# At a particular temperature, K = 3.75 for the reaction SO 2 ( g ) + NO 2 ( g ) ⇌ SO 3 ( g ) + NO ( g ) If all four gases had initial concentrations of 0.800 M, calculate the equilibrium concentrations of the gases.

### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

Chapter
Section

### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 12, Problem 51E
Textbook Problem
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## At a particular temperature, K = 3.75 for the reaction SO 2 ( g ) + NO 2 ( g ) ⇌ SO 3 ( g ) + NO ( g ) If all four gases had initial concentrations of 0.800 M, calculate the equilibrium concentrations of the gases.

Interpretation Introduction

Interpretation: The value of the equilibrium constant for the reaction between SO2 and NO2 is given. The equilibrium concentrations of the four gases involved in the system are to be calculated.

Concept introduction: The state when the reactants involved in a chemical reaction and the products formed in the reaction exist in concentrations having no further tendency to change is known as an equilibrium state of the reaction. When the equilibrium constant is expressed in terms of concentration, it is represented as K .

To determine: The equilibrium concentrations of the four gases involved in the system.

### Explanation of Solution

Given

The stated reaction is,

SO2(g)+NO2(g)SO3(g)+NO(g)

The initial concentration of SO2(g) is 0.800M .

The initial concentration of NO2(g) is 0.800M .

The initial concentration of SO3(g) is 0.800M .

The initial concentration of NO(g) is 0.800M .

The equilibrium constant (K) value is 3.75 .

At equilibrium, the equilibrium ratio is expressed by the formula,

K=ConcentrationofproductsConcentrationofreactants

Where,

• K is the equilibrium constant.

The equilibrium ratio for the given reaction is,

K=[NO][SO3][NO2][SO2] (1)

The concentration of SO2 and NO2 consumed is assumed to be x .

The equilibrium concentrations are represented as,

SO2(g)+NO2(g)SO3(g)+NO(g)Initialconcentration0.8000.8000.8000.800Change-x-x+x+xEquilibriumconcentration0.800-x0.800-x0.800+x0.800+x

According to the formulated ICE table,

The equilibrium concentration of SO2(g) is (0.800x)M .

The equilibrium initial concentration of NO2(g) is (0.800x)M .

The equilibrium initial concentration of SO3(g) is (0.800+x)M .

The equilibrium initial concentration of NO(g) is (0

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