   Chapter 10, Problem 80GQ

Chapter
Section
Textbook Problem

Consider the following gases: He, SO2, CO2, and Cl2. (a) Which has the largest density (assuming that all gases are at the same T and P)? (b) Which gas will effuse fastest through a porous plate?

Interpretation Introduction

Interpretation:

Given the four different molecules largest density and gas effect should be identified.

Concept Introduction:

Ideal gas Equation:

Any gas is described by using four terms namely pressure, volume, temperature and the amount of gas.  Thus combining three laws namely Boyle’s, Charles’s Law and Avogadro’s Hypothesis the following equation could be obtained.  It is referred as ideal gas equation.

nTPV = RnTPPV = nRTwhere,n = moles of gasP = pressureT = temperatureR = gas constant

Under some conditions gases don not behave like ideal gas that is they deviate from their ideal gas properties.  At lower temperature and at high pressures the gas tends to deviate and behave like real gases.

Boyle’s Law:

At given constant temperature conditions the mass of given ideal gas in inversely proportional to its volume.

Charles’s Law:

At given constant pressure conditions the volume of ideal gas is directly proportional to the absolute temperature.

Explanation

Let us consider the pressure and temperature values are

T = 273.15 JKP = 209 mmHg

The ideal gas equation

Let us consider the CO2 molecule density

PV=nRTn=PVRT209mmHg1atm209mmHg760mmHg=0.275732mL=1LitSo1lit=103ml0.732LMassMolarmass=0.275×0.7320.0821×294.15KMassMolarmass=0.275×0.73224.149715MolarmassMass=8.34×1031MolarmassMass=119.9Molarmass=119.9×MassGivenmassvalueis0.37gMolarmass=119.9×0

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