The equilibrium constant for the reaction SO 2 (g) + NO 2 (g) ⇌ SO 3 (g) + NO(g) is K c = 3.0. Find the amount of NO 2 that must be added to 2.4 mol of SO 2 in order to form 1.2 mol of SO 3 at equilibrium.

Hello. And this problem we are told the reaction A plus B goes to C plus D where the equilibrium constant is equal to 0.60. To calculate the molds will be required to react with 1.8 moles of A to acquire 0. moles of C when the reaction reaches equilibrium. So we begin by creating an ice table. So first ride our reaction and then we have initial change in equilibrium. Initially, we have 1.8 moles of A. We're trying to determine our initial moles B and we have no sea and no D R changes minus X minus X. And then plus X plus X will combine the initial and the change to get our equilibrium. We're told that we have 0.9 moles of C at equilibrium. So that means X equals 0.90 at equilibrium, our equilibrium constant expression. Then we have the concentration of our products over that of our reactant. So plugging things in from the ice table, we have .90 times .90 All over 1.8 -1 which is again .90 and Y -X. So Y -0.90. And this is then equal to 0.60. Simplifying this, we then get 0.90 over Y minus 0.90, world 0.60. We will multiply both sides by Why -0.90. And then we'll simplify, Remove our 0.54 to the other side and then solve the why, Why works out to them 2.4 moles? This is our moles of B that we need them to react with 1.8 moles of a to produce 0.9 moles of c at equilibrium note here that we've made you some moles rather than polarity. And so we look at our concentrations that we would enter into our equilibrium constant expression, most similarity of our products over that of our reactant, we see then our units of volume cancel. So in this case, we can just make you some moles as we did in solving this problem. Thanks for watching. Hope this helps.

Ch.16 - Chemical Equilibrium

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Tro 6th Edition

Ch.16 - Chemical Equilibrium

Problem 92

Chapter 16, Problem 92

The equilibrium constant for the reaction SO₂(g) + NO₂(g) ⇌ SO₃(g) + NO(g) is K_c = 3.0. Find the amount of NO₂ that must be added to 2.4 mol of SO₂ in order to form 1.2 mol of SO₃ at equilibrium.

Verified step by step guidance

Identify the balanced chemical equation: \( \text{SO}_2(g) + \text{NO}_2(g) \rightleftharpoons \text{SO}_3(g) + \text{NO}(g) \).

Write the expression for the equilibrium constant \( K_c \): \( K_c = \frac{[\text{SO}_3][\text{NO}]}{[\text{SO}_2][\text{NO}_2]} \).

Set up an ICE (Initial, Change, Equilibrium) table to track the concentrations of each species. Initially, you have 2.4 mol of \( \text{SO}_2 \) and 0 mol of \( \text{SO}_3 \). Let \( x \) be the amount of \( \text{NO}_2 \) added.

At equilibrium, the concentration of \( \text{SO}_3 \) is 1.2 mol. Use the stoichiometry of the reaction to express the changes in concentrations of all species in terms of \( x \).

Substitute the equilibrium concentrations into the \( K_c \) expression and solve for \( x \), the amount of \( \text{NO}_2 \) needed.

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Key Concepts

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

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. The equilibrium constant (Kc) quantifies this balance, indicating the ratio of product concentrations to reactant concentrations at equilibrium. Understanding this concept is crucial for predicting how changes in concentration affect the system.

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their coefficients in the balanced equation. For the reaction SO2(g) + NO2(g) ⇌ SO3(g) + NO(g), Kc = 3.0 means that at equilibrium, the concentration of SO3 and NO is three times that of SO2 and NO2. This constant helps in calculating the necessary concentrations to achieve equilibrium.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on the balanced equation. It allows us to determine the amounts of substances consumed and produced. In this question, stoichiometry is essential for calculating how much NO2 must be added to achieve the desired amount of SO3 at equilibrium, using the initial amounts and the equilibrium constant.