pH of a Weak Acid (0.1 M Acetic Acid) EXAMPLE

chemistNATE
6 Mar 201208:39
EducationalLearning
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TLDRThe video script explains the process of finding the pH of a weak acid solution, specifically acetic acid, using its dissociation constant (Ka). It introduces the dissociation equation, the ICE (Initial Concentrations and Equilibrium) table method, and the assumption that simplifies the calculation when Ka is small relative to the initial concentration. The script then demonstrates solving for the concentration of H+ (X) using both the assumption method and the quadratic formula, followed by calculating the pH as the negative logarithm of the H+ concentration. The accuracy of the assumption is verified by ensuring the calculated X is less than 5% of the initial concentration.

Takeaways
  • 📚 The script is an update on finding the pH of a weak acid solution, specifically using acetic acid as an example.
  • 🧪 The initial concentration of acetic acid is given as 0.1 moles per liter, with a Ka (acid dissociation constant) of 1.8 × 10^(-5).
  • 🌟 The first step is to write down the dissociation equation for acetic acid, which involves the breakdown into H+ and CH3COO- (acetate ion).
  • 📊 The ICE (Initial, Change, Equilibrium) table is introduced to help determine the concentrations of each species at equilibrium.
  • 🔢 The equilibrium concentrations are filled into the Ka expression to solve for the unknown concentration of H+ (X).
  • 📈 Two methods for solving for X are presented: using the quadratic equation or making a mathematical assumption due to the small value of Ka.
  • 🎯 The 'hundred rule' is mentioned as a quick way to check if the assumption method is valid by comparing the initial concentration to Ka.
  • 👌 The assumption simplifies the equation to Ka = (X^2) / 0.1, allowing for easier calculation of X, the concentration of H+.
  • 🧮 To find X, the equation is rearranged and solved using basic algebra and the square root function on a calculator.
  • 🔍 Verification of the assumption is suggested by ensuring that X is less than 5% of the initial concentration to maintain accuracy.
  • 📝 Finally, the pH is calculated by taking the negative logarithm (base 10) of the concentration of H+, resulting in a pH of 2.87 for this example.
Q & A

  • What is the main topic of the video?

    -The main topic of the video is finding the pH of a weak acid solution, specifically acetic acid.

  • What is the dissociation equation for acetic acid in water?

    -The dissociation equation for acetic acid in water is H_a (acetic acid) breaking up into H+ (proton) and A- (acetate ion with a minus charge).

  • What is the equilibrium expression for a weak acid like acetic acid?

    -The equilibrium expression for a weak acid is the concentration of products (H+ and A-) divided by the concentration of reactants (H_a), which is represented by the acid dissociation constant (K_a).

  • What does ICE table stand for?

    -ICE table stands for Initial Concentration and Equilibrium concentrations, which is a method used to determine the changes in concentrations of species during dissociation equilibrium.

  • How does the video suggest solving for the concentration of H+ (X) in the dissociation of acetic acid?

    -The video suggests solving for the concentration of H+ (X) by setting up the K_a equation with equilibrium concentrations and solving for X, either by using the quadratic formula or by making an approximation when K_a is small relative to the initial concentration.

  • What is the 'hundred rule' mentioned in the video and when is it applicable?

    -The 'hundred rule' is a mathematical assumption used when K_a is very small compared to the initial concentration. It involves dividing the initial concentration by K_a; if the result is much greater than 100, it indicates that X is very small relative to the initial concentration, allowing for simplification in calculations.

  • How is the assumption verified in the calculation?

    -The assumption is verified by ensuring that the calculated concentration of H+ (X) is less than five percent of the initial concentration. If it is more than five percent, the accuracy of the assumption is questioned, and the quadratic formula should be used for the calculation.

  • What is the final step in calculating the pH of the weak acid solution?

    -The final step is to take the negative logarithm (log) of the concentration of H+ (X) to find the pH value.

  • What was the calculated pH of the acetic acid solution in the video?

    -The calculated pH of the acetic acid solution in the video was 2.87.

  • Why is it important to verify the assumption when using the approximation method?

