Mercury vapor is dangerous because breathing it brings this toxic element into the lungs. We wish to estimate the vapor pressure of mercury at two different temperatures from the following data: Estimate the temperature at which K p for the process Hg( ℓ ) ⇄ Hg(g) is equal to 1.00 (and the vapor pressure of Hg is 1.00 bar). Next, estimate the temperature at which the vapor pressure is (1/760) bar. (Experimental vapor pressures are 1.00 mm Hg at 126.2 °C and 1.00 bar at 356.6 °C.) ( Note: The temperature at which P = 1.00 bar can be calculated from thermodynamic data. To find the other temperature, you will need to use the temperature for P = 1.00 bar and the Clausius-Clapeyron equation in Section 11.6.)

Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

Chapter
Section

Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 18, Problem 67SCQ
Textbook Problem
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Mercury vapor is dangerous because breathing it brings this toxic element into the lungs. We wish to estimate the vapor pressure of mercury at two different temperatures from the following data:Estimate the temperature at which Kp for the process Hg(ℓ) ⇄ Hg(g) is equal to 1.00 (and the vapor pressure of Hg is 1.00 bar). Next, estimate the temperature at which the vapor pressure is (1/760) bar. (Experimental vapor pressures are 1.00 mm Hg at 126.2 °C and 1.00 bar at 356.6 °C.) (Note: The temperature at which P = 1.00 bar can be calculated from thermodynamic data. To find the other temperature, you will need to use the temperature for P = 1.00 bar and the Clausius-Clapeyron equation in Section 11.6.)

Interpretation Introduction

Interpretation:

The temperature at which equilibrium constant for the given reaction is one and the temperature at which vapor pressure is 1760 bar should be estimated. The temperature used for P=1bar should be identified.

Concept introduction:

The vapor pressure of a substance is related to its enthalpy of vaporisation by the

expression,

ln(p2p1)=ΔHvapR(1T1-1T2)

Here, p1 and p2 are the vapour pressures at two different temperatures T1 and T2.

This equation is known as Clausius-Clapeyron equation and is used to estimate the vapor pressure of a substance at a particular temperature.

Explanation of Solution

The temperature at which equilibrium constant for the given reaction is one and the temperature at which vapor pressure is 1760 bar is calculated below.

Given:

The given reaction is,

Hg(l)Hg(g)

At any temperature, Kp= pHg(g)

So, the value of Kp is one when pHg(g) is 1 bar.

Now,

ΔGo=ΔHo-TΔSo

The value of ΔfH° is,

ΔfH°=(61.38-0)kJ/mol-rxn= 61.38 kJ/mol-rxn.

The value of ΔrS° is,

ΔrS°=(174.97-76.02)J/K×mol-rxn=98.95 J/K×mol-rxn.

At equilibrium, ΔGo is zero

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