Chapter 15, Problem 46GQ

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# When solid ammonium carbamate sublimes, it dissociates completely into ammonia and carbon dioxide according to the following equation:(NH4)(H2NCO2)(s) ⇄ 2 NH3(g) + CO2(g)At 25 °C, experiment shows that the total pressure of the gases in equilibrium with the solid is 0.116 atm. What is the equilibrium constant, Kp?

Interpretation Introduction

Interpretation:

The Kp for the reaction when the dissociation of solid ammonium carbamate into ammonia and carbon dioxide has to be calculated.

Concept Introduction:

Equilibrium constant in terms of pressure[Kp]: Equilibrium constant can be expressed in terms of partial pressures in atmospheres.

aA(g)+bB(g)cC(g)+dD(g)KP=PCc×PDdPAa×PBb

The activity of solid substance will not appear in equilibrium and numerically it is considered as one.

Explanation

Given:

(NH4)(H2NCO2)(s)â€‰â‡„â€‰â€‰2â€‰NH3â€‰(g)+â€‰CO2â€‰(g)Totalâ€‰pressureâ€‰=â€‰0.116â€‰atm

In the given reaction ammonium carbamate is in solid state and thus its pressure can be taken as unity. There is no role of ammonium carbamate in the equilibrium expression.

Initially only (NH4)(H2NCO2) is present and the amount of NH3â€‰andâ€‰CO2 will be zero.

â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰(NH4)(H2NCO2)(s)â€‰â‡„â€‰â€‰2â€‰NH3â€‰(g)+â€‰CO2â€‰(g)Initialâ€‰concentrationâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰aâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰0â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰0Ifâ€‰xâ€‰molesâ€‰ofâ€‰â€‰NH4Iâ€‰dissociatesâ€‰toâ€‰formâ€‰2xâ€‰molesâ€‰ofâ€‰NH3â€‰andâ€‰â€‰xâ€‰molesâ€‰ofâ€‰HI,â€‰thenEquilibriumâ€‰concentrationâ€‰â€‰â€‰â€‰a-xâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰2xâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰x

From this it is clear that,

amountâ€‰ofâ€‰NH3â€‰â€‰â€‰â€‰â€‰â€‰=â€‰â€‰â€‰doubleâ€‰theâ€‰amountâ€‰ofâ€‰CO2

Therefore total pressure will be the sum of 2xâ€‰andâ€‰x

2xâ€‰+â€‰xâ€‰â€‰=â€‰â€‰0

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