac{1.13}{40} = 0.028 mol$

Find the expected concentration by dividing the volume of the solution made by this number of moles.
For example, the NaOH used was diluted to 250 mL (0.25 L):

$concentration\; (M) = \frac{moles \; (mol)}{volume\; (L)}$

$concentration\; (M) =\frac{0.028\; mol}{0.25 (L)} = 0.112\; M$

$moles \; (mol) \; = 0.097M * 0.0279L = 0.0027 mol$
$concentration \; (M) = \frac{0.0027\; mol}{0.025\; L} = 0.108M$
$\% \; purity = \frac{actual \; concentration}{expected \; concentration} * 100= \frac{1.08\;M}{1.12\;M} * 100 = 96.4 \%$