    -Verifying the assumption ensures the accuracy and reliability of the results. If the calculated concentration of H+ (X) is not significantly smaller than the initial concentration, the approximation method may not provide a sufficiently accurate result, and the quadratic formula should be used instead.

  • How does the video demonstrate the process of solving for X using the approximation method?

    -The video demonstrates the process by first setting up the K_a equation with equilibrium concentrations, making the assumption that X is very small, simplifying the equation, solving for X using basic algebraic operations, and then verifying the assumption by comparing X to the initial concentration.

Outlines
00:00
📚 Introduction to Finding pH of a Weak Acid Solution

This paragraph introduces the process of calculating the pH of a weak acid solution, specifically using acetic acid as an example. It explains the need for the dissociation equation, which describes the reaction of acetic acid in water, breaking it down into H+ and its corresponding anion. The paragraph also introduces the concept of the equilibrium expression (Ka) and the ICE table (Initial, Change, Equilibrium) to determine the concentrations of the species at equilibrium. The main theme is setting up the problem and explaining the initial steps required to solve for the pH of a weak acid solution.

05:02
🧪 Solving the pH Calculation with Mathematical Assumptions

This paragraph delves into the methods of solving the pH calculation by first discussing the quadratic equation approach and then introducing a simplification technique based on the assumption that the change in concentration (X) is small relative to the initial concentration. The paragraph explains how to use the 'hundred rule' to justify this assumption and proceeds to solve for X, the concentration of H+ ions, using this simplification. It then describes the verification of the assumption to ensure its validity and concludes with the calculation of the pH using the negative logarithm of the H+ concentration. The main focus is on the practical application of mathematical techniques and assumptions to efficiently solve chemistry problems.

Mindmap
Keywords
💡pH
pH is a measure of the hydrogen ion concentration in a solution, which indicates its acidity or alkalinity. In the video, the main objective is to calculate the pH of a weak acid solution, specifically an acetic acid solution. The pH is determined by taking the negative logarithm of the hydrogen ion concentration, which is derived from the dissociation of acetic acid in water. A lower pH value indicates a more acidic solution, while a higher value indicates a more alkaline solution.
💡weak acid
A weak acid is an acid that does not completely dissociate in water, meaning it only partially releases its hydrogen ions (protons) into the solution. Acetic acid, the subject of the video, is an example of a weak acid. Weak acids have a lower degree of ionization compared to strong acids, which fully dissociate in solution. The strength of an acid is often quantified by its dissociation constant (Ka), with weak acids having smaller Ka values.
💡dissociation equation
A dissociation equation is a chemical equation that represents the process of a compound breaking down into its constituent ions when dissolved in a solvent, such as water. In the context of the video, the dissociation equation for acetic acid (CH3COOH) is written as CH3COOH → H+ + CH3COO-, indicating that acetic acid donates a proton (H+) and forms its conjugate base (CH3COO-). This equation is essential for understanding how acetic acid contributes to the acidity of the solution and for calculating the pH.
💡Ka
Ka, or the acid dissociation constant, is a measure of the strength of a weak acid in water. It is the equilibrium constant for the dissociation reaction of the acid. A higher Ka value indicates a stronger acid, meaning it has a greater tendency to donate protons. In the video, the Ka value for acetic acid is given as 1.8 x 10^-5, which is used to calculate the equilibrium concentrations of the species involved in the dissociation reaction and ultimately the pH of the solution.
💡equilibrium
In chemistry, equilibrium refers to the state in which the concentrations of reactants and products in a reversible reaction remain constant over time. This does not mean the reaction has stopped; rather, the forward and reverse reactions are occurring at the same rate. In the context of the video, the equilibrium between acetic acid, its dissociated hydrogen ions, and acetate ions is crucial for determining the pH of the solution. The equilibrium concentrations are used in the Ka expression to solve for the unknown concentration of H+ ions.
💡ICE table
An ICE table, which stands for Initial, Change, and Equilibrium table, is a method used in chemistry to keep track of the concentrations of reactants and products at different stages of a reversible reaction. In the context of the video, the ICE table is used to determine the equilibrium concentrations of acetic acid, hydrogen ions, and acetate ions, which are necessary for calculating the pH of the solution. The table helps to visualize the initial concentrations, changes that occur as the reaction reaches equilibrium, and the final equilibrium concentrations.
💡mathematical assumption
In the context of the video, a mathematical assumption refers to a simplification made to solve a problem more easily. Specifically, when dealing with the dissociation of a weak acid like acetic acid, the assumption is that the change in concentration (X) is very small compared to the initial concentration. This allows for simplifying the Ka expression and solving for X without resorting to more complex methods like the quadratic formula. The assumption is verified by ensuring that X is less than five percent of the initial concentration, which maintains the accuracy of the simplification.
💡concentration
Concentration in chemistry refers to the amount of a particular substance (solute) present in a given volume of solution (solvent). It is typically expressed in moles per liter (M). In the video, the concentration of acetic acid and the resulting hydrogen ions are central to calculating the pH of the solution. Understanding and manipulating concentration values is essential for solving equilibrium problems and finding the pH of weak acid solutions.
💡negative logarithm
The negative logarithm, often denoted as 'log', is a mathematical operation used in various scientific fields, including chemistry. In the context of pH calculation, the negative logarithm is used to determine the pH value from the concentration of hydrogen ions (H+). The formula is pH = -log[H+], where [H+] represents the molar concentration of hydrogen ions. The negative logarithm transforms the exponential relationship between the acidity of a solution and its pH into a linear scale, making it easier to calculate and interpret.
💡quadratic equation
A quadratic equation is a polynomial equation of degree two, in the form of ax^2 + bx + c = 0, where x represents an unknown variable. In the context of the video, the quadratic equation could be used to solve for the unknown concentration of H+ ions (X) in the dissociation of acetic acid, if the mathematical assumption does not hold. The quadratic formula is used to find the values of x that satisfy the equation, which can be complex and time-consuming compared to the simplification allowed by the assumption that X is small.
💡verification
Verification in the context of the video refers to the process of confirming that the mathematical assumption made (i.e., that X is very small compared to the initial concentration) is valid. This is done by checking whether the calculated value of X is less than five percent of the initial concentration. If the condition is met, it confirms that the simplification used to solve for X is accurate and the resulting pH calculation is reliable.
Highlights

