   Chapter 11, Problem 42IL

Chapter
Section
Textbook Problem

If you place 1.0 L of ethanol (C2H5OH) in a small laboratory that is 3.0 m long, 2.5 m wide, and 2.5 m high, will all the alcohol evaporate? If some liquid remains, how much will there be? The vapor pressure of ethanol at 25 °C is 59 mm Hg, and the density of the liquid at this temperature is 0.785 g/cm3.

Interpretation Introduction

Interpretation: The 1L of ethanol kept in the laboratory is whether got vaporized completely or not has to be determined. If the ethanol is not completely vaporized, the remaining amount of ethanol has to be determined.

Concept Introduction:

• According to ideal gas equation

nTPV = RnTPPV = nRT

Where,

n = molesofgasP = pressureT = temperatureR = gas constant

• Equation for density is,

Density=MassVolume

• From its given mass is,

Number of moles=GivenmassMolecularmass

Explanation

Given,

Volumeofethanol=1.0LVolumeoflaboratory=(3.0m×2.02.5m)=15m3=15m3×1000L1m3=15×103LTemperature=25oC=(25+273)=298KVaporPressure=59mmHg=59mmHg×1atm760mmHg=0.0776atmDensityofethanol=0.785g/cm3Molarmassofethanol=46.07g/mol

The number of moles of ethanol in the laboratory (vapor) is,

According to ideal gas law,

PV=nRT

Substituting the values,

(0

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