Chemistry: The Molecular Nature of Matter and Change
Chemistry: The Molecular Nature of Matter and Change
8th Edition
ISBN: 9781259631757
Author: Martin Silberberg Dr., Patricia Amateis Professor
Publisher: McGraw-Hill Education
Question
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Chapter 12, Problem 12.126P
Interpretation Introduction

Interpretation:

The temperature at the flash point of n-hexane is to be calculated.

Concept introduction:

Clausius-Clapeyron equation is used to find the vapor pressure at one temperature when vapor pressure at another temperature and heat of enthalpy is given. It determines the change in vapor pressure with a change in temperature. The expression of the Clausius-Clapeyron equation is as follows:

ln(P2P1)=ΔHvapR(1T21T1)        (1)

Here,

P1 and P2 are the vapor pressure.

T1 and T2 are the temperature.

R is the gas constant.

ΔHvap is the heat of vaporization.

The conversion factor to convert °C to Kelvin is as follows:

T(K)=T(°C)+273.2        (2)

Expert Solution & Answer
Check Mark

Answer to Problem 12.126P

The temperature at flash point of n-hexane is 30.2°C.

Explanation of Solution

Substitute 20.0°C in equation (2) to calculate the temperature T1 in Kelvin as follows:

T1(K)=20.0°C+273.2=293.2 K

Substitute 68.7°C in equation (2) to calculate the temperature T2 in Kelvin as follows:

T2(K)=68.7°C+273.2=341.9 K

Rearrange the equation (1) to calculate ΔHvap.

ΔHvap=(R)ln(P2P1)(1T21T1)        (3)

Substitute 8.314 J/Kmol for R, 293.2 K for T1, 341.9 K for T2 and 121mmHg for P1 and 1atm for P2 in the equation (3).

ΔHvap=(8.314 J/Kmol)ln(1atm121mmHg(760mmHg1atm))(1341.9 K1293.2 K)=3.1447×104 J/mol3.14×104J/mol

The LFL of n-hexane is 1.1% and therefore the mole fraction of n-hexane is 0.011. The formula to calculate the pressure of hexane at flash point is as follows:

Pflash point=(Xhexane)(PTotal)        (4)

Substitute 0.011 for Xhexane and 1atm for PTotal in the equation (4)

Pflash point=(0.011)(1atm)(760mmHg1atm)=8.36mmHg8.4mmHg

The expression to calculate the temperature at flash point is as follows:

1Tflash point=(ln(Pflash pointP2)ΔHvapR+1T2)        (5)

Substitute 8.314 J/Kmol for R, 341.9 K for T2, 8.4mmHg for Pflash point, 1atm for P2 and 3.1447×104 J/mol for ΔHvap in the equation (5).

1Tflash point=(ln(8.4mmHg1atm(1atm760mmHg))3.1447×104 J/mol8.314 J/Kmol+1341.9 K)=1242.961KTflash point=242.961K243.0K

Rearrange the equation to convert the temperature at flash point from Kelvin to °C is as follows:

Tflash point(°C)=Tflash point(K)273.2        (6)

Substitute 243.0K for Tflash point(K) in the equation (6).

Tflash point(°C)=243.0K273.2=30.2°C

Conclusion

The temperature at the flash point of n-hexane is 30.2°C.

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Chapter 12 Solutions

Chemistry: The Molecular Nature of Matter and Change

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