The process of finding the pH of a weak acid solution is discussed, specifically using acetic acid as an example.

Acetic acid has a Ka (acid dissociation constant) of 1.8 x 10^-5, which is crucial for the calculation.

The dissociation equation for acetic acid (CH3COOH) is written as CH3COOH ⇌ H+ + CH3COO-.

An ICE (Initial, Change, Equilibrium) table is introduced to determine the concentrations of species at equilibrium.

The assumption that Ka is small relative to the initial concentration allows for simplification in the calculation.

The 'hundred rule' is mentioned as a method to determine if the assumption of Ka being small is valid.

The calculation involves solving an equation for the concentration of H+ (X) based on the Ka expression and equilibrium concentrations.

The quadratic formula is one method to solve for X, though it can be simplified if certain conditions are met.

Verification of the assumption is necessary to ensure accuracy, typically requiring that the calculated concentration change is less than 5% of the initial concentration.

The pH is calculated using the negative logarithm of the concentration of H+.

The final pH calculated for the acetic acid solution is 2.87, matching the value in the textbook.

The video provides a step-by-step guide on how to approach and solve the problem of finding the pH of a weak acid solution.

The use of mathematical assumptions and simplifications is emphasized to make the calculation process more manageable.

The importance of verifying the simplification assumption is highlighted to ensure the accuracy of the results.

The method can be applied to other weak acids with similar dissociation behavior.

The process is explained in a way that is accessible to students learning about acid-base chemistry.

The video provides a clear and detailed explanation of the chemistry behind finding the pH of a weak acid solution.

Transcripts

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Chemistry TutorialpH CalculationWeak AcidsAcetic AcidDissociation EquationEquilibrium ConstantICE TableMathematical AssumptionQuadratic EquationLogarithm