ALEKS - Calculating Equilibrium Composition from an Equilibrium Constant

Tony St John
5 Dec 201611:03
EducationalLearning
32 Likes 10 Comments

TLDRThis video script outlines a chemistry lesson on calculating equilibrium composition using an equilibrium constant. The instructor walks through the steps of solving a problem involving a reaction between nitrogen and oxygen gases to form nitrogen monoxide. The unique challenge is the need to solve for 'X', which cannot be considered negligible. The script details the use of an ICE table, the equilibrium constant expression, and the application of the quadratic formula to find the equilibrium molarity of O2. The lesson emphasizes the importance of algebraic manipulation and critical thinking in chemistry.

Takeaways
  • 🧪 The video is a chemistry tutorial focusing on calculating equilibrium composition from an equilibrium constant.
  • 🔍 It emphasizes the importance of solving for 'x' in this problem, which is often not negligible as it is in simpler cases.
  • 📚 The problem involves a reaction in a 500 mL flask with gases N2 and O2 reacting to form NO, with an equilibrium constant Kc given.
  • 📈 The equilibrium constant expression is set up using molarity, considering the coefficients of the balanced chemical equation.
  • 🔢 The value of Kc is 0.614, indicating a balanced equilibrium that doesn't favor one side over the other.
  • 📉 The initial concentrations of N2 and O2 are converted into molarity for use in the ICE table (Initial, Change, Equilibrium).
  • ⚖️ The reaction is expected to shift to the left to reach equilibrium due to the absence of O2 initially.
  • 📝 An ICE table is constructed to track the changes in molarity of the reactants and products as the reaction reaches equilibrium.
  • 🔑 The equilibrium expression is plugged into the Kc value to form a quadratic equation that must be solved for 'x'.
  • 📱 Solving the quadratic equation can be done using a calculator with a solver function, an online math solver, or by hand using the quadratic formula.
  • 🤔 The solution process involves choosing the correct 'x' value that makes sense in the context of the problem, avoiding negative concentrations.
  • 📊 The final answer is the equilibrium molarity of O2, which is found to be 0.3 after rounding to one decimal place.
Q & A

  • What is the main topic of the video script?

    -The main topic of the video script is calculating equilibrium composition from an equilibrium constant in a chemistry context.

  • Why is solving for X in this problem more challenging than usual?

    -Solving for X in this problem is more challenging because the equilibrium constant (Kc) value is neither very large nor very small, which means the equilibrium does not favor one side or the other, and X cannot be treated as negligible.

  • What is the reaction taking place in the 500 milliliter flask as described in the script?

    -The reaction taking place in the 500 milliliter flask is N2(g) + O2(g) ⇌ 2NO(g), which is the formation of nitrogen monoxide from nitrogen and oxygen gases.

  • What is the equilibrium constant expression for the given reaction?

    -The equilibrium constant expression for the given reaction is Kc = [NO]^2 / ([N2] * [O2]), where the concentrations of N2 and O2 are in molarity.

  • What is the initial molarity of N2 and O2 in the flask, and how is it determined?

    -The initial molarity of N2 is 0.200 M, and for O2, it is 1.000 M. These are determined by converting the given moles of N2 and O2 to molarity using the volume of the flask (500 mL or 0.500 L).

  • Why does the reaction shift to the left according to the script?

    -The reaction shifts to the left because there is no O2 initially present in the flask, making it impossible to shift the reaction to the right to reach equilibrium.

  • What is the significance of the equilibrium constant value of 0.614 in this context?

    -The equilibrium constant value of 0.614 indicates that the reaction is not strongly favoring the formation of products or the reactants, which is why the value of X cannot be neglected in the calculations.

  • What method is suggested in the script for solving the equilibrium problem when a calculator or software is not available?

    -The script suggests using algebra and the quadratic formula as a method for solving the equilibrium problem when a calculator or software is not available.

  • What is the final equilibrium molarity of O2 that the script aims to find?

    -The final equilibrium molarity of O2 that the script aims to find is 0.3 M, after solving for X using the quadratic formula and selecting the valid solution that does not result in negative concentrations.

  • Why is it incorrect to use the x value of 0.883 in the equilibrium calculations?

    -Using the x value of 0.883 is incorrect because it results in a negative concentration for NO, which is not possible in real-world scenarios as concentrations cannot be negative.

  • What is the purpose of using an ICE table in this context?

    -The purpose of using an ICE table in this context is to systematically keep track of the changes in concentrations of reactants and products as the reaction proceeds towards equilibrium, making it easier to set up and solve the equilibrium constant expression.

Outlines
00:00
🧪 Calculating Equilibrium Composition

The video script introduces a chemistry problem involving the calculation of equilibrium composition from an equilibrium constant. It emphasizes the complexity of solving for the variable 'X', which is not negligible in this scenario. The problem involves a reaction in a 500 milliliter flask with nitrogen (N2) and oxygen (O2) gases reacting to form nitrogen monoxide (NO). The equilibrium constant (KC) is given, and the script explains the importance of using molarity in the equilibrium expression. The initial step is to set up an ICE table (Initial, Change, Equilibrium) to understand how the reaction will shift towards equilibrium, considering the initial molarities of the reactants.

05:02
🔍 Solving the Quadratic Equation for Equilibrium

This section of the script delves into the process of solving the equilibrium problem without taking shortcuts, as the equilibrium constant (KC) is neither very large nor very small, indicating a balanced reaction. The script suggests using a calculator or an online solver for complex problems but also outlines the algebraic method involving the quadratic formula. It explains the steps to set up the quadratic equation based on the equilibrium expression and how to solve for 'X'. The script also discusses the importance of selecting the correct 'X' value that results in a physically meaningful concentration of reactants and products, ultimately arriving at the equilibrium molarity of O2.

10:04
📚 Detailed Algebraic Solution Using Quadratic Formula

The final paragraph of the script provides a detailed walkthrough of solving the equilibrium problem using algebra and the quadratic formula. It starts by rewriting the equilibrium constant expression and expanding it to form a standard quadratic equation. The script carefully guides through the algebraic manipulations, emphasizing the importance of accuracy to avoid mistakes. After forming the quadratic equation, the script uses the values of a, b, and c to apply the quadratic formula, resulting in two potential 'X' values. It concludes by selecting the valid 'X' value that corresponds to a positive and meaningful concentration of O2 at equilibrium, rounding the final answer to one decimal place as per the problem's requirement.

Mindmap
Keywords
💡Equilibrium Constant (Kc)
The equilibrium constant (Kc) is a fundamental concept in chemistry that describes the ratio of products to reactants at equilibrium in a chemical reaction. In the video, Kc is used to express the concentrations of gases involved in the reaction at equilibrium. The value of Kc (0.614) indicates that the reaction is not strongly favoring either the reactants or products, which is why the exact value of x (change in concentration) must be calculated, as it cannot be considered negligible.
💡500 Milliliter Flask
A 500 milliliter flask is a piece of laboratory equipment used to contain and react gases in a controlled environment. In the context of the video, the flask is where the chemical reaction between nitrogen (N2) and oxygen (O2) to form nitrogen monoxide (NO) takes place. The size of the flask is important as it sets the volume in which the reaction occurs and affects the calculation of molarities.
💡Gaseous Reaction
A gaseous reaction involves gases as reactants and/or products. In the video, the reaction between N2 and O2 is gaseous, which is why the concentrations of these gases are considered in moles per liter (molarity). The script discusses the importance of using molarity for gases in ICE tables and equilibrium calculations.
💡ICE Table
An ICE table is a method used in chemistry to systematically keep track of the changes in concentration of reactants and products as a reaction approaches equilibrium. In the video, the ICE table is used to organize the initial concentrations, changes, and equilibrium concentrations of N2, O2, and NO, facilitating the calculation of the equilibrium state.
💡Molarity
Molarity is a measure of concentration that expresses the number of moles of a substance per liter of solution. In the video, molarity is used to express the initial and equilibrium concentrations of the gases involved in the reaction. The script emphasizes the importance of using molarity in ICE tables and Kc expressions for consistency and accuracy in calculations.
💡Quadratic Formula
The quadratic formula is a mathematical tool used to solve quadratic equations of the form ax^2 + bx + c = 0. In the video, the quadratic formula is mentioned as a method to solve for x when the equilibrium expression results in a quadratic equation. The script describes how the formula can be applied to find the exact value of x, which is crucial for determining the equilibrium concentrations.
💡Reaction Quotient
The reaction quotient (Q) is similar to the equilibrium constant but is used to determine the direction in which a reaction will proceed to reach equilibrium. In the video, the concept is briefly mentioned in the context of deciding the direction of the reaction based on the initial concentrations and the value of Kc.
💡Significant Figures
Significant figures are the digits in a number that carry meaningful information about its precision. In the script, the presenter initially uses three significant figures but then corrects to two, illustrating the importance of precision in scientific calculations and the need to be consistent with the number of significant figures used.
💡Concentration
Concentration in chemistry refers to the amount of a substance present in a given volume of a mixture or solution. In the video, the equilibrium concentrations of N2, O2, and NO are calculated to determine the molarity at equilibrium. The script uses the terms 'concentration' and 'molarity' interchangeably, emphasizing the need for accurate concentration measurements.
💡Equilibrium Molarity of O2
The equilibrium molarity of O2 is the final concentration of oxygen at equilibrium in the reaction. In the video, solving for x (the change in concentration) ultimately gives the equilibrium molarity of O2, which is a key piece of information sought in the problem. The script concludes with the calculation of this value, rounding it to one decimal place as per the instructions.
Highlights

Introduction to calculating equilibrium composition from an equilibrium constant.

Challenge of solving for X when it cannot be treated as negligible.

Description of a 500 milliliter flask containing N2 and O2 gases.

Reaction of N2 and O2 to form nitrogen monoxide (NO).

Writing out the equilibrium constant expression for KC.

Discussion on the significance of the value of KC in determining the position of equilibrium.

Use of an ICE table to determine initial concentrations and changes.

Initial molarity calculations for N2 and O2.

Direction of the reaction shift based on initial concentrations.

Equilibrium concentrations of N2, O2, and NO calculated using an ICE table.

Plugging equilibrium expressions into the equilibrium constant formula.

Explanation of why shortcuts are not possible in this problem.

Use of a quadratic formula to solve for X.

Discussion on the use of calculators or online solvers for solving equations.

Result of solving for X using algebraic methods.

Determination of the valid X value by checking against negative concentrations.

Final answer for the equilibrium molarity of O2.

Explanation of why molarities are used in ICE tables for direct answers.

Demonstration of solving the quadratic equation using algebra.

Final validation of the X value and its practical significance in the problem.

Transcripts

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