   Chapter 17, Problem 111CP

Chapter
Section
Textbook Problem

# If wet silver carbonate is dried in a stream of hot air. the air must have a certain concentration level of carbon dioxide to prevent silver carbonate from decomposing by the reaction Ag 2 CO 3 ( s ) ⇌ Ag 2 O ( s ) + CO 2 ( g ) ∆H° for this reaction is 79.14 kJ/mol in the temperature range of 25 to 125°C. Given that the partial pressure of carbon dioxide in equilibrium with pure solid silver carbonate is 6.23 × 10−3 torr at 25°C, calculate the partial pressure of CO2 necessary to prevent decomposition ofAg2CO3 at 110°C. (Hint: Manipulate the equation in Exercise 79.)

Interpretation Introduction

Interpretation: The partial pressure of CO2 necessary to prevent decomposition of Ag2CO3 at 110οC is to be calculated.

Concept introduction: Thermodynamics is associated with heat, temperature and its relation with energy and work. It helps us to predict whether a process will take place or not. The terms associated with thermodynamics are system, surrounding, entropy, spontaneity and many more.

Explanation

Explanation

Given

The ΔHο for the reaction is 79.14kJ/mol .

The temperature range is 25 οC to 125 οC .

The partial pressure of CO2 in equilibrium with pure silver carbonate is 6.23×103 torr at 25 οC .

The given reaction is,

Ag2CO3(s)Ag2O(s)+CO2(g) .

The concentration of pure solid reactants and products is equal to 1 . Therefore, the equilibrium constant (K1) expression for the above reaction is,

K1=PCO2

Where,

• PCO2 is the partial pressure of CO2 in equilibrium with pure silver carbonate.

The value of PCO2 is 6.23×103 torr , hence K1=6.23×103 torr .

Temperature at which partial pressure of CO2 in equilibrium with pure silver carbonate is T1=25 οC=298K .

Temperature at which decomposition of Ag2CO3 prevented is T2=110οC=383K

The equilibrium constant ( K2 ) at temperature T2 is calculated by the Vant Hoff equation,

ln(K2K1)=ΔHοR(1T21T1)

Where,

• ΔHο is the standard enthalpy change

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