Use your answer from Problem 7.53 to calculate the following: a. [N 2 O 4 ] at equilibrium when [NO 2 ] = 0.0250 mol/L

Welcome back, everyone. We need to consider the equilibrium reaction and calculate the concentration of flooring gas at equilibrium. When our concentration of flooring equals 5.25 times 10 to the negative fourth power moles per liter. Our reaction given is di atomic flooring gas in equilibrium with two moles of flooring gas where our equilibrium constant K is equal to 7.40 times 10 to the negative 13th power at 500. Kelvin. Let's write out our equilibrium expression where we have our given K value equilibrium constant equal to 7.40 times 10 to the negative 13 power from the prompt. And recall that our equilibrium constant K is equal to our concentration of products raised to their geometric coefficients as exponents divided by our concentration of reactant raised to their psychometric coefficients as exponents. So this will be interpreted as 7.40 times 10 to the negative 13 power equal to in our numerator. Our concentration of our only gaseous product being flooring gas raised to its documentary coefficient of two. As an exponents in our denominator, we have our concentration of our only gaseous reactant being di atomic flooring F sub two with its metric coefficient of one which is implied. So we don't need to write it in as an exponents. So plugging in our given concentration of flooring in the numerator, we have our equilibrium constant K 7.40 times 10 to the negative 13 power equal to in our numerator. Our concentration of flooring is 5.25 times 10 to the negative fourth power moles per liter. This is squared and this is divided by our concentration of di atomic flooring gas. So to get our concentration of diatonic flooring gas, we're going to multiply both sides by our concentration of diatonic flooring so that it cancels out on the right. And now in our next line will have 7.40 times 10 to the negative 13th power times the concentration of flooring gas equal to 5.25 times 10 to the negative fourth power moles per liter as our concentration of flooring. So to isolate for our concentration of di atomic flooring, we want to divide both sides by our equilibrium constant 7.40 times 10 to the negative 13th power so that it will cancel it on the left. And what we'll find is that our concentration of di atomic flooring is equal to the value and sorry, just to make a correction, our numerator should still be squared as it was before. So we have 5.25 times 10 to the negative fourth power moles per liter squared divided by 7.40 times 10 to the negative 13th power. And this result of this quotient gives us our final answer of three 0.72 times 10 to the ninth power moles per leader as our concentration of di atomic flooring at equilibrium. And this would be our final answer highlighted in yellow corresponding to choice C in the multiple choice. So I hope that this made sense and let us know if you have any questions.

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7. Energy, Rate and Equilibrium

The Equilibrium Constant

GOB Chemistry

7. Energy, Rate and Equilibrium

The Equilibrium Constant

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3:08 minutes

Problem 55a

Textbook Question

Use your answer from Problem 7.53 to calculate the following:
a. [N₂O₄] at equilibrium when [NO₂] = 0.0250 mol/L

Verified step by step guidance

Identify the chemical equilibrium reaction involved. The reaction is typically: N₂O₄ ⇌ 2NO₂. This means dinitrogen tetroxide (N₂O₄) dissociates into nitrogen dioxide (NO₂).

Write the equilibrium constant expression for the reaction: Kc = ([NO₂]²) / [N₂O₄]. Here, [NO₂] and [N₂O₄] represent the equilibrium concentrations of NO₂ and N₂O₄, respectively.

Rearrange the equilibrium constant expression to solve for [N₂O₄]: [N₂O₄] = ([NO₂]²) / Kc. This step isolates the concentration of N₂O₄ at equilibrium.

Substitute the given value of [NO₂] = 0.0250 mol/L into the rearranged equation. You will also need the value of Kc, which should have been determined in Problem 7.53. Ensure the units of Kc are consistent with the concentration units (mol/L).

Perform the calculation by squaring the [NO₂] value, dividing it by the Kc value, and solving for [N₂O₄]. This will give you the equilibrium concentration of N₂O₄ in mol/L.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. It is calculated using the formula Kc = [products]^[coefficients] / [reactants]^[coefficients]. Understanding Kc is essential for predicting the concentrations of species in a chemical reaction at equilibrium.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust itself to counteract the change and restore a new equilibrium. This principle helps in understanding how changes in concentration, pressure, or temperature affect the position of equilibrium in a chemical reaction.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions based on the balanced chemical equation. It involves using mole ratios derived from the coefficients of the balanced equation to relate the amounts of different substances. Mastery of stoichiometry is crucial for determining the concentrations of reactants and products at equilibrium.